A standard option is a contract between the option holder and the option writer, which gives the holder the right to buy or sell a specified financial instrument at a predetermined strike price on a specified date. Rainbow options are classified as exotic options, as they differ from standard options in that their payoff depends on the value of two or more underlying financial instruments. We focus on European rainbow options. We examine their properties, valuation methods and give some examples. Their valuation requires a financial market model that simultaneously describes the price dynamics of multiple financial instruments.
First, we examine how to value them in a discrete one-period market model, and then how to value them in a discrete multi period market model. We begin by deriving the parametrization of the trinomial model, which is suitable for valuing options on a single financial instrument, and extend it to a model with two financial instruments, where the value of each financial instrument follows its own trinomial model. Using this model, we then value rainbow options on two financial instruments.
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