Using monte carlo simulation to price options
You can use mvrnorm from MASS package to generate multivariate normal distribution. Then if your option is European, using Monte Carlo to price it is straightforward, but this is not the case if the option is American.
--- On Sun, 21/9/08, Chiquoine, Ben <BChiquoine at tiff.org> wrote:
From: Chiquoine, Ben <BChiquoine at tiff.org> Subject: [R-SIG-Finance] Using monte carlo simulation to price options To: "r-sig-finance" <r-sig-finance at stat.math.ethz.ch> Received: Sunday, 21 September, 2008, 8:55 AM Hi, I'm trying to use monte carlo simulation to price a worst of three asset currency option. I'm trying to follow what Haug does in his book "The Complete Guide to Option Pricing Formulas" Unfortunately he only carries the monte carlo simulation logic out to an option on two assets and I'm not able to infer how the underlying asset prices should be modeled for an option with 3 underlying assets. I know this might not be the perfect forum for this question but it was the best I could think of. Any help you can provide would be greatly appreciated. The formula that Haug gives for simulating two correlated asset prices which follow geometric Brownian motion is.... S1+ ChangeS1 = S1exp((u1-1/2*std1^2)*t + std1*a1*sqrt(t)) S2+ ChangeS2 = S2exp((u2-1/2*std2^2)*t + std2*a2*sqrt(t)) a1=e1 a2=rho12*e1+ e2*sqrt(1-rho^2) where e1 and e2 are independent random numbers from standard normal distributions Again, Im basically just trying to add an S3 to this model so that rho12, rho13, and rho23 are all incorporated. Thanks again for any insight you can provide! Ben
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