Bond (JMSL Numerical Library)

java.lang.Object
- com.imsl.finance.Bond

```
public class Bond
extends Object
```
Collection of bond functions.
Definitions

rate is an annualized rate of return based on the par value of the bills.
yield is an annualized rate based on the purchase price and reflects the actual yield to maturity.
coupons are interest payments on a bond.
redemption is the amount a bond pays at maturity.
frequency is the number of times a year that a bond makes interest payments.
basis is the method used to calculate dates. For example, sometimes computations are done assuming 360 days in a year.
issue is the day a bond is first sold.
settlement is the day a purchaser acquires a bond.
maturity is the day a bond's principal is repaid.
Discount Bonds
Discount bonds, also called zero-coupon bonds, do not pay interest during the life of the security, instead they sell at a discount to their value at maturity. The discount bond methods all have settlement, maturity, basis, and redemption as arguments. In the following list these common arguments are omitted.
- price = pricedisc(rate)
- price = priceyield(yield)
- price = pricemat(issue, rate, yield)
- rate = disc(price)
- yield = yielddisc(price)
A related method is accrintm, which returns the interest that has accumulated on the discount bond.
Treasury Bills
US Treasury bills are a special case of discount bonds. The basis is fixed for treasury bills and the redemption value is assumed to be $100. So these functions have only settlement and maturity as common arguments.
- price = tbillprice(rate)
- yield = tbillyield(price)
- yield = tbilleq(rate)
Interest-Paying Bonds
Most bonds pay interest periodically. The interest-paying bond methods all have settlement, maturity, basis, and frequency as arguments. Again suppressing the common arguments,
- price = price(rate, yield, redemption)
- yield = yield(rate, price, redemption)
- redemption = received(price, rate)
A related method is accrint, which returns the interest that has accumulated at settlement from the previous coupon date.
Interest-Paying Bonds with Odd Coupon Periods
An odd coupon period is one that is either shorter or longer than the regular coupon period. Odd coupon periods typically occur in the first or the last payment period. The yield and price functions accept two additional arguments in order to make the proper adjustments for odd coupon periods: issueDate and firstCouponDate or lastCouponDate.
- oddFirstPrice = price(settlement, maturity, issueDate, firstCouponDate, rate, yield, redemption, frequency, basis)
- oddLastPrice = price(settlement, maturity, lastCouponDate, rate, yield, redemption, frequency, basis)
- oddFirstYield = yield(settlement, maturity, issueDate, firstCouponDate, rate, price, redemption, frequency, basis)
- oddLastYield = yield(settlement, maturity, lastCouponDate, rate, price, redemption, frequency, basis)
Coupon days
In this diagram, the settlement date is shown as a hollow circle and the adjacent coupon dates are shown as filled circles.
- coupppcd is the coupon date immediately prior to the settlement date.
- coupncd is the coupon date immediately after the settlement date.
- coupdaybs is the number of days from the immediately prior coupon date to the settlement date.
- coupdaysnc is the number of days from the settlement date to the next coupon date.
- coupdays is the number of days between these two coupon dates.
A related method is coupnum, which returns the number of coupons payable between settlement and maturity.
Another related method is yearfrac, which returns the fraction of the year between two days.
Duration
Duration is used to measure the sensitivity of a bond to changes in interest rates. Convexity is a measure of the sensitivity of duration.

Field Summary

Fields
Modifier and Type	Field and Description
`static int`	`ANNUAL` Coupon payments are made annually.
`static int`	`BIMONTHLY` Coupon payments are made bimonthly (6 times per year).
`static int`	`MONTHLY` Coupon payments are made monthly.
`static int`	`QUARTERLY` Coupon payments are made quarterly.
`static int`	`SEMIANNUAL` Coupon payments are made semiannually (twice per year).

