Growth Optimal Investment and Pricing of Derivatives

TL;DR

This paper proposes a new derivative pricing method in incomplete markets based on growth optimal strategies, extending to correlated stocks and validating with empirical tests.

Contribution

It introduces a growth optimal strategy-based derivative pricing framework, including market correlation and error estimation, advancing beyond traditional models.

Findings

The new pricing method aligns with existing procedures in certain conditions.

The approach is extended to markets with correlated stocks.

Empirical tests support the validity of the estimation error formula.

Abstract

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.