Package com.imsl.test.example.math

Class FeynmanKacEx4

java.lang.Object

com.imsl.test.example.math.FeynmanKacEx4

public class FeynmanKacEx4
extends Object

Evaluates the price of a convertible bond.

This example evaluates the price of a convertible bond. Here, convertibility means that the bond may, at any time of the bond holder's choosing, be converted to a multiple of the specified asset. Thus a convertible bond with price \(x\) returns an amount \(K\) at time \(T\) \(unless\) the owner has converted the bond to \(\nu x,\, \nu \ge 1\) units of the asset at some time prior to \(T\). This definition, the differential equation and boundary conditions are given in Chapter 18 of Wilmott et al. (1996). Using a constant interest rate and volatility factor, the parameters and boundary conditions are:

1. Bond face value \(K = {1}\) , conversion factor \( \nu = 1.125\)
2. Volatility \( \sigma = {0.25}\)
3. Times until expiration = {1/2, 1}
4. Interest rate \(r\) = 0.1, dividend \(D\) = 0.02
5. \(x_{\min} = 0,\, x_{\max} = 4\)
6. \(nx = 61,\, n = 3 \times nx = 183\)
7. Boundary conditions \(f(0,t) = K \exp(r-(T-t)),\, f(x_{\max},t)=\nu x_{\max}\)
8. Terminal data \(f(x,T)=\max(K,\nu x)\)
9. Constraint for bond holder \(f(x,t) \ge \nu x \)

Note that the error tolerance is set to a pure absolute error of value \(10^{-3}\). The free boundary constraint \(f(x,t) \ge \nu x\) is achieved by use of a non-linear forcing term in interface ForcingTerm. The coefficient values of the Hermite quintic spline representing the approximate solution of the differential equation at the initial time point are provided with the interface InitialData.

See Also:

• Code
• Output

Constructor Summary

Constructors

Constructor	Description
FeynmanKacEx4()

Method Summary

Modifier and Type	Method	Description
static void	main(String[] args)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

FeynmanKacEx4

public FeynmanKacEx4()

Method Details

main

public static void main(String[] args)
                 throws Exception

Throws:

Exception