Method Summary

Methods
Modifier and Type	Method and Description
`static double`	`accrint(GregorianCalendar issue, GregorianCalendar firstCoupon, GregorianCalendar settlement, double rate, double par, int frequency, DayCountBasis basis)` Returns the interest which has accrued on a security that pays interest periodically.
`static double`	`accrintm(GregorianCalendar issue, GregorianCalendar maturity, double rate, double par, DayCountBasis basis)` Returns the interest which has accrued on a security that pays interest at maturity.
`static double`	`amordegrc(double cost, GregorianCalendar issue, GregorianCalendar firstPeriod, double salvage, int period, double rate, DayCountBasis basis)` Returns the depreciation for each accounting period.
`static double`	`amorlinc(double cost, GregorianCalendar issue, GregorianCalendar firstPeriod, double salvage, int period, double rate, DayCountBasis basis)` Returns the depreciation for each accounting period.
`static double`	`convexity(GregorianCalendar settlement, GregorianCalendar maturity, double coupon, double yield, int frequency, DayCountBasis basis)` Returns the convexity for a security.
`static int`	`coupdaybs(GregorianCalendar settlement, GregorianCalendar maturity, int frequency, DayCountBasis basis)` Returns the number of days starting with the beginning of the coupon period and ending with the settlement date.
`static double`	`coupdays(GregorianCalendar settlement, GregorianCalendar maturity, int frequency, DayCountBasis basis)` Returns the number of days in the coupon period containing the settlement date.
`static int`	`coupdaysnc(GregorianCalendar settlement, GregorianCalendar maturity, int frequency, DayCountBasis basis)` Returns the number of days starting with the settlement date and ending with the next coupon date.
`static GregorianCalendar`	`coupncd(GregorianCalendar settlement, GregorianCalendar maturity, int frequency, DayCountBasis basis)` Returns the first coupon date which follows the settlement date.
`static int`	`coupnum(GregorianCalendar settlement, GregorianCalendar maturity, int frequency, DayCountBasis basis)` Returns the number of coupons payable between the settlement date and the maturity date.
`static GregorianCalendar`	`couppcd(GregorianCalendar settlement, GregorianCalendar maturity, int frequency, DayCountBasis basis)` Returns the coupon date which immediately precedes the settlement date.
`static double`	`disc(GregorianCalendar settlement, GregorianCalendar maturity, double price, double redemption, DayCountBasis basis)` Returns the implied interest rate of a discount bond.
`static double`	`duration(GregorianCalendar settlement, GregorianCalendar maturity, double coupon, double yield, int frequency, DayCountBasis basis)` Returns the Macaulay duration of a security where the security has periodic interest payments.
`static double`	`intrate(GregorianCalendar settlement, GregorianCalendar maturity, double investment, double redemption, DayCountBasis basis)` Returns the interest rate of a fully invested security.
`static double`	`mduration(GregorianCalendar settlement, GregorianCalendar maturity, double coupon, double yield, int frequency, DayCountBasis basis)` Returns the modified Macaulay duration for a security with an assumed par value of $100.
`static double`	`price(GregorianCalendar settlement, GregorianCalendar maturity, double rate, double yield, double redemption, int frequency, DayCountBasis basis)` Returns the price, per $100 face value, of a security that pays periodic interest.
`static double`	`price(GregorianCalendar settlement, GregorianCalendar maturity, GregorianCalendar lastCoupon, double rate, double yield, double redemption, int frequency, DayCountBasis basis)` Returns the price of an odd last period coupon bond, given its yield.
`static double`	`price(GregorianCalendar settlement, GregorianCalendar maturity, GregorianCalendar issueDate, GregorianCalendar firstCoupon, double rate, double yield, double redemption, int frequency, DayCountBasis basis)` Returns the price of an odd first period, coupon bond, given its yield.
`static double`	`pricedisc(GregorianCalendar settlement, GregorianCalendar maturity, double rate, double redemption, DayCountBasis basis)` Returns the price of a discount bond given the discount rate.
`static double`	`pricemat(GregorianCalendar settlement, GregorianCalendar maturity, GregorianCalendar issue, double rate, double yield, DayCountBasis basis)` Returns the price, per $100 face value, of a discount bond.
`static double`	`priceyield(GregorianCalendar settlement, GregorianCalendar maturity, double yield, double redemption, DayCountBasis basis)` Returns the price of a discount bond given the yield.
`static double`	`received(GregorianCalendar settlement, GregorianCalendar maturity, double investment, double rate, DayCountBasis basis)` Returns the amount one receives when a fully invested security reaches the maturity date.
`static double`	`tbilleq(GregorianCalendar settlement, GregorianCalendar maturity, double rate)` Returns the bond-equivalent yield of a Treasury bill.
`static double`	`tbillprice(GregorianCalendar settlement, GregorianCalendar maturity, double rate)` Returns the price, per $100 face value, of a Treasury bill.
`static double`	`tbillyield(GregorianCalendar settlement, GregorianCalendar maturity, double price)` Returns the yield of a Treasury bill.
`static double`	`yearfrac(GregorianCalendar start, GregorianCalendar end, DayCountBasis basis)` Returns the fraction of a year represented by the number of whole days between two dates.
`static double`	`yield(GregorianCalendar settlement, GregorianCalendar maturity, double rate, double price, double redemption, int frequency, DayCountBasis basis)` Returns the yield of a security that pays periodic interest.
`static double`	`yield(GregorianCalendar settlement, GregorianCalendar maturity, GregorianCalendar lastCoupon, double rate, double price, double redemption, int frequency, DayCountBasis basis)` Returns the yield of a security with an odd last coupon period that pays periodic interest.
`static double`	`yield(GregorianCalendar settlement, GregorianCalendar maturity, GregorianCalendar issueDate, GregorianCalendar firstCoupon, double rate, double price, double redemption, int frequency, DayCountBasis basis)` Returns the yield of a security with an odd first coupon period that pays periodic interest.
`static double`	`yielddisc(GregorianCalendar settlement, GregorianCalendar maturity, double price, double redemption, DayCountBasis basis)` Returns the annual yield of a discount bond.
`static double`	`yieldmat(GregorianCalendar settlement, GregorianCalendar maturity, GregorianCalendar issue, double rate, double price, DayCountBasis basis)` Returns the annual yield of a security that pays interest at maturity.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail
- ANNUAL
```
public static final int ANNUAL
```
  Coupon payments are made annually.
  
  See Also:
  Constant Field Values
- BIMONTHLY
```
public static final int BIMONTHLY
```
  Coupon payments are made bimonthly (6 times per year).
  
  See Also:
  Constant Field Values
- MONTHLY
```
public static final int MONTHLY
```
  Coupon payments are made monthly.
  
