An Empirical Comparison of Option-Pricing Models in Hedging Exotic Options

Article excerpt

This paper examines the empirical performance of various option-pricing models in hedging exotic options, such as barrier options and compound options. A practical and relevant testing approach is adopted to capture the essence of model risk in option pricing and hedging. Our results indicate that the exotic feature of the option under consideration has a great impact on the relative performance of different option-pricing models. In addition, for any given model the more "exotic" the option, the poorer the hedging effectiveness.

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Since the publication of the path-breaking contribution by Black and Scholes (1973), more realistic and complicated models have been proposed in the option-pricing literature. For example, deterministic volatility function models assume that the volatility of the underlying asset depends on both the price of the underlying asset and time (Derman and Kani, 1994). Another example is the jump diffusion models, which allow the stochastic process of the underlying asset to have discontinuous breaks (Merton, 1976). Stochastic volatility models, on the other hand, assume that the volatility follows a particular stochastic process (Heston, 1993). While these alternative models provide important theoretical insights, they are motivated primarily by their analytical tractability. Moreover, each model differs fundamentally in its implications for valuing and hedging derivative contracts. Consequently, a test of the empirical validity and performance of these models is necessary before they can be applied fully in practice. It is also important to determine the most suitable model when each particular option is considered.

The performance of various option-pricing models has been studied extensively in the existing literature. Bakshi, Cao, and Chen (1997) explore the pricing and hedging performance of a comprehensive model that includes the Black and Scholes 0973) (BS) model, the stochastic volatility and stochastic interest rate model, and the stochastic volatility and jump diffusion model as special cases. Their results indicate that the alternative models outperform the BS model in terms of out-of-sample pricing errors. The hedging performance, however, is relatively insensitive to model misspecifications. Dumas, Fleming, and Whaley (1998) evaluate a few deterministic volatility function models and demonstrate that they perform no better in out-of-sample pricing and hedging than the implied volatility model. The testing approach in most of the existing empirical work in current literature is common. The parameters of the model under consideration are estimated such that the model prices for some European options match those prices that are observed in the market (e.g., from market transactions or broker quotes) at a specific time. The resulting model is used to price other European or American options later. Next, these model prices are compared to the prices observed from the market at this time. However, this out-of-sample test does not fully capture the essence of model risk, as option-pricing models are chiefly used to price or hedge exotic or illiquid options at the time they are calibrated. Moreover, model specification is relatively less important when vanilla options are concerned, since they are actively traded in the market and a great deal of information on the value of these options is readily available.

The purpose of this paper is to evaluate the BS model and three other major alternative models: 1) the jump diffusion (JD) model, 2) the stochastic volatility (SV) model, and 3) the stochastic volatility and jump diffusion (SVJ) model using a different, but more appropriate approach. The methodology employed in this paper is practical and relevant, as it properly addresses the issue of model risk in option pricing and hedging. First, the models under consideration are calibrated to the observed cross-sectional vanilla option prices and the resulting models are used to set up replicating portfolios for other options at the same time. …