XploRe Help : MertonCall

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:	MertonPut BatesCall BatesPut HestonCall HestonPut BlackScholes

Quantlet:		MertonCall
Description:		calculates European call option prices in Merton model using FFT.

Reference(s):

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

Usage:	`y = MertonCall(S,K,T,r,lambda,sigma,delta,mu)`
Input:
	`S`	scalar or array, asset price
	`K`	scalar or array, exercise price
	`T`	scalar or array, time to maturity
	`r`	scalar or array, interest rate
	`lambda`	scalar or array, expected number of jumps in time unit
	`sigma`	scalar or array, standard deviation of jump
	`delta`	scalar or array, standard deviation of jump
	`mu`	scalar or array, expected value of jump
Output:
	`y`	scalar or array, call option price

Note:

1. Each parameter is either a scalar or an array. All non scalar parameters must have the same dimension as the first array declared. 2. The Merton model is the model with normaly distributed jumps: dS = r S dt + sigma S dW1 + dZ lambda is the expected number of jumps in one year delta is standard deviation of jumps, mu the expected value of particular jump.

Example:

library("finance") S=100 K=50|100|150 T=1 r=0.02 lambda= 12 sigma =0.1 delta = 0.01 mu = 0.1 y=MertonCall(S,K,T,r,lambda,sigma,delta,mu) K~y

Result:

[1,]       50   51.132
[2,]      100   15.558
[3,]      150   3.8765

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