XploRe Help : HestonCall

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	finance
See also:	HestonPut BatesCall MertonCall BatesPut MertonPut BlackScholes

Quantlet:		HestonCall
Description:		calculates European call option prices in Heston model using FFT

Reference(s):

P.Carr, D. Madan, "Option valuation using the fast Fourier transform" J. Computat. Finance, 2 (1998) pp.61-73

Usage:	`y = HestonCall(S,K,T,r,kappa,theta,sigma,rho,v0)`
Input:
	`S`	array: asset price
	`K`	array: exercise price
	`T`	array: time to maturity
	`r`	array: interest rate
	`kappa`	array: rate of mean-reversion
	`theta`	array: average level of volatility
	`sigma`	array: volatility of volatility
	`rho`	array: corelation between two Wiener processes
	`v0`	array: initial volatility
Output:
	`y`	array: call option price

Note:

The Heston model is the model with stochastic volatility: dS = r S dt + sqrt(V)SdW1 dV = kappa ( theta - V)dt + sigma sqrt(V) dW2 V(0)= v0 rho is the corelation between W1 and W2

Example:

library("finance") S=100 K=50|100|150 T=1 r= 0.2 kappa =0.1 rho = 0.0 theta = 0.9 sigma = 0.8 v0 = 0.05 y=HestonCall(S,K,T,r,kappa,theta,sigma,rho,v0) K~y

Result:

[1,]       50   59.216
[2,]      100   21.669
[3,]      150   4.2241

Author: S. Borak, K. Detlefsen, W.Haerdle 20040508 license MD*Tech