Pricing Rainbow Options

Peter Ouwehand, Graeme West derive the Black—Scholes prices of several styles of (multi-asset) rainbow options using change-of-numeraire machinery. Hedging issues and deviations from the Black-Scholes pricing model are also briefly considered

A previous paper (West 2005) tackled the issue of calculating accurate uni-, bi- and trivariate normal probabilities. This has important applications in the pricing of multiasset options, e.g. rainbow options. In this paper, we derive the Black—Scholes prices of several styles of (multi-asset) rainbow options using change-of-numeraire machinery. Hedging issues and deviations from the Black-Scholes pricing model are also briefly considered.

1. Definition of a Rainbow Option

Rainbow Options refer to all options whose payoff depends on more than one underlying risky asset; each asset is referred to as a colour of the rainbow. Examples of these include:
• “Best of assets or cash” option, delivering the maximum of two risky assets and cash at expiry (Stulz 1982), (Johnson 1987), (Rubinstein 1991)
• “Call on max” option, giving the holder the right to purchase the maximum asset at the strike price at expriry, (Stulz 1982), (Johnson 1987)
• “Call on min” option, giving the holder the right to purchase the minimum asset at the strike price at expiry (Stulz 1982), (Johnson 1987)
• “Put on max” option, giving the holder the right to sell the maximum of the risky assets at the strike price at expiry, (Margrabe 1978), (Stulz 1982), (Johnson 1987)
• “Put on min” option, giving the holder the right to sell the minimum of the risky assets at the strike at expiry (Stulz 1982), (Johnson 1987)

Logged-in members can download the article by clicking the link below. To log in or register visit here.

Related Posts

An Asymptotic FX Option Formula in the Cross Curre... In this article, we introduce analytic approximation formulae for FX options in the Libor market model (LMM). The method to derive the formulae is an ...
Rootless Vol Even if you started out clueless about the volatility σ , given a good enough measuring stick and fast enough hands you ought to be able to measure ...
Forecasting the Yield Curve with S-Plus Methods capable of forecasting the entire yield curve based on a time series extension of the Nelson-Siegel model Nelson and Siegel (1987) were su...
Amaranthus Extermino On September 19, 2006 the hedge fund Amaranth Advisors of Greenwich, Connecticut announced that it had lost $6 billion, about two thirds of the $9...
Order Statistics for Value at Risk Estimation and ... We apply order statistics to the setting of VaR estimation. Here techniques like historical and Monte Carlo simulation rely on using the k-th heaviest...
Poker as a Lottery Doyle Brunson , two-time winner of the World Series of Poker main event, has likened a poker tournament to a lottery in which more skilled players...
Building Your Wings on the Way Down Ray Bradbury famously defined “living at risk” as jumping off a cliff and building your wings on the way down. Too many financial risk managers wh...
Internal LGD Estimation in Practice Driven by a competitive market and motivated by the new Basel Capital Accord (Basel II), banks have put a lot of effort into development and impro...
Download Paper Here
120201_rainbow-2