Journal of Risk

Farid AitSahlia    
Warrington College of Business, University of Florida

This issue of The Journal of Risk addresses the link between the implied volatility surface of an asset and its future realized volatility; the role of stochastic dominance and pricing kernel monotonicity in contrasting risk-neutral and real-measure forecasting; the Pareto-optimality of certain reinsurance policies across multiple reinsurers with heterogeneous loss beliefs; and the efficacy of an algorithm to estimate value-at-risk non-parametrically in high dimensions.

The issue’s first paper, “Forecasting realized volatility with the implied volatility surface: an image-based approach” by Jinting Yang, Wenjing Xia and Wuyi Ye, uses a convolutional neural network (CNN) to establish a direct link between the implied volatility surface (IVS) of an asset’s return and its future realized volatility. Moreover, the forecasts generated by the CNN model, designated the CNN-IVS factor, are integrated into a heterogeneous autoregressive model of realized volatility (HAR-RV) framework. Yang et al show that integrating CNN into an HAR model of realized volatility results in additional explanatory power relative to the baseline HAR. They also show that the CNN-IVS approach leads to strong out-of-sample performance while extracting predictive information from the IVS, capturing economically meaningful signals relating to jump risk and downside risk, and providing unique incremental information for volatility forecasting.

The second paper in the issue, “Pricing kernel monotonicity and the conservativeness of risk-neutral forecasts” by Mamiko Yamashita, shows that when the pricing kernel is weakly decreasing in the terminal payoff, the real-world distribution dominates the risk-neutral one first-order stochastically, implying that the risk-neutral forecast is more conservative. However, the reverse is true when the pricing kernel is weakly decreasing in the terminal payoff, suggesting that the risk-neutral forecasts are more optimistic. Yamashita derives sufficient conditions for monotonicity in a consumption-based model and argues that when dominance holds, risk-neutral VaR, expected shortfall and Foster–Hart risk measures are conservative.

In our third paper, “Convex combination optimal reinsurance with multiple reinsurers and heterogeneous beliefs”, Yanhong Chen studies an optimal reinsurance problem for one insurer with multiple reinsurers. Chen accounts for heterogeneous beliefs about the probability distribution of losses and aims to optimize a weighted sum of risk measures. The author establishes conditions under which the optimal convex combination of reinsurance policies is also Pareto-optimal. Chen also offers explicit solutions for the VaR measure and the expected value premium principle, and illustrates the impact of heterogeneous beliefs on the optimal reinsurance policies.

Finally, in “A generic nonparametric value-at-risk estimator for high dimensions”, the issue’s fourth paper, Siyuan Sun presents a fast nonparametric VaR algorithm that works for a large number of underlying positions (or a high-dimensional multiasset scenario) and that makes use of the market value of a financial instrument and its recent volatility behavior. The algorithm scales linearly in the number of instruments and is shown to perform well on a portfolio of futures contracts.