  See Also:
  Constant Field Values
- QUARTERLY
```
public static final int QUARTERLY
```
  Coupon payments are made quarterly.
  
  See Also:
  Constant Field Values
- SEMIANNUAL
```
public static final int SEMIANNUAL
```
  Coupon payments are made semiannually (twice per year).
  
  See Also:
  Constant Field Values

Method Detail

accrint
```
public static double accrint(GregorianCalendar issue,
             GregorianCalendar firstCoupon,
             GregorianCalendar settlement,
             double rate,
             double par,
             int frequency,
             DayCountBasis basis)
```
Returns the interest which has accrued on a security that pays interest periodically. In the equation below, A_i represents the number of days which have accrued for the ith quasi-coupon period within the odd period. The quasi-coupon periods are periods obtained by extending the series of equal payment periods to before or after the actual payment periods. NC represents the number of quasi-coupon periods within the odd period, rounded to the next highest integer. NL_i represents the length of the normal ith quasi-coupon period within the odd period. NL_i is expressed in days. Function accrint can be found by solving the following:

${it par} left({{{it rate} over {it frequency}} {sumlimits_{i = 1}^{it NC} {{{{A_i } over {{it NL}_i }}}} }} right)$

Parameters:
issue - a GregorianCalendar issue date of the security
firstCoupon - a GregorianCalendar date of the security's first interest date
settlement - a GregorianCalendar settlement date of the security
rate - a double which specifies the security's annual coupon rate
par - a double which specifies the security's par value
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the accrued interest
See Also:
Example

accrintm
```
public static double accrintm(GregorianCalendar issue,
              GregorianCalendar maturity,
              double rate,
              double par,
              DayCountBasis basis)
```
Returns the interest which has accrued on a security that pays interest at maturity.

$= {it par} times {it rate} times {frac{A}{D}}$
In the above equation, represents the number of days starting at issue date to maturity date and represents the annual basis.

Parameters:
issue - a GregorianCalendar issue date of the security
maturity - a GregorianCalendar date of the security's maturity
rate - a double which specifies the security's annual coupon rate
par - a double which specifies the security's par value
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the accrued interest
See Also:
Example

amordegrc
```
public static double amordegrc(double cost,
               GregorianCalendar issue,
               GregorianCalendar firstPeriod,
               double salvage,
               int period,
               double rate,
               DayCountBasis basis)
```
Returns the depreciation for each accounting period. This method is similar to amorlinc. However, in this method a depreciation coefficient based on the asset life is applied during the evaluation of the function.

Parameters:
cost - a double which specifies the cost of the asset
issue - a GregorianCalendar issue date of the asset
firstPeriod - a GregorianCalendar date of the end of the first period
salvage - a double which specifies the asset's salvage value at the end of the life of the asset
period - an int which specifies the period
rate - a double which specifies the rate of depreciation
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the depreciation
See Also:
Example

amorlinc
```
public static double amorlinc(double cost,
              GregorianCalendar issue,
              GregorianCalendar firstPeriod,
              double salvage,
              int period,
              double rate,
              DayCountBasis basis)
```
Returns the depreciation for each accounting period. This method is similar to amordegrc, except that amordegrc has a depreciation coefficient that is applied during the evaluation that is based on the asset life.

Parameters:
cost - a double which specifes the cost of the asset
issue - a GregorianCalendar issue date of the asset
firstPeriod - a GregorianCalendar date of the end of the first period
salvage - a double which specifies the asset's salvage value at the end of the life of the asset
period - an int which specifies the period
rate - a double which specifies the rate of depreciation
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the depreciation
See Also:
Example

convexity
```
public static double convexity(GregorianCalendar settlement,
               GregorianCalendar maturity,
               double coupon,
               double yield,
               int frequency,
               DayCountBasis basis)
```
Returns the convexity for a security. Convexity is the sensitivity of the duration of a security to changes in yield. It is computed using the following:

${{{1 over {left( {q times {it frequency}} right)^2 }}left{ {sumlimits_{t = 1}^n {tleft( {t + 1} right)} left( {{{it coupon} over {it frequency}}} right)q^{ - t} + nleft( {n + 1} right)q^{ - n} } right}} over {left( {sumlimits_{t = 1}^n {left( {{{it coupon} over {it frequency}}} right)q^{ - t} } + q^{ - n} } right)}}$
where n is calculated from coupnum, and .

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
coupon - a double which specifies the security's annual coupon rate
yield - a double which specifies the security's annual yield
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the convexity for a security
See Also:
Example

coupdaybs
```
public static int coupdaybs(GregorianCalendar settlement,
            GregorianCalendar maturity,
            int frequency,
            DayCountBasis basis)
```
Returns the number of days starting with the beginning of the coupon period and ending with the settlement date. For a good discussion on day count basis, see SIA Standard Securities Calculation Methods 1993, vol. 1, pages 17-35.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
an int which specifies the number of days from the beginning of the coupon period to the settlement date
See Also:
Example

coupdays
```
public static double coupdays(GregorianCalendar settlement,
              GregorianCalendar maturity,
              int frequency,
              DayCountBasis basis)
```
Returns the number of days in the coupon period containing the settlement date. For a good discussion on day count basis, see SIA Standard Securities Calculation Methods 1993, vol. 1, pages 17-35.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the number of days in the coupon period that contains the settlement date
See Also:
Example

