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American Rainbow Option Pricing Formulae in Uncertain Environment
  • Rong Gao,
  • Xiaofang Yin
Rong Gao
Hebei University of Technology
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Xiaofang Yin
Hebei University of Technology
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Abstract

American rainbow option is an exotic option on multiple assets and its return depends on the prices variations of these assets. The option grants investors the right that they can choose the best or worst among multiple assets to purchase or sell at the strike price on or before the maturity, but it is not an obligation. For a call option, investors have the right to purchase the stock at the strike price if market price is higher than the strike price, otherwise they will waive the option. For a put option, investors are entitled to sell the stock at the strike price if market price is lower than the strike price, otherwise the option will be waived. Due to the flexibility of trading time for American option and the investment preference of investors for buying multiple stocks simultaneously, this article mainly studies the pricing issue of American rainbow option where the stock price is portrayed by uncertain differential equation. Six types of pricing formulae were derived, including call on max, call on min, put on max, put on min, put 2 and call 1, better of assets. Furthermore, examples are given to verify the feasibility of the pricing formulae.