A genetic programming approach for delta hedging

Effective hedging of derivative securities is of paramount importance to derivatives investors and to market makers. The standard approach used to hedge derivative instruments is delta hedging. In a Black-Scholes setting, a continuously rebalanced delta hedged portfolio will result in a perfect hedge with no associated hedging error. In reality, continuous rehedging is impossible and this raises the important practical question such as when should a portfolio manager rebalance the portfolio? In practice, many portfolio managers employ relatively simple deterministic rebalancing strategies, such as rebalancing at uniform time intervals, or rehedging when the underlying asset moves by a fixed number of ticks. While such strategies are easy to implement they will expose the portfolio to hedging risk, both in terms of timing and also as the strategies do not adequately consider market conditions. In this study we propose a rebalancing trigger based on the output from a GP-evolved hedging strategy that rebalances the portfolio based on dynamic nonlinear factors related to the condition of the market, derived from the theoretical literature, including a number of liquidity and volatility factors. The developed GP-evolved hedging strategy outperforms the deterministic time based hedging methods when tested on FTSE 100 call options. This paper represents the first such application of GP for this important application.