coupdaysnc
```
public static int coupdaysnc(GregorianCalendar settlement,
             GregorianCalendar maturity,
             int frequency,
             DayCountBasis basis)
```
Returns the number of days starting with the settlement date and ending with the next coupon date. For a good discussion on day count basis, see SIA Standard Securities Calculation Methods 1993, vol. 1, pages 17-35.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
an int which specifies the number of days from the settlement date to the next coupon date
See Also:
Example

coupncd
```
public static GregorianCalendar coupncd(GregorianCalendar settlement,
                        GregorianCalendar maturity,
                        int frequency,
                        DayCountBasis basis)
```
Returns the first coupon date which follows the settlement date. For a good discussion on day count basis, see SIA Standard Securities Calculation Methods 1993, vol. 1, pages 17-35.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis

Returns:
a GregorianCalendar which specifies the next coupon date after the settlement date
See Also:
Example

coupnum
```
public static int coupnum(GregorianCalendar settlement,
          GregorianCalendar maturity,
          int frequency,
          DayCountBasis basis)
```
Returns the number of coupons payable between the settlement date and the maturity date. For a good discussion on day count basis, see SIA Standard Securities Calculation Methods 1993, vol. 1, pages 17-35.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
an int which specifies the number of coupons payable between the settlement date and maturity date
See Also:
Example

couppcd
```
public static GregorianCalendar couppcd(GregorianCalendar settlement,
                        GregorianCalendar maturity,
                        int frequency,
                        DayCountBasis basis)
```
Returns the coupon date which immediately precedes the settlement date. For a good discussion on day count basis, see SIA Standard Securities Calculation Methods 1993, vol. 1, pages 17-35.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis

Returns:
a GregorianCalendar which specifies the previous coupon date before the settlement date
See Also:
Example

disc
```
public static double disc(GregorianCalendar settlement,
          GregorianCalendar maturity,
          double price,
          double redemption,
          DayCountBasis basis)
```
Returns the implied interest rate of a discount bond. The discount rate is the interest rate implied when a security is sold for less than its value at maturity in lieu of interest payments. It is computed using the following:

In the equation above, represents the number of days in a year based on the annual basis and represents the number of days starting with the settlement date and ending with the maturity date.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
price - a double which specifies the security's price per $100 face value
redemption - a double which specifies the security's redemption value per $100 face value
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the discount rate for a security
See Also:
Example

duration
```
public static double duration(GregorianCalendar settlement,
              GregorianCalendar maturity,
              double coupon,
              double yield,
              int frequency,
              DayCountBasis basis)
```
Returns the Macaulay duration of a security where the security has periodic interest payments. The Macaulay duration is the weighted-average time to the payments, where the weights are the present value of the payments. It is computed using the following:

$left({{{{{left({N - 1 + {{it DSC}over E}}right)times 100}over {left({1 + {{it yield}over {it freq}}} right)^{left({N - 1 + {{it DSC}over E}}right)}}} + sumlimits_{k = 1}^N {}left({left({{{100times {it coupon}}over {{it freq}times left({1 + {{it yield}over {it freq}}}right)^{left({k - 1 + {{it DSC}over E}}right)}}}}right)timesleft({k - 1 + {{it DSC}over E}} right)}right)}over{{{100} over {left({1 + {{it yield}over {it freq}}}right)^{left(N - 1 + {{it DSC}over E}right)}}} + sum limits_{k = 1}^N {}left({{{100 times {it coupon}}over {{it freq} timesleft({1 + {{it yield}over {it freq}}}right)^{left(k - 1 + {{ it DSC}over E}right)}}}} right)}}}right)times {1over {it freq}}$
In the equation above, represents the number of days starting with the settlement date and ending with the next coupon date. represents the number of days within the coupon period. represents the number of coupons payable from the settlement date to the maturity date. represents the frequency of the coupon payments annually.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
coupon - a double which specifies the security's annual coupon rate
yield - a double which specifies the security's annual yield
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the annual duration of a security with periodic interest payments
See Also:
Example

intrate
```
public static double intrate(GregorianCalendar settlement,
             GregorianCalendar maturity,
             double investment,
             double redemption,
             DayCountBasis basis)
```
Returns the interest rate of a fully invested security. It is computed using the following:

In the equation above, represents the number of days in a year based on the annual basis, and represents the number of days in the period starting with the settlement date and ending with the maturity date.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
investment - a double which specifies the amount invested
redemption - a double which specifies the amount to be received at maturity
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the interest rate for a fully invested security
See Also:
Example

mduration
```
public static double mduration(GregorianCalendar settlement,
               GregorianCalendar maturity,
               double coupon,
               double yield,
               int frequency,
               DayCountBasis basis)
```
Returns the modified Macaulay duration for a security with an assumed par value of $100. It is computed using the following:

where is calculated from mduration.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
coupon - a double which specifies the security's annual coupon rate
yield - a double which specifies the security's annual yield
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the modified Macaulay duration for a security with an assumed par value of $100
See Also:
Example

price
```
public static double price(GregorianCalendar settlement,
           GregorianCalendar maturity,
           double rate,
           double yield,
           double redemption,
           int frequency,
           DayCountBasis basis)
```
Returns the price, per $100 face value, of a security that pays periodic interest. It is computed using the following:

