Hedging option contracts with locally weighted regression, functional data analysis, and Markov chain Monte Carlo techniques

The delta-gamma Approximation (DGA) is a technique that is often used for hedging options in practice. For its simplicity, it is widely used because it can immediately indicate the number of shares of the underlying assets to be reinvested to hedge the original investments. However, the DGA requires that the change of the underlying asset price to be small for an acceptable performance. Therefore, when this change of the underlying asset price is large, then the hedging performance is not acceptable implying losses, and frequent rebalancing operations of the portfolio may be needed. But, a rebalancing operation has an associated transaction fee and a high frequency of rebalancing operations imply high additional costs. Hence, there is a trade-off between losses due to low performance of the DGA (when the change of the underlying asset price is large) and additional costs due to rebalancing operations to compensate the low performance of the DGA. In the present work, we propose a hedging framework that improves its performance with the purpose to reduce losses by improving the quality of approximating the option prices. This framework consists of estimating the implied volatility using the Markov chain Monte Carlo, predicting the change of the underlying asset price using the functional data analysis, and approximating the option price using the locally weighted regression.