Option pricing, Bayes risks and Applications
Abstract
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, RB, of a 2-parameter estimation problem, thus justifying calling C Bayes (B-)price. The result provides new insight in option pricing, among others obtaining C for some stock-price models using the underlying probability instead of the risk neutral probability and giving RB an economic interpretation. When logarithmic stock prices follow Brownian motion, discrete normal mixture and hyperbolic Levy motion the obtained B-prices are "fair" prices. A new expression for the price of American call option is also obtained and statistical modeling of RB can be used when pricing European and American call options.
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