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

 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.

 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
(C) MD*TECH Method and Data Technologies, 05.02.2006