# Basket option pricing: step by step tutorial for beginners

I would like to learn how to price options written on basket of several underlyings.

I've never tried to do it and I would appreciate if you can provide some documents, papers, web sites and so on in order I can collect materials to build my own step by step guide.

I know the first step should be Black & Scholes formula, then I found out other methods exist like Beisser, Gentle, Ju, Milevsky etc.

At the end of my studies, I would like to price basket options in R building my own index by weighted sum of several assets' prices.

• Hi, what books do you have on the subject so far? – Nikos Dec 13 '12 at 12:23
• No books, I've got just what I found by Google but this doesn't allow me to build up a smoothed learning curve. I will look for something on J. Hull's Options, futures and derivatives on Tuesday, I hope something is there. – Lisa Ann Dec 14 '12 at 14:11

Once you have slogged through all the relatively useless theoretical literature, this paper is a rediscovery (and pretty good write-up) of how basket option pricing is really done in serious quant packages at the big banks.

• Is this the title of the paper? The link no longer works. "American Basket and Spread Option pricing by a Simple Binomial Tree" – PBD10017 Mar 2 '16 at 5:20
• The link is now fixed – Brian B Jul 28 '16 at 23:25
• While this approach may be ok for simple basket options, it is not true in general. For more exotics basket options, the typical approach is to use local volatility Monte-Carlo simulations. – jherek Mar 20 '19 at 12:31
• @jherek - i would agree with this. I would be surprised if anyone used anything akin to the zoo of options pricing functions available (i.e. all of Espen Haugs) for actual pricing or risk management - they have far too many caveats and pitfalls, which are easily avoided by just throwing them into a montecarlo. – will Dec 4 '19 at 22:05

You may find my recent paper helpful.

Choi (2018) Sum of All Black-Scholes-Merton Models: An Efficient Pricing Method for Spread, Basket, and Asian Options (arxiv)

The method can handle the options on any linear combination of assets such as spread, basket and Asian options. You can obtain fairly accurate deterministic (i.e., not Monte Carlo) values with very light computation.

• It appears that the volatility skew is completely ignored. – Gordon Aug 3 '18 at 15:32
• True, the paper assumes the geometric Brownian motion for each asset price. – Jaehyuk Choi Aug 4 '18 at 0:16

To add (and contradict a bit) to what Brian B said. The exo desks that have multiple positions in basket options frequently price and manage these positions using the moment matching models (for efficiency reasons). For baskets with a lot of stocks, most desks would use a single vol, usually using a proxy like a liquid index with a spread or a multiplier.

To develop it from scratch, you could simulate the portfolio of the security combination, and utilize the portfolio's notional value, volatilities into Black Scholes Merton for fair values of ATM options.

• If I understand, you mean that my underlying should be the weighted average of each asset's price. Underlying's volatility should therefore come from covariance matrix and the final value of option is BMS with my underlying in input. Is it correct? Is it possible to use all further models (like Heston) on this "synthetic" underlying like I would do with the single option? – Lisa Ann Dec 16 '12 at 15:39
• hi Lisa, yes I'd start the synthetic underlying value as a weighted average of each asset's value. As for the basket variance/vol, I meant to get it empirically by simulating basket (e.g. create a column of the summed prices in excel). That's enough to derive the variables needed for models such as Heston's. Hope that helped! – Rock Dec 16 '12 at 20:27