Journal of Risk

Generalizations of the celebrated Black–Scholes formula have been pursued in a variety of directions. Variations that account for stylized facts such as stochastic volatility and jumps have resulted in statistical estimation challenges. This issue of The Journal of Risk evaluates option pricing alternatives, particularly nonparametric models and those developed ad hoc by practitioners. Other topics of practical importance, namely the impact of high-frequency trading on parameter estimation and the optimal execution of share repurchases by firms, are also considered in this issue.

In the first paper, “Pricing and hedging options with rollover parameters”, Sol Kim contrasts rollover strategies to update parameter estimates and their impact on pricing and hedging models. Using Standard & Poor’s 500 data, Kim shows that the so-called absolute smile ad hoc modification of the Black–Scholes model is simple to implement, and tends to provide pricing and hedging results that are more accurate than extension models accounting for stochastic volatility and jumps.

These extension models are also assessed by Xiaolong Zhong, Jie Cao, Yong Jin and Wei Zheng in “On empirical likelihood option pricing”, the second paper in this issue. Here, through Standard & Poor’s data and simulation, the authors implement an empirical likelihood model, which they show also generates more accurate prices than classic nonparametric and stochastic volatility with jumps models.

Ben Charoenwong and Guanhao Feng contrast the long-horizon volatility forecasting accuracy of high- and low-frequency data in “Does higher-frequency data always help to predict longer-horizon volatility?”. Their paper, the third in this issue, shows that mean model misspecification leads to a deterioration in the quality of volatility estimates as data frequency increases, especially in the presence of high conditional autocorrelation.

In our fourth and final paper, “Optimal execution of accelerated share repurchase contracts with fixed notional”, Olivier Guéant considers the problem of a firm that wants to repurchase a subset of its own shares while only making a minimal impact on their price. Guéant proposes a discrete dynamic programming model to determine the best price for the accelerated share repurchase (ASR) contract that the firm arranges with its investment bankers, as well as its optimal execution. This approach highlights certain features of ASR contracts: namely, that they involve issues related to optimal trade execution as well as the pricing of Asian and Bermudan options.

Farid AitSahlia
University of Florida

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