Growth Optimal Investment and Pricing of Derivatives

Details Growth Optimal Investment and Pricing of Derivatives Growth Optimal Investment and Pricing of Derivatives

1999-10-14

arxiv.org/abs/cond-mat/9910212v1

Physics

Condensed Matter

Statistical Mechanics

21 pages, 5 figures

Scientific paper

10.1016/S0378-4371(00)00005-4

We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant to the problem of pricing derivatives. We compare our result with other alternative pricing procedures in the literature, and discuss the limits of validity of the lognormal approximation. We also generalize the pricing method to a market with correlated stocks. The expected estimation error of the optimal investment fraction is derived in a closed form, and its validity is checked with a small-scale empirical test.

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