Option pricing and hedging with determinsitic volatility functions

Abstract

The deterministic volatility approach is developed to find an option valuation model that is consistent with observed volatility structures without introducing additional non-traded sources of risk. Dumas, Fleming, and Whaley examine whether the deterministic volatility approach is valid in tracing the true volatility surface by applying deterministic volatility functions to S&P 500 index option prices. With its poor one-week-ahead prediction and hedging performance, they conclude that the deterministic volatility approach tends to overfit the data, and therefore, fails in constructing the true volatility surface. In this paper, we examine the prediction and hedging performance of deterministic volatility approach over a shorter horizon than Dumas, Fleming, and Whaley ; one day and three hours. We find that, on the contrary to the results of Dumas, Fleming, and Whaley, the prediction performance of deterministic volatility function models is better than that of the benchmark model over a shorter time interval. We also find that the deterministic volatility function models outperform the benchmark model in hedging out-of-the-money call options.