${{{it redemption} over {left( {1 + {{it yield} over {it frequency}}} right)^{left( {N - 1 + {{it DSC} over E}} right)} }}} + {sumlimits_{k = 1}^N {{{100 times {{it rate} over {it frequency}}} over {left( {1 + {{it yield} over {it frequency}}} right)^{left( {k - 1 + {{it DSC} over E}} right)} }}} } - left( {100 times {{it rate} over {it frequency}} times {A over E}} right)$
In the above equation, represents the number of days in the period starting with the settlement date and ending with the next coupon date. represents the number of days within the coupon period. represents the number of coupons payable in the timeframe from the settlement date to the redemption date. represents the number of days in the timeframe starting with the beginning of coupon period and ending with the settlement date.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
rate - a double which specifies the security's annual coupon rate
yield - a double which specifies the security's annual yield
redemption - a double which specifies the security's redemption value per $100 face value
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the price per $100 face value of a security that pays periodic interest
See Also:
Example

price

public static double price(GregorianCalendar settlement,
           GregorianCalendar maturity,
           GregorianCalendar lastCoupon,
           double rate,
           double yield,
           double redemption,
           int frequency,
           DayCountBasis basis)

Returns the price of an odd last period coupon bond, given its yield.

In the case of a short last period with one coupon period or less to redemption, the following formula is used:

$everymath{displaystyle} P=left[frac{redemption+left(frac{100*rate}{frequency}*frac{DLC}{E} right)}{1+left(frac{DSR}{E}*frac{yield}{frequency}right)}right] -left[frac{A}{E}*frac{100*rate}{frequency}right]$

where

Variable	Description
A	Number of days from last coupon date before redemption to settlement date.
DLC	Number of days from last coupon date before redemption to redemption.
DSR	Number of days from settlement date to redemption date.
E	Number of days in the quasi-coupon period.

In the case of a short last period with more than one coupon period to redemption, the following formula is used:

$everymath{displaystyle} begin{array}{lcl} P & = & left[frac{redemption}{left(1+frac{yield}{frequency} right)^{N-1+frac{DSC}{E}+frac{DLC}{NLL}}}right] +left[sum^N_{K=1}frac{100*frac{rate}{frequency}}{left({1+ frac{yield}{frequency}}right)^{K-1+frac{DSC}{E}}}right]\[.7cm] & + & left[frac{100*frac{rate}{frequency}*frac{DLC}{NLL}}{left({1+ frac{yield}{frequency}}right)^{N-1+frac{DSC}{E}+frac{DLC}{NLL}}}right]- left[100*frac{rate}{frequency}*frac{A}{E}right] end{array}$

where

Variable	Description
A	Number of days from beginning of coupon period to settlement date.
DLC	Number of days from last coupon date before redemption to redemption.
DSC	Number of days from settlement date to next coupon date.
E	Number of days in coupon period in which the settlement date falls.
N	Number of coupons payable between settlement date and last coupon date before redemption.
NLL	Number of days in the full quasi-coupon period in which the odd last period falls.

In the case of a long last period with one coupon period or less to redemption, the following formula is used:

$everymath{displaystyle} P=left[frac{redemption+left(left(sumlimits^{NCL}_{i=1} frac{{DLC}_i}{{NLL}_i}right)*frac{100*rate}{frequency} right)}{1+left(sumlimits^{NCL}_{i=1}frac{{DSC}_i}{{NLL}_i}right)* frac{yield}{frequency}}right] -left[left(sumlimits^{NCL}_{i=1}frac{{A}_i}{{NLL}_i}right)* frac{100*rate}{frequency}right]$

where

Variable	Description
A_i	Number of accrued days for the i^th quasi-coupon period within the odd period counting forward from the last interest date before redemption.
DLC_i	Number of days in the i^th quasi-coupon period as delimited by the length of the actual coupon period.
DSC_i	Number of days from settlement date (or beginning of quasi-coupon period) to next quasi-coupon within odd period (or to redemption date) for the i^th quasi-coupon period.
NCL	Number of quasi-coupon periods that fit in odd period.
NLL_i	Normal length in days of the full i^th quasi-coupon period within odd last period.

In the case of a long first period with more than one coupon period to redemption, the following formula is used:

$everymath{displaystyle} begin{array}{lcl} P & = & left[frac{redemption}{left(1+frac{yield}{frequency} right)^{N-1+frac{DSC}{E}+Nqf+frac{DLQ}{LQL}}}right] +left[sum^N_{K=1}frac{100*frac{rate}{frequency}}{left({1+ frac{yield}{frequency}}right)^{K-1+frac{DSC}{E}}}right]\[.7cm] & + & left[frac{100*frac{rate}{frequency}*left(sumlimits^{NCL}_{i=1} frac{{DLC}_i}{{NLL}_i}right)}{left({1+frac{yield}{frequency}} right)^{N-1+frac{DSC}{E}Nqf+frac{DLQ}{LQL}}}right]- left[100*frac{rate}{frequency}*frac{A}{E}right] end{array}$

where

Variable	Description
A	Number of days from beginning of coupon period to settlement date.
DLC_i	Number of days from last coupon date before redemption to first quasi-coupon or number of days in quasi-coupon.
DLQ	Number of days counted in the last quasi-coupon period within the last odd period.
DSC	Number of days from settlement date to next coupon date.
E	Number of days in coupon period in which the settlement falls.
LQL	Normal length in days of the last quasi-coupon period within the odd last period.
N	Number of coupons payable between settlement date and last coupon date before redemption.
NCL	Number of quasi-coupon periods that fit in odd period.
NLL_i	Normal length in days of the full i^th quasi-coupon period within odd last period.
Nql	Number of whole quasi-coupon periods between last coupon date before redemption and the redemption date.

