XploRe Help : BatesPut

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:	BatesCall MertonCall MertonPut HestonCall HestonPut BlackScholes

Quantlet:		BatesPut
Description:		calculates European call option prices in Bates 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 = BatesPut(S,K,T,r,lambda,delta,kquer,kappa,theta,sigma,rho,v0)`
Input:
	`S`	array: asset price
	`K`	array: exercise price
	`T`	array: time to maturity
	`r`	array: interest rate
	`lambda`	array: expected number of jumps in time unit
	`delta`	array: standard deviation of the jumps
	`kquer`	array: part of the mean of the jumps
	`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: put option price

Note:

The Bates model is the model with stochastic volatility and jumps: dS = r S dt + sqrt(V)SdW1 + dZ dV = kappa ( theta - V)dt + sigma dW2 V(0)= v0 rho is the corelation between W1 and W2 Expected number of jumps is lambda and jumps are normally distributed where: ln(1 + jump) is N(ln(1+kquer)-0.5*delta^2, delta^2)

Example:

library("finance") S=100 K=50|100|150 T=1 r= 0.02 lambda=5 delta = 0.1 kquer = 0.1 kappa =0.1 rho = 0.0 theta = 0.9 sigma = 0.8 v0 = 0.05 y=BatesPut(S,K,T,r,lambda,delta,kquer,kappa,theta,sigma,rho,v0) K~y

Result:

[1,]       50  0.63864
[2,]      100   15.494
[3,]      150    52.83

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