Approximating Option Prices under Large Changes of Underlying Asset Prices

When investing in derivatives portfolios (such as options), the delta-gamma approximation (DGA) is often used as a risk management strategy to reduce the risk associated with the underlying asset price. However, this approximation is accepted only for small changes of the underlying asset price. When these changes become large, the option prices estimated by the DGA may significantly differ from those of the market, depending mainly on the time-to-maturity, implied volatility, and moneyness. Hence, in practice, before the change of the underlying asset price becomes large, rebalancing operations are demanded to minimize the losses occurred due to the error introduced by the DGA. The frequency of rebalancing may be high when the rate at which the underlying asset price significantly changes. Nonetheless, frequent rebalancing may be unattainable, as there are associated transaction costs. Hence, there is a trade-off between the losses resulting from the inaccuracy inherent to the DGA and the transaction costs incurring from frequent hedging operations. In the present work, with the objective to increase the accuracy of estimating the option prices, we propose a modified version of the DGA that outperforms the original DGA. As another approach to increase the accuracy, we propose the locally weighted regression to regress the option prices. Finally, we compare the performance of these two methods to that of some other existing methods.