Parameters:: settlement - a GregorianCalendar settlement date of the security; maturity - a GregorianCalendar maturity date of the security; lastCoupon - a GregorianCalendar last interest date of the security; rate - a double which specifies the security's annual coupon rate; yield - a double which specifies the security's annual yield; redemption - a double which specifies the security's redemption value per $100 face value; frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly; basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.
Returns:: a double that indicates the bond price.
See Also:: Example 1, Example 2, Example 3, Example 4

price

public static double price(GregorianCalendar settlement,
           GregorianCalendar maturity,
           GregorianCalendar issueDate,
           GregorianCalendar firstCoupon,
           double rate,
           double yield,
           double redemption,
           int frequency,
           DayCountBasis basis)

Returns the price of an odd first period, coupon bond, given its yield.

In the case of a short first period, the following formula is used:

$everymath{displaystyle} begin{array}{lcl} P & = & left[frac{redemption}{left(1+frac{yield}{frequency}right)^{ N-1+frac{DSC}{E}}}right]+left[frac{100*frac{rate}{frequency}* frac{DFC}{E}}{left(1+frac{yield}{frequency}right)^frac{DSC}{E}} right]\[.4cm] & + & left[sum^N_{K=2}frac{100*frac{rate}{frequency}}{left({1+ frac{yield}{frequency}}right)^{K-1+frac{DSC}{E}}}right]-left[100* frac{rate}{frequency}*frac{A}{E}right] end{array}$

where

Variable	Description
A	Number of days from the beginning of coupon period to the settlement date (accrued days).
DFC	Number of days from the beginning of odd first coupon period (`issueDate`) to the first coupon date.
DSC	Number of days from the settlement date to first coupon date.
E	Number of days in the quasi-coupon period in which the settlement date falls.
N	Number of coupons payable between settlement date and redemption date.

In the case of a long first period, the following formula is used:

$everymath{displaystyle} begin{array}{lcl} P & = & left[frac{redemption}{left(1+frac{yield}{frequency} right)^{N-{Nqf}+frac{DSC}{E}}}right]+left[frac{100* frac{rate}{frequency}*left[sumlimits^{NCF}_{i=1} frac{{DFC}_i}{{NLF}_i}right]}{left(1+frac{yield}{frequency} right)^{{Nqf}+frac{DSC}{E}}}right]\[.7cm] & + & left[sum^N_{K=1}frac{100*frac{rate}{frequency}}{left({1+ frac{yield}{frequency}}right)^{K+{Nqf}+frac{DSC}{E}}}right]- left[100*frac{rate}{frequency}*left[sumlimits^{NCF}_{i=1} frac{A_i}{{NLF}_i}right]right] end{array}$

where

Variable	Description
A_i	Number of accrued days for the i^th quasi-coupon period within the odd period.
DFC_i	Number of days from the `issueDate` to the first quasi-coupon or number of days in the the quasi-coupon.
DSC	Number of days from the settlement date to the next coupon or quasi-coupon date.
E	Number of days in the quasi-coupon or coupon period in which the settlement date falls.
N	Number of coupon periods between the first real coupon date and redemption date.
NCF	Number of quasi-coupon periods that fall in the odd period.
NLF_i	Number of days in the full i^th quasi-coupon period within the odd period.
Nqf	Number of whole quasi-coupon periods between `settlement` and `firstCoupon`.

Parameters:: settlement - a GregorianCalendar settlement date of the security; maturity - a GregorianCalendar maturity date of the security; issueDate - a GregorianCalendar issue date of the security; firstCoupon - a GregorianCalendar first coupon date of the security; rate - a double which specifies the security's annual coupon rate; yield - a double which specifies the security's annual yield; redemption - a double which specifies the security's redemption value per $100 face value; frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly; basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.
Returns:: a double that indicates the bond price.
See Also:: Example 1, Example 2

pricedisc
```
public static double pricedisc(GregorianCalendar settlement,
               GregorianCalendar maturity,
               double rate,
               double redemption,
               DayCountBasis basis)
```
Returns the price of a discount bond given the discount rate. It is computed using the following:

In the equation above, represents the number of days starting at the settlement date and ending with the maturity date. represents the number of days in a year based on the annual basis.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
rate - a double which specifies the security's discount rate
redemption - a double which specifies the security's redemption value per $100 face value
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the price per $100 face value of a discounted security
See Also:
Example

pricemat
```
public static double pricemat(GregorianCalendar settlement,
              GregorianCalendar maturity,
              GregorianCalendar issue,
              double rate,
              double yield,
              DayCountBasis basis)
```
Returns the price, per $100 face value, of a discount bond. It is computed using the following:

