Managing options risk with genetic algorithms

The Black-Scholes model asserts that a portfolio consisting of a short (long) call and its long (short) underlying asset earns the riskless rate of return if the portfolio hedge ratio is continuously rebalanced so that its asset price sensitivity, also known as delta, is kept equal to zero. In practice, delta rebalancing does not represent a perfect hedge because of market friction not accounted for in the Black-Scholes model. Researchers have studied hedging in a discrete-time framework and the impact on return due to transaction costs. Because of these and other factors, the distribution of returns on a delta-hedged portfolio departs substantially from the guaranteed riskless return of the Black-Scholes model. In a realistic scenario, investors wanting to hedge their portfolios are often faced with the problem of finding a tradeoff strategy between the extremes of minimizing risk by frequent rebalancing and minimizing cost by limiting the number of trades. The article addresses a tradeoff strategy issue by formulating a general hedging strategy aimed at optimizing the portfolio return distribution via periodic adjustments of portfolio weights, according to the hedger´s preference toward investment in an imperfect market. The parameters that determine trading decisions are computed by simulating the portfolio behavior with genetic optimization of the return distribution. The author applies the trading strategy to two classic examples of hedge of a short call position and its results are briefly discussed. Finally, he addresses extensions and limitations of this new strategy