Black-Scholes Price of European Geometric Mean Basket Option

[JSanter]

Hey,

im trying to get the exact price for a European Call Option on the geometric mean of a basket of stocks in the multivariate Black-Scholes Model. I already found some solutions online but so far my Monte-Carlo Algorithm doesnt converge to the values i computed with those solutions. It does however converge to the black-scholes solution for a standard European Call on one stock. So the error should either be in how i correlate the random brownian increments or the payoff function but they seem correct.
So can anyone give me the link to an exact solution of such a geometric basket option he has confirmed is correct? Or even a specific example of a value for a basket with covariance matrix, same drift for all stocks, starting prices etc so i can compare those values to mine.

Thanks in advance

 

[vickymaj]

Just to be curious, why exactly are you doing this?

 

[JSanter]

I did find the error in the meantime. Was a sign error. And i was going over the solution for like 1000 times. Now it seems to work.
As to why im doing this:
My professor wants me to use a exact solution as reference value for this algorithm he wants me to implement as my master thesis. And since im using the Monte-Carlo solution of the arithmetic basket as reference value i wanted to see if theres something wrong with my Monte-Carlo algorithm or if the solution was wrong. I hope that clarifies it.

 

[xapit]

Consider a 1-period binomial model with R=1.02, S0=100,

u=1/d=1.05. Compute the value of a European call option on the stock

with strike K=102. The stock does not pay dividends.

Please submit your answer rounded to two decimal places. So for example, if your answer is 3.4567 then you should submit an answer of 3.46.

 

[Daniel Duffy]

1-period??

 

[xapit]

1-period??

Yes 1-period.