# [R-SIG-Finance] Using monte carlo simulation to price options

Moshe Olshansky m_olshansky at yahoo.com
Mon Sep 22 03:26:09 CEST 2008

```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
>  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
>
>
>
>
>
>
> ___________________________________________
> This message and any attached documents contain
> information which may be confidential, subject to
> privilege or exempt from disclosure under applicable
> law. These materials are solely for the use of the
> intended recipient. If you are not the intended
> recipient of this transmission, you are hereby
> notified that any distribution, disclosure, printing,
> copying, storage, modification or the taking of any
> action in reliance upon this transmission is strictly
> prohibited. Delivery of this message to any person
> other than the intended recipient shall not
> compromise or waive such confidentiality, privilege
> or exemption from disclosure as to this
> communication.
>
> If you have received this communication in error,
> please notify the sender immediately and delete
> this message from your system.
>
> 	[[alternative HTML version deleted]]
>
> _______________________________________________
> R-SIG-Finance at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only.
> -- If you want to post, subscribe first.

```