No-arbitrage implied volatility functions: Empirical evidence from KOSPI 200 index options

Implied and local volatility are very important variables to market practitioners because such variables can be exploited in numerous option models for the pricing and hedging of diverse exotic options. In the present study, we propose a method to implement no-arbitrage constraints in estimating the implied and local volatility surfaces extracted from data on option prices. With the aid of multiple local bandwidths, we increase the functional flexibility of estimators and provide a simple method by which to construct no-arbitrage volatility surfaces, such that the ready-in-computation advantage of the derivatives in local quadratic smoothing is preserved. To show the effectiveness of the arbitrage-free models, we perform a comprehensive empirical study on the performance of the competing models using the KOSPI 200 index options from January 2001 through December 2010. Using experiments, we examine the performance of the models based on three measures: in-sample pricing, out-of-sample pricing, and hedging errors. We find that implied and local volatility modeling under arbitrage-free conditions show better performance in terms of estimation, pricing, and hedging near the out-of-the-money with short maturities. From the range depicted in the findings, we often observe clear differences between the models with and without no-arbitrage conditions imposed.