Basket options (Implied Volatility)

johnywaker · June 19th, 2007, 4:36 pm

Do any one have an idea of how to build the basket implied volatility surface from the implied volatility surface of the underlying equities?I saw the paper of damiano Brigo and Fabio Mercurio et al on Moment-Matching techniques but the volatility only depends on time not on strique or asset value.Any other solution??Thanks

helix · June 19th, 2007, 4:58 pm

A brute force approach would be to use MonteCarlo with skew/smile dynamics (e.g. local vol, heston,...) on each underlying to simulate the basket, and then fit a local vol surface or stoch vol params to the resultsing basket distribution. If we used a stoch vol process for each asset, the next question is how to correlate the dynamics. What are the implications for the smiles on the crosses (e.g. for basket of currencies will the cross smiles be correct)? My feeling is that this is a tough problem - would love to hear peoples' views.

johnywaker · June 20th, 2007, 1:27 pm

I think by using the Monte Carlo approach, I'll only be able to build a volatility surface for the basket depending on time. How can I use such a process to build a volatility surface depending on time and strike?Your other questions are still opened.thanks

eye51 · June 22nd, 2007, 9:44 am

Look on the website of Avellaneda. He presents a method, I think it's in "Reconstruction of Volatility: Pricing index options using the steepest-descent approximation".also "Weighted Monte Carlo Methods for Multi-Asset Equity Derivatives: Theory and Practice " and "Empirical Aspects of Dispersion Trading in U.S. Equity Markets " might interest you.If you are trying to implement dispersion trading strategy, there are better methods though, that doesn't rely on a huge set of assumptions, like log-normality, constant correlations ect.

Bazman2 · December 13th, 2007, 4:28 pm

Hey There eye51,Have you used either of the methods presented in "Reconstruction of volatility" or "Weighted monte Carlo methods for multi-asset euity derivatives" in practice?What were the relative strengths of each?Kind RegardsBaz

eye51 · December 14th, 2007, 9:36 am

Hi Bazman2,I haven't used it, because I found it too dependent on a lot of parameters which are not so straightforward to estimate.At that time, I was interested to price the index-options based on the underlying options. (index-basket arb type)I was not interested in pricing something exotic. Where do you want to use it for ?

Bazman2 · December 17th, 2007, 2:48 pm

Hi,Specifically, I want to use it in the pricing of basket options to keep the marginal distributions (smile) of the underlyings and the total distribution (smile) of the basket consistent.More generally I am looking into exotic option pricing generally and am trying to identify the key problems facing practitioners currently. I hope to make this the basis of the final chapter of my PhD. So any ideas are most welcome!Baz