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: BlackScholesPathIndependentMD Description: calculates the option price and its standard deviation for path independent options in the multi-dimensional Black Scholes model by Monte Carlo simulation.

 Usage: {z,v} = BlackScholesPathIndependentMD(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 random source which is used in the simulation Output: z scalar, estimated option price. v scalar, standard deviation of the price estimate.

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)
BlackScholesPathIndependentMD(s0,r,vola,dt,"SpecialOPT",10000,3)

```
Result:
```The results can slightly vary with every execution
of this example!

Contents of _tmp.z
[1,]   23.315

Contents of _tmp.v
[1,]   0.2135
```

Author: J. Schumacher, W. Haerdle, 20020214 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006