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: BatesPut MertonCall MertonPut HestonCall HestonPut BlackScholes

 Quantlet: BatesCall 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 = BatesCall(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: call 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=BatesCall(S,K,T,r,lambda,delta,kquer,kappa,theta,sigma,rho,v0)
K~y

Result:
[1,]       50   51.629
[2,]      100   17.474
[3,]      150   5.7997

Author: S. Borak, K. Detlefsen, W.Haerdle 20040508 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006