Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation,
Business and Law
Accounting, Finance and Economics
A growing literature advocates the use of high-frequency data for the purpose of volatility estimation. However, despite the successes in modeling the conditional mean of realized volatility empirical evaluations of this class of models outside the realm of short run forecasting is limited. How can realized volatility be used for pricing options? What are the modeling qualities introduced by realized volatility models for pricing derivatives? In this short paper, we propose an options pricing framework based on a new realized volatility model that captures all the relevant empirical regularities of the realized volatility series of the S&P 500 index. We emphasize two main empirical regularities for our volatility model and that are potentially very relevant for option pricing purposes. Fist, realized variation measures constructed from high-frequency returns reveal a large degree of time series unpredictability in the volatility of asset returns. Even though returns standardized by (ex-post) quadratic variation measures are nearly gaussian, this unpredictability brings substantially more uncertainty to the empirically relevant (ex-ante) distribution of returns. In this setting carefully modeling the stochastic structure of the time series disturbances of realized volatility is fundamental. Second, there is evidence of very large leverage effects; large falls (rises) in prices being associated with persistent regimes of high (low) variance in the index returns. We propose a model for the conditional volatility, skewness and kurtosis of daily index and stocks returns. The main new feature of this model is to recognize that volatility is itself more volatile and more persistent in high volatility periods. Contrary to “peso problem” considerations, we show that when volatility is (nearly) observable it is not necessary to rely on rare realizations on past return data to learn about the tails of the return distribution, an unexplored and large modeling gain enabled by high frequency data. We conduct a brief empirical illustration analysis of the pricing performance of this approach against some benchmark models using data from the S&P 500 options in the 2001-2004 period. The results indicate thatas expected the superior forecasting accuracy of realized volatility translates into signiﬁcantly smaller pricing errors when compared to models of the GARCH family. More signiﬁcantly, our results indicate that modeling leverage effects and the volatility of volatility are paramount reducing common pricing anomalies.