AHMAD RADAIDEH - APRIL 29, 2016
PREDICTIVE ASSESSMENT OF HESTON’S MODEL FOR EMPIRICAL ASSET RETURNS
In the early 1970s, Fischer Black, Myron Scholes and Robert Merton developed what is now known as the Black-Scholes model, an important concept in modern ﬁnancial theory. The model was a major breakthrough in the pricing of complex ﬁnancial instruments, known as derivatives,and received global recognition. The formula underpinning the model assumes that percentage changes in ﬁnancial asset prices are normally distributed with constant volatility.
Motivated by the evidence of asset return distributions that exhibit heavy tails and that volatility is of a time-varying nature, stochastic volatility modeling represents a long-standing and active area of research in empirical ﬁnance. Among stochastic volatility models, Heston's model is arguably the most popular, and is known for its simplicity and analytical tractability. The focus of our paper is to evaluate the performance of Heston's model in predicting the empirical dynamics of asset returns. Our objective is to go beyond a simple accept/reject framework of the model. As such, we are interested in gaining a better understanding of the models strengths and limitation in terms of predicting asset returns. To the best of our knowledge, such an analysis of the predictive properties of Heston's model has yet to be undertaken. Given the vast body literature on the empirical performance of stochastic volatility models, our study distinguishes itself along three main considerations:
• The model parameters are estimated using observable asset market prices only. In contrast to other studies, we do not exploit derivatives prices in calibrating the model, nor for performance evaluation purposes. As demonstrated by several authors, derivatives pricing involves a number of additional assumptions and complexities. Therefore, the performance of a model becomes heavily inﬂuenced by the assumptions of derivatives pricing, and not just its predictive capacity.
• The model is evaluated purely based on its out-of-sample predictions. Given that many ﬁnancial applications, such as derivatives pricing, portfolio optimization and risk management, rely on the evolution of prices in the future, it is desirable to conduct an out-of-sample assessment, rather than focus on the in-sample performance. Existing studies in the literature have typically focused on in-sample evaluations of the models performance.
• To evaluate the model, we conduct an empirical forecast assessment which relies on Rosenblatts residuals, a standardizing transformation that has a long history in the literature. To compute the residuals, we implement a challenging MCMC algorithm, which under the null hypothesis provides a powerful framework for goodness-of-ﬁt evaluations.
Our testing data are the Dow-Jones Industrial Average (DJIA) index returns between June 2007 and May 2011, which includes the ﬁnancial crisis of 2008. A key aspect of the analysis is to evaluate entire forecasted return distributions. This includes a Value-at-Risk investigation (i.e. extreme tail risk), an assessment for the majority of returns when neglecting tail events, and separate tests under different market conditions. Our ﬁndings show that the model signiﬁcantly understates the left tail of return distributions, and does not accurately characterize the downside risk under extreme market conditions. However, under normal market conditions, the model’s performance noticeably improves out-of-sample. When neglecting acute tail events, we ﬁnd that the model is capable of predicting the bulk of return distributions.