In the equation above, represents the number of days in a year based on the annual basis. represents the number of days in the period starting with the settlement date and ending with the maturity date. represents the number of days in the period starting with the issue date and ending with the maturity date. represents the number of days in the period starting with the issue date and ending with the settlement date.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
issue - a GregorianCalendar issue date of the security
rate - a double which specifies the security's interest rate at issue date
yield - a double which specifies the security's annual yield
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the price per $100 face value of a security that pays interest at maturity
See Also:
Example

priceyield
```
public static double priceyield(GregorianCalendar settlement,
                GregorianCalendar maturity,
                double yield,
                double redemption,
                DayCountBasis basis)
```
Returns the price of a discount bond given the yield. It is computed using the following:

In the equation above, represents the number of days starting at the settlement date and ending with the maturity date. represents the number of days in a year based on the annual basis.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
yield - a double which specifies the security's yield
redemption - a double which specifies the security's redemption value per $100 face value
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis

Returns:
a double which specifies the price per $100 face value of a discounted security
See Also:
Example

received
```
public static double received(GregorianCalendar settlement,
              GregorianCalendar maturity,
              double investment,
              double rate,
              DayCountBasis basis)
```
Returns the amount one receives when a fully invested security reaches the maturity date. It is computed using the following:

In the equation above, represents the number of days in a year based on the annual basis, and represents the number of days in the period starting with the issue date and ending with the maturity date.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
investment - a double which specifies the amount invested in the security
rate - a double which specifies the security's rate at issue date
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the amount received at maturity for a fully invested security
See Also:
Example

tbilleq
```
public static double tbilleq(GregorianCalendar settlement,
             GregorianCalendar maturity,
             double rate)
```
Returns the bond-equivalent yield of a Treasury bill. It is computed using the following:
If
otherwise,

${{ - {{it DSM} over {365}} + sqrt {left( {{{it DSM} over {365}}} right)^2 - left( {2 times {{it DSM} over {365}} - 1} right) times {{{it rate} times {it DSM}} over {{it rate} times {it DSM} - {360}}}} } over {{{it DSM} over {365}} - 0.5}}$
In the above equation, represents the number of days starting at settlement date to maturity date.

Parameters:
settlement - a GregorianCalendar settlement date of the Treasury bill
maturity - a GregorianCalendar maturity date of the Treasury bill. The maturity cannot be more than a year after the settlement.
rate - a double which specifies the Treasury bill's discount rate at issue date. The discount rate is an annualized rate of return based on the par value of the bills. The discount rate is calculated on a 360-day basis (twelve 30-day months).

Returns:
a double which specifies the bond-equivalent yield for the Treasury bill. This is an annualized rate based on the purchase price of the bills and reflects the actual yield to maturity.
See Also:
Example

tbillprice
```
public static double tbillprice(GregorianCalendar settlement,
                GregorianCalendar maturity,
                double rate)
```
Returns the price, per $100 face value, of a Treasury bill. It is computed using the following:

In the equation above, represents the number of days in the period starting with the settlement date and ending with the maturity date (any maturity date that is more than one calendar year after the settlement date is excluded).

Parameters:
settlement - a GregorianCalendar settlement date of the Treasury bill
maturity - a GregorianCalendar maturity date of the Treasury bill. The maturity cannot be more than a year after the settlement
rate - a double which specifies the Treasury bill's discount rate at issue date. The discount rate is an annualized rate of return based on the par value of the bills. The discount rate is calculated on a 360-day basis (twelve 30-day months).

Returns:
a double which specifies the price per $100 face value for the Treasury bill
See Also:
Example

tbillyield
```
public static double tbillyield(GregorianCalendar settlement,
                GregorianCalendar maturity,
                double price)
```
Returns the yield of a Treasury bill. It is computed using the following:

In the equation above, represents the number of days in the period starting with the settlement date and ending with the maturity date (any maturity date that is more than one calendar year after the settlement date is excluded).

Parameters:
settlement - a GregorianCalendar settlement date of the Treasury bill
maturity - a GregorianCalendar maturity date of the Treasury bill. The maturity cannot be more than a year after the settlement.
price - a double which specifies the Treasury bill's price per $100 face value

Returns:
a double which specifies the yield for the Treasury bill. This is an annualized rate based on the purchase price of the bills and reflects the actual yield to maturity.
See Also:
Example

yearfrac
```
public static double yearfrac(GregorianCalendar start,
              GregorianCalendar end,
              DayCountBasis basis)
```
Returns the fraction of a year represented by the number of whole days between two dates. It is computed using the following:

where equals the number of days from start to end, equals annual basis.

