George J. Jiang

Estimation of Continuous-Time Processes via the Empirical Characteristic Function

This article examines the class of continuous-time stochastic processes commonly known as affine diffusions (ADs) and affine jump diffusions (AJDs). By deriving the joint characteristic function, we are able to examine the statistical properties as well as develop an efficient estimation technique based on empirical characteristic functions (ECFs) and a generalized method of moments (GMM) estimation procedure based on exact moment conditions. We demonstrate that our methods are particularly useful when the diffusions involve latent variables. Our approach is illustrated with a detailed examination of a continuous-time stochastic volatility (SV) model, along with an empirical application using S&P 500 index returns.

Extracting Model-Free Volatility from Option Prices

The CBOEs VIX index is a measure of the implied volatility (IV) in 30-day stock index options. Originally constructed as a weighted average of Black-Scholes IVs from 8 at the money calls and puts, the VIX was redesigned in 2003. The new VIX uses a nonparametric procedure to extract an IV from out of the money calls and puts over the full range of strikes. Implementation of the theoretical procedure, however, requires several approximations, for example to deal with the fact that only a discrete set of strikes are traded in the market, rather than a continuum over the full range from zero to infinity, as required by the theory. In this article, Jiang and Tian look carefully at the new VIX algorithm to assess the impact of these approximations on its accuracy. They find that some of them may produce substantial errors, even in simply recovering the volatility input from a set of options in a pure Black-Scholes world. They then propose a modified calculation technique using a smoothing algorithm, that can almost entirely eliminate the errors.

Finite Sample Comparison of Alternative Estimators of Itô Diffusion Processes -- A Monte Carlo Study

In this paper, we consider alternative approaches to the estimation of Itˆo diffusion processes from discretely sampled observations. Based on Monte Carlo simulation, we investigate the finite sample properties of various estimators and in particular compare the performance of the nonparametric estimators proposed in Jiang and Knight (1997) with common parametric estimators, namely the ML, NLS (or OLS), and GMM estimators. The simulation results show that, with certain large samples over a short sampling period, both the nonparametric diffusion and drift estimators perform reasonably well. However, while all the parametric diffusion estimators perform very well, the parametric drift estimators perform very poorly.

Valuing Illiquid Common Stock

Illiquid common stock is worth less than stock that can be readily sold because the investor incurs an opportunity cost by being locked into the investment. Quantifying the amount of this illiquidity discount is an important issue in valuing certain common stock, especially for estate valuations. We examine whether a previously developed analytical model for valuing the lost “option to sell” when a stock is illiquid is a useful, practical tool for valuing illiquid common stock. The value of an illiquid asset is generally lower than that of a similar asset that is readily marketable. Investors value liquidity because its absence limits the owner’s option to convert the asset to cash; thus, illiquidity increases potential opportunity costs. Investors locked into a holding of nonmarketable stock are subject to losses resulting from changing stock prices. Valuations of illiquid stock are required for estate valuations for tax purposes, merger and acquisition transactions, divorce settlements and other forms of partnership dissolutions, and situations in which the valuation has important financial consequences for the parties involved. Therefore, valuing illiquid stock can be a contentious issue, and it frequently involves large amounts of money. We examine the usefulness of an options-based framework developed in 1995 to estimate the value of the marketability (i.e., liquidity) of a particular common stock for a particular investor at a particular time. This model explicitly takes into account the put option inherent in a liquid asset. It requires two inputs—namely, the volatility of the shares’ returns and the length of time for which the shares are illiquid. We first report cross-sectional variations in volatility for NYSE and NASDAQ stocks. We then apply the model in an actual case study to assess the extent to which the illiquidity discount for a specific stock holding depends on the volatility of the company’s stock and on other characteristics of the case. We conclude that the model provides a more analytical approach to determining discounts than do current practices but that there is still a role for judgment in determining the appropriate discount in a specific case.

Nonparametric Estimation of the Short Rate Diffusion Process from a Panel of Yields

In this paper, we propose a nonparametric estimator of the short rate diffusion process using observations of a panel of yields. The proposed estimator can greatly reduce the bias of the nonparametric estimator proposed in Stanton (1997) that uses a single time series of short rate observations. Simulations confirm that the new method significantly attenuates the spurious nonlinearity of the drift function as documented in Chapman and Pearson (2000). We apply the method to estimate the U.S. short rate process using a panel of six Treasury yields. With 42 years’ daily observations of the panel of yields, the proposed drift function estimator achieves the same efficiency as the Stanton (1997) estimator based on 145 years of daily short rate observations. Finally, we show that the proposed estimator also has significant economic implications on the pricing of bonds and interest rate derivatives.

Dissecting the Idiosyncratic Volatility Anomaly

The idiosyncratic volatility anomaly, as first documented in Ang, Hodrick, Xing, and Zhang (2006), has received considerable attention in the literature. In this paper, we examine the pervasiveness of the anomaly in various stock samples and provide evidence towards distinguishing potential explanations. Our results show that the idiosyncratic volatility anomaly is a common stock phenomenon. It is rather robust once we exclude microcaps, as defined in Fama and French (2008), or penny stocks (with prices below

Momentum strategies for style and sector indexes

5), or the month of January, corroborating the findings in Doran, Jiang, and Peterson (2010). In addition, we show that the idiosyncratic volatility anomaly is not due to the market microstructure effect and cannot be explained by short-term stock return reversal.

ECF Estimation of Markov Models Where the Transition Density is Unknown

The existing literature shows that cross-sectional stock returns exhibit both price momentum and earnings momentum. In this paper, we examine whether commonly used style and sector indexes also have momentum patterns. We show that style indexes exhibit strong price momentum, but give little evidence of earnings momentum. On the other hand, sector indexes exhibit both significant price momentum and earnings momentum. Moreover, we provide evidence that price momentum in style indexes can be explained by individual stock return momentum, whereas price momentum in sector indexes is driven by earnings momentum. Finally, we show that a dynamic momentum strategy can further enhance the performance of style investment even after adjusting for transaction costs.

Forecasting Volatility Using Long Memory and Comovements: An Application to Option Valuation under SFAS 123R

In this paper, we consider the estimation of Markov models where the transition density is unknown. The approach we propose is based on the empirical characteristic function estimation procedure with an approximate optimal weight function. The approximate optimal weight function is obtained through an EdgeworthsGram--Charlier expansion of the logarithmic transition density of the Markov process. We derive the estimating equations and demonstrate that they are similar to the approximate maximum likelihood estimation (AMLE). However, in contrast to the conventional AMLE our approach ensures the consistency of the estimator even with the approximate likelihood function. We illustrate our approach with examples of various Markov processes. Monte Carlo simulations are performed to investigate the finite sample properties of the proposed estimator in comparison with other methods. Copyright The Author(s). Journal compilation Royal Economic Society 2010.

The Shrinking Space for Anomalies

Horizon-matched historical volatility is commonly used to forecast future volatility for option valuation under the Statement of Financial Accounting Standards (SFAS) 123R. In this paper, we empirically investigate the performance of using historical volatility to forecast long-term stock return volatility in comparison with a number of alternative forecasting methods. In analyzing forecasting errors and their impact on reported income due to option expensing, we find that historical volatility is a poor forecast for long-term volatility and that shrinkage adjustment toward comparable-firm volatility only slightly improves its performance. Forecasting performance can be improved substantially by incorporating both long memory and comovements with common market factors. We also experiment with a simple mixed-horizon realized volatility model and find its long-term forecasting performance to be more accurate than historical forecasts but less accurate than long-memory forecasts.