A Jump-Diffusion Model for Option Pricing under Fuzzy Theory - Theoretical and Empirical Perspectives

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Title:	A Jump-Diffusion Model for Option Pricing under Fuzzy Theory - Theoretical and Empirical Perspectives
Authors:	Ying-Hsiu Chen;Chin-Jui Chang;Shang-En Yu;Tsung-Hao Chen;Chen-Yuan Chen;Pei-Yin Chung
Keywords:	fuzzy set theory;option pricing;warrant;tree model;membership function
Date:	2010-05
Issue Date:	2011-09-27T06:47:36Z (UTC)
Abstract:	Warrants supply investors with choices for financial leverage. When the price of the underlying asset rises, the owner of the warrant can buy the stocks at the specified price, the return will be a simple multiple of the purchased stocks. When the price of the underlying asset goes down, at most the premium is lost. If we can accurately predict the optimal range of an option price, investors can make a profit and hedge against losses from the derivatives. Option pricing is a tool that investors often use for the purpose of arbitrage or hedging. However, both the Black-Scholes model and the CRR model can only provide a theoretical reference value. The volatility in the CRR model cannot always appear in the precise sense because the financial markets fluctuate from time to time. Hence, the fuzzy volatility is naturally to be considered. The main purpose of this paper is the application of fuzzy sets theory to the CRR model (Wu, 2004). It is expected that fuzzy volatility, instead of the crisp values conventionally used in the CRR model, can provide reasonable ranges and corresponding memberships for option prices, as a result of which, investors can interpret optimal values differently for different risk preferences.
Relation:	World Academy of Science, Engineering and Technology, Vol. 65
Appears in Collections:	[Department of Information Management] Papers

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