Parameters:
start - a GregorianCalendar start date of the security
end - a GregorianCalendar end date of the security
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the annual yield of a security that pays interest at maturity
See Also:
Example

yield
```
public static double yield(GregorianCalendar settlement,
           GregorianCalendar maturity,
           double rate,
           double price,
           double redemption,
           int frequency,
           DayCountBasis basis)
```
Returns the yield of a security that pays periodic interest. If there is one coupon period, use the following:

In the equation above, represents the number of days in the period starting with the settlement date and ending with the redemption date. represents the number of days within the coupon period. represents the number of days in the period starting with the beginning of coupon period and ending with the settlement date.
If there is more than one coupon period, use the following:

${it price} - {{it redemption} over {left( {1 + {it yield} over {it frequency}} right)}^{N - 1 + {it DSC} over E}} - {left( {sumlimits_{k = 1}^N { {100 times {{it rate} over {it frequency}}} over {left( {1 + {it yield} over {it frequency}} right)}^{k - 1 + {it DSC} over E} }} right) } + {100 times {{it rate} over {it frequency}} times {A over E} }$
In the equation above, represents the number of days in the period from the settlement to the next coupon date. represents the number of days within the coupon period. represents the number of coupons payable in the period starting with the settlement date and ending with the redemption date. represents the number of days in the period starting with the beginning of the coupon period and ending with the settlement date.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
rate - a double which specifies the security's annual coupon rate
price - a double which specifies the security's price per $100 face value
redemption - a double which specifies the security's redemption value per $100 face value
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the yield of a security that pays periodic interest
See Also:
Example

yield
```
public static double yield(GregorianCalendar settlement,
           GregorianCalendar maturity,
           GregorianCalendar lastCoupon,
           double rate,
           double price,
           double redemption,
           int frequency,
           DayCountBasis basis)
```
Returns the yield of a security with an odd last coupon period that pays periodic interest.
The yield is determined by finding the zero of the function desired price - computed price, where computed price is the output of price(java.util.GregorianCalendar, java.util.GregorianCalendar, java.util.GregorianCalendar, double, double, double, int, com.imsl.finance.DayCountBasis).

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
lastCoupon - a GregorianCalendar last coupon date of the security
rate - a double which specifies the security's annual coupon rate
price - a double which specifies the security's price per $100 face value
redemption - a double which specifies the security's redemption value per $100 face value
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the yield of a security that pays periodic interest
See Also:
Example 1, Example 2, Example 3, Example 4

yield
```
public static double yield(GregorianCalendar settlement,
           GregorianCalendar maturity,
           GregorianCalendar issueDate,
           GregorianCalendar firstCoupon,
           double rate,
           double price,
           double redemption,
           int frequency,
           DayCountBasis basis)
```
Returns the yield of a security with an odd first coupon period that pays periodic interest.
The yield is determined by finding the zero of the function desired price - computed price, where computed price is the output of price(java.util.GregorianCalendar, java.util.GregorianCalendar, java.util.GregorianCalendar, java.util.GregorianCalendar, double, double, double, int, com.imsl.finance.DayCountBasis).

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
issueDate - a GregorianCalendar issueDate date of the security
firstCoupon - a GregorianCalendar first coupon date of the security
rate - a double which specifies the security's annual coupon rate
price - a double which specifies the security's price per $100 face value
redemption - a double which specifies the security's redemption value per $100 face value
frequency - an int which specifies the number of coupon payments per year: ANNUAL for annual, SEMIANNUAL for semiannual, and QUARTERLY for quarterly
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the yield of a security that pays periodic interest
See Also:
Example 1, Example 2

yielddisc
```
public static double yielddisc(GregorianCalendar settlement,
               GregorianCalendar maturity,
               double price,
               double redemption,
               DayCountBasis basis)
```
Returns the annual yield of a discount bond. It is computed using the following:

In the equation above, represents the number of days in a year based on the annual basis, and represents the number of days starting with the settlement date and ending with the maturity date.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
price - a double which specifies the security's price per $100 face value
redemption - a double which specifies the security's redemption value per $100 face value
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the annual yield for a discounted security
See Also:
Example

yieldmat
```
public static double yieldmat(GregorianCalendar settlement,
              GregorianCalendar maturity,
              GregorianCalendar issue,
              double rate,
              double price,
              DayCountBasis basis)
```
Returns the annual yield of a security that pays interest at maturity. It is computed using the following:

In the equation above, represents the number of days in the period starting with the issue date and ending with the maturity date. represents the number of days in the period starting with the settlement date and ending with the maturity date. represents the number of days in the period starting with the issue date and ending with the settlement date. represents the number of days in a year based on the annual basis.

Parameters:
settlement - a GregorianCalendar settlement date of the security
maturity - a GregorianCalendar maturity date of the security
issue - a GregorianCalendar issue date of the security
rate - a double which specifies the security's interest rate at date of issue
price - a double which specifies the security's price per $100 face value
basis - a DayCountBasis object which contains the type of day count basis to use. See DayCountBasis.

Returns:
a double which specifies the annual yield of a security that pays interest at maturity
See Also:
Example

Class Bond

Definitions

Discount Bonds

Treasury Bills

Interest-Paying Bonds

Interest-Paying Bonds with Odd Coupon Periods

Coupon days

Duration

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ANNUAL

BIMONTHLY

MONTHLY

QUARTERLY

SEMIANNUAL

Method Detail

accrint

accrintm

amordegrc

amorlinc

convexity

coupdaybs

coupdays

coupdaysnc

coupncd

coupnum

couppcd

disc

duration

intrate

mduration

price

price

price

pricedisc

pricemat

priceyield

received

tbilleq

tbillprice

tbillyield

yearfrac

yield

yield

yield

yielddisc

yieldmat