A general methodology to price and hedge derivatives in incomplete markets

Details A general methodology to price and hedge derivatives in incomplete markets A general methodology to price and hedge derivatives in incomplete markets

1998-10-20

arxiv.org/abs/cond-mat/9810257v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

24 pages, LaTeX, epsfig.sty, 5 eps figures, changes in the presentation of the method, submitted to International J. of Theore

Scientific paper

We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in repeated multiplicative games originally introduced by Kelly. As particular cases we obtain the Cox-Ross-Rubinstein and Black-Scholes in the complete markets case and the Schweizer and Bouchaud-Sornette as a quadratic approximation of our prescription. Technical and numerical aspects for the practical option pricing, as large deviation theory approximation and Monte Carlo computation are discussed in detail.

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