State price density estimation with an application to the recovery theorem

This article introduces a model to estimate the risk-neutral density of stock prices derived from option prices. To estimate a complete risk-neutral density, current estimation techniques use a single mathematical model to interpolate option prices on two dimensions: strike price and time-to-maturity. Instead, this model uses B-splines with at-the-money knots for the strike price interpolation and a mixed lognormal function that depends on the option expiration horizon for the time-to-maturity interpolation. The results of this “hybrid” methodology are significantly better than other risk-neutral density extrapolation methods when applied to the recovery theorem.

A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps

Estimates of risk-neutral densities of future asset returns have been commonly used for pricing new financial derivatives, detecting profitable opportunities, and measuring central bank policy impacts. We develop a new nonparametric approach for estimating the risk-neutral density of asset prices and reformulate its estimation into a double-constrained optimization problem. We evaluate our approach using the S&P 500 market option prices from 1996 to 2015. A comprehensive cross-validation study shows that our approach outperforms the existing nonparametric quartic B-spline and cubic spline methods, as well as the parametric method based on the normal inverse Gaussian distribution. As an application, we use the proposed density estimator to price long-term variance swaps, and the model-implied prices match reasonably well with those of the variance future downloaded from the Chicago Board Options Exchange website.

The role of an option-implied distribution in improving an asset allocation model

The objective of this paper is to extend the information embedded in option-implied distribution to asset allocation model. This paper examines whether a parameter estimated from an option-implied distribution can improve a minimum-variance portfolio which consists of many risky assets. The option-implied distribution under a risk-neutral assumption is called risk-neutral density (RND) whereas a risk-world density (RWD) is calculated by incorporating a risk-premium. The computation of option-implied distributions is based on the Dow Jones Industrial Average (DJIA) index options and its constituents. The data covers the period from January 2009 until December 2015. Portfolio performance is evaluated based on portfolio volatility and Sharpe ratio. The performance of a portfolio based on an option-implied distribution is compared to a naive diversification portfolio. The empirical evidence shows that for a portfolio based on an option-implied distribution, the volatility of the portfolio is reduced and the Sharpe ratio is increased.

The impact of monetary policy on option-implied stock market expectations

Purpose The purpose of this paper is to investigate the impact of Federal Open Market Committee (FOMC) meetings and the changes of the target rates on stock market uncertainty. Design/methodology/approach Multivariate regression analysis is applied to the historical data of VIX, FOMC meetings and target rates. Subtle relations are revealed by further categorizing the FOMC meetings into being scheduled and unscheduled and distinguishing the signs of the changes in VIX and target rates. CPI and the prime rate are used for robustness test. Findings The authors first examine the relation between FOMC meetings and target surprises; the results indicate that unscheduled FOMC meetings heavily impact the target surprises. Then, the authors investigate the relation between FOMC meetings and VIX changes; the results show that both unscheduled and scheduled FOMC meetings impact VIX, where the impacts of scheduled FOMC meetings are more substantial. The authors also analyze the responses of VIX to the target surprises, and the results reveal that there is an asymmetric effect of target surprises on VIX, where the influences of the scheduled positive target surprises are more significant. Finally, by examining the relation between the FOMC meeting and the risk-neutral density of the VIX option, the authors conclude that both KURT and SKEW are more affected by unscheduled FOMC meetings. Originality/value Deeper dimensions of the relations between VIX, FOMC meetings and target rates are analyzed and more insightful understandings of such relations are gained.