XploRe Help : BlackScholesPathIndependentMDQMC

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:	BlackScholesPathIndependentMDDiv BlackScholesPathDependent1DQMC BlackScholesPathIndependent1D BlackScholesPathDependent1D

Quantlet:		BlackScholesPathIndependentMDQMC
Description:		calculates the option price for path independent options in the multi-dimensional Black Scholes model by Quasi-Monte Carlo simulation.

Reference(s):

Niederreiter, H. (1992). Random Number Generation and Quasi-Monte Carlo Methods. Capital City Press, Monpellier Vermont.

Link:

Applied Quantitative Finance

Usage:	`z = BlackScholesPathIndependentMDQMC(s0,r,vola,dt,payoff,iterations,gennum)`
Input:
	`s0`	n x 1 vector of the underlying values at time 0
	`r`	scalar, risk free interest rate 5% = 0.05
	`vola`	covariance matrix of the log-price processes
	`dt`	scalar, time to maturity in years
	`payoff`	string, name of the payoff function for the option product
	`iterations`	scalar, number of simulations
	`gennum`	scalar, number of the low-discrepancy generator which is used in the simulation
Output:
	`z`	scalar, estimated option price

Example:

library("finance") proc(v) = SpecialOPT(s0) maxcall = 1.4*(s0[1]-40) next = 0.95*(s0[2]-60) if(next>maxcall) maxcall = next endif next = 2.1*(s0[4]-27) if(next>maxcall) maxcall = next endif next = 0.16*(s0[5]-340) if(next>maxcall) maxcall = next endif next =(s0[6]-57.5) if(next>maxcall) maxcall = next endif maxput =(55-s0[3]) if((maxput+maxcall)>0) v = maxput+maxcall else v = 0 endif endp s0 = #(40.14,59.4,56.57,26.79,335.3,58.65) r = 0.048 dt = 1 vola = #(0.1744942,0.0570134,0.0305491,0.0123347,0.0250993,0.0225357) vola = vola|#(0.0570134,0.1024468,0.0456498,0.0212167,0.0207358,0.0278711) vola = vola|#(0.0305491,0.0456498,0.0924536,0.0150578,0.0139953,0.0179354) vola = vola|#(0.0123347,0.0212167,0.0150578,0.0776464,0.0037853,0.0078510) vola = vola|#(0.0250993,0.0207358,0.0139953,0.0037853,0.0975046,0.0439312) vola = vola|#(0.0225357,0.0278711,0.0179354,0.0078510,0.0439312,0.1670526) BlackScholesPathIndependentMDQMC(s0,r,vola,dt,"SpecialOPT",10000,3)

Result:

Contents of z
[1,]    23.24

Author: J. Schumacher, W. Haerdle, 20020214 license MD*Tech