Mutual fund performance: false discoveries, bias, and power

We analyze the performance of mutual funds from a multiple inference perspective. When the number of funds is large, random fluctuations will cause some funds falsely to appear to outperform the rest. To account for such “false discoveries,” a multiple inference approach is necessary. Performance evaluation measures are unlikely to be independent across mutual funds. At the same time, the data are typically not sufficient to estimate the dependence structure of performance measures. In addition, the performance evaluation model can be misspecified. We contribute to the existing literature by applying an empirical Bayes approach that offers a possible way to take these factors into account. We also look into the question of statistical power of the performance evaluation model, which has received little attention in mutual fund studies. We find that the assumption of independence of performance evaluation measures results in significant bias, such as over-estimating the number of outperforming mutual funds. Adjusting for the mutual fund investment objective is helpful, but it still does not result in the discovery of a significant number of successful funds. A detailed analysis reveals a very low power of the study. Even if outperformers are present in the sample, they might not be recognized as such and/or too many years of data might be required to single them out.     

Estimation and pricing under long-memory stochastic volatility

We treat the problem of option pricing under a stochastic volatility model that exhibits long-range dependence. We model the price process as a Geometric Brownian Motion with volatility evolving as a fractional Ornstein–Uhlenbeck process. We assume that the model has long-memory, thus the memory parameter H in the volatility is greater than 0.5. Although the price process evolves in continuous time, the reality is that observations can only be collected in discrete time. Using historical stock price information we adapt an interacting particle stochastic filtering algorithm to estimate the stochastic volatility empirical distribution. In order to deal with the pricing problem we construct a multinomial recombining tree using sampled values of the volatility from the stochastic volatility empirical measure. Moreover, we describe how to estimate the parameters of our model, including the long-memory parameter of the fractional Brownian motion that drives the volatility process using an implied method. Finally, we compute option prices on the S&P 500 index and we compare our estimated prices with the market option prices.     

Option pricing under a Gamma-modulated diffusion process

We study a Gamma-modulated diffusion process as a long-memory generalization of the standard Black-Scholes model. This model introduces a time dependent volatility. The option pricing problem associated with this type of processes is computed.     

Portfolio optimization in discrete time with proportional transaction costs under stochastic volatility

This paper is devoted to evaluating the optimal self-financing strategy and the optimal trading frequency for a portfolio with a risky asset and a risk-free asset. The objective is to maximize the expected future utility of the terminal wealth in a stochastic volatility setting, when transaction costs are incurred at each discrete trading time. A HARA utility function is used, allowing a simple approximation of the optimization problem, which is implementable forward in time. For each of various transaction cost rates, we find the optimal trading frequency, i.e. the one that attains the maximum of the expected utility at time zero. We study the relation between transaction cost rate and optimal trading frequency. The numerical method used is based on a stochastic volatility particle filtering algorithm, combined with a Monte-Carlo method. The filtering algorithm updates the estimate of the volatility distribution forward in time, as new stock observations arrive; these updates are used at each of these discrete times to compute the new portfolio allocation.     

Symposium on stochastic volatility: an introductory overview

We describe the context and summarize the contents of the ten contributions to the Symposium on Stochastic Volatility. These articles concentrate mainly on questions pertaining to option pricing under various uncertainty assumptions about market volatility. Tools from stochastic analysis and statistical inference are used to present solutions via explicit computations or numerical methods, with model estimation and calibration based on market and simulated data.     

Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria

In this paper, an ambiguity-averse insurer (AAI) whose surplus process is approximated by a Brownian motion with drift, hopes to manage risk by both investing in a Black–Scholes financial market and transferring some risk to a reinsurer, but worries about uncertainty in model parameters. She chooses to find investment and reinsurance strategies that are robust with respect to this uncertainty, and to optimize her decisions in a mean-variance framework. By the stochastic dynamic programming approach, we derive closed-form expressions for a robust optimal benchmark strategy and its corresponding value function, in the sense of viscosity solutions, which allows us to find a mean-variance efficient strategy and the efficient frontier. Furthermore, economic implications are analyzed via numerical examples. In particular, our conclusion in the mean-variance framework differs qualitatively, for certain parameter ranges, with model-uncertainty robustness conclusions in the framework of utility functions: model uncertainty does not always result in an agent deciding to reduce risk exposure under mean-variance criteria, opposite to the conclusions for utility functions in Maenhout and Liu. Our conclusion can be interpreted as saying that the mean-variance problem for the AAI explains certain counter-intuitive investor behaviors, by which the attitude to risk exposure, for an AAI facing model uncertainty, depends on positive past experience.