Hedging Under Model and Parameter Uncertainty

Underwriting over-the-counter (OTC) commodity derivatives is an important source of revenue for banks and financial institutions. Institutions expect to earn risk-free interest plus fees by offsetting their short positions in OTC derivatives via delta hedging. Valuation of derivatives and understanding their price dynamics are an integral part of the risk management processes. In turn, choosing the model and calibrating the model to market data are the main steps of understanding and forecasting the price and risk-reward profiles of the derivatives. In this work, we aim to analyze the impact of model selection, calibration, and hedging frequency on profit and loss distribution of delta hedging of derivatives written on oil futures. We develop three criteria for ideal hedging and analyze the impact of violating the criteria under simulations, before analyzing historical delta hedging performances. Specifically, we apply the geometric Brownian motion, Schwartz (1997) one factor, and two-factor models to historical West Texas Intermediate data spanning over 25 years with 5-year look-back periods and analyze the delta hedging performances for in-the-money (ITM), at-the-money (ATM), and out-of-the-money (OTM) options on the futures. It was found that local minima of the objective function impact calibration and delta hedging performance, hedging on a monthly frequency outperforms weekly hedging and that the Schwartz (1997) two-factor model outperforms the other tested models in producing more optimal hedging results