Option Portfolio Management in a Risk-Neutral World

Abstract

The most commonly used strategy of the speculative investments in options is a statistical arbitrage between the objective underlying price distribution which the price is following and the risk-neutral distribution on the basis of which options were priced. This article investigates an alternative approach which does not demand these two distributions to be different. Instead, it uses a periodical roll-over of an investment horizon with including options of the next expirations in the portfolio. We consider a risk-neutral world where the real distribution coincides with the risk-neutral distribution as a model of the market. In such a market, the expected return from investments in any option portfolio corresponds with the risk-free rate. However, it is possible to construct and manage the portfolio dynamically in such a way that it provides higher return with a probability close to unity or lower return (possibly a large negative return) with a given very low probability. To optimize the portfolio a stochastic program with the approximative safety-first criterion for option portfolio was developed along with the corresponding multinomial scenario tree. The results of the Monte-Carlo simulation of the portfolio management are presented. The very low probability of loss during option portfolio management is provided by the strategy with periodical rolling horizon of the optimization. The developed portfolio management strategy can be used as a basis for constructing trading strategies for the real option markets.