Hello, Recently, I have read some articles on pricing of basket option. All these articles try to find a way to approximate the dynamics of basket in order to obtain a closed formula for pricing. Are these approximations are really applicated while pricing?In the pricers actually used, what are the methods mostly used for pricing a simple (arithematic) basket option?(finite difference? MonteCarlo?) What are their disadvantages?What are the difficulties encountered while pricing basket options except the correlation problem?Whether we can easily integrate smile in the pricer?Any proposition of literature for this subject pls?Thanks in advance for your help.W.P. (beginner)

Sure, approximations are used:If you know all the components' dynamics and the relevant correlations, you need a perfect price and have pleanty of computation time to spare on the basket option, go ahead, do a Monte Carlo and finite differences greeks.In reality, analytic approximations often are largely sufficient. I once made some tests of comparing Asian basket options priced with Monte Carlo and via shifted lognormal moment matching. The analytic prices were very satisfying when reasonable vols and correlations are used.

Thanks a lot, Speedy. I have also tested the moment matching on european basket option, it dose work well. How could I obtain the moments of the underlyings via the market data pls? (a stupid question)I have other questions on basket option. Any answer and proposition will be highly appreciated.Whether I could use CEV to simulate the dynamics of a basket, and calibrate the parameters by moments matching in stead of prices. Is it possible? thanks in advance,WP

Hello,I would like to price a basket opton using Monte carlo. I consider a multivariate model such as :ST_i=S0_i + r*St_i*dt + integral btw 0 and T of St*sigma_i*dWt_iI got the Cholesky matrix and I would like to simulate the path of each assets. How can I express it using the Cholesky matrix.I mean for two assets I did : S=S1*exp(((r-(sigma1*sigma1)/2.)*T)+sigma1*sqrt(T)*GaussianAlea()[0]);S0=S2*exp(((r-(sigma2*sigma2)/2.)*T)+sigma2*rho*sqrt(T)*GaussianAlea()[0]+ sigma2*sqrt(1-rho*rho)*sqrt(T)*GaussianAlea()[1]);but when we have several assets, I'm confused...Help please.

This book discusses 2,3 and N factors using MC