Business and Personal Finance Dictionary

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• RAINBOW OPTION
  
  Definition: An option that has several risk factors of the same type, e.g., two stock prices or three exchange rates. Examples: The earliest Rainbow Option in the derivatives literature was probably Margrabe’s Option to Exchange One Asset for Another, an Outperformance Option (q.v.), with a payoff that depends on the difference between two prices. An Equity Index Option (q.v.) has a payoff that depends on the average of underlying share prices. Pricing: Margrabe (1976) published the first pricing model for a Rainbow Option, namely the "Margrabe Option." In some cases one can price a Rainbow Option with a Black-Scholes-Merton model by computing the appropriate adjusted volatility and dividend yield. The most common way to price a general Rainbow Option is with Monte Carlo pricing. Next most common is with a multinomial model (a generalization of the binomial model). Explicit finite difference pricing is easily feasible, but rarely seen. Risk Management: Rainbow options with n sources of risk have n Deltas, n Kappas, n(n+1)/2 Gammas, and sensitivity to n dividend yields and n(n-1)/2 correlations. With large n this can get complicated. Comment: If the several risk factors are of two or more types, e.g., a stock price and an exchange rate, then the option is a Hybrid Option (q.v.).
  
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