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Derivatives and Financial Engineering
Asset Pricing
Financial Econometrics
Empirical Finance

Derivatives and Financial Engineering
Investment
Asset Pricing
Empirical Finance
Econometrics

Finance and Econometrics, 2003
Microeconomic Theory and Macroeconomic Theory, 2001

Option Pricing Puzzles

Professor Jonathan E. Ingersoll, Jr.
Professor Zhiwu Chen
Professor Charles Q. Cao

May 2006

Ph.D. in Financial Economics, Yale University, May 2006, expected
M.Phil. and M.A. in Financial Economics, Yale University, 2004
M.A. in Finance and International Economics and minor in Probability and Statistics, Wuhan University, 1997
B.S. in Sports Management, with honors, Wuhan Institute of Physical Education, 1994

Yale University Graduate Dissertation Fellowship, 2004–2005
Yale University Summer Research Fund, 2003
Cowles Foundation Fellowship, 2000–2004
Yale University Fan’s Fellowship, 2000–2004

Undergraduate Level
  Teaching Assistant, Econometrics, Yale University, 2004
  Teaching Assistant, Finance, Yale University, 2003
Graduate Level
  Teaching Assistant, Econometrics, Yale University, 2002
  Instructor, Time Series Analysis, Guanghua SOM, Peking University, 2000
  Instructor, Econometrics of Financial Economics, Guanghua SOM, Peking University, 1999
  Instructor, Microeconomic Analysis, Guanghua SOM, Peking University, 1999

Programming: C++, Matlab, SAS
Financial Databases: OptionMetrics and Berkeley options data, Compustat, CRSP, I/B/E/S, individual stock/option trading data

Professor Jonathan E. Ingersoll, Jr.
Adrian C. Israel Professor of International Trade
  and Finance
School of Management
Yale University
PO Box 208200
New Haven, CT 06520-8200
Phone: (203) 432-5924
Fax: (203) 432-8931
Email: jonathan.ingersoll@yale.edu

Charles Q. Cao
David McKinley Professor of Business Administration
  and Professor of Finance
The Smeal College of Business
The Pennsylvania State University
University Park, PA 16802
Phone: (814) 865-7891
Fax: (814) 865-3362
Email: charles@loki.smeal.psu.edu

Professor Zhiwu Chen
Professor of Finance
School of Management
Yale University
PO Box 208200
New Haven, CT 06520-8200
Phone: (203) 432-5948
Fax: (203) 432-6970
Email: zhiwu.chen@yale.edu

My dissertation consists of three studies in financial economics. The first chapter formulates a new option pricing model to explain the volatility puzzle and the skewness puzzle. This paper also proposes a more accurate method to estimate the latent variable model. The second chapter shows that individual option traders perform better than the market and individual stock traders. Furthermore, the paper demonstrates that the excess trading profits are more likely due to inside information. The third chapter in my dissertation tests whether financial constraints are quantitatively important in explaining the cross-sectional behavior of expected returns in both aggregate level and firm level.

Chapter 1: Option Pricing Puzzles

There are two challenges in option literature. One is to find a model to fit option and stock prices and solve the option pricing puzzles. The other is to estimate latent variable models with unobservable volatility.

Since the innovation of the Black–Scholes model in 1973, researchers have found many option pricing puzzles, in particular, the volatility puzzle and the skewness puzzle. These puzzles exist extensively, not only in stock or stock index options, but also in currency options and interest rate options. Many factors such as stochastic volatility, stochastic interest rate, jumps in returns, nonlinear factors, or multi-factor volatility have been introduced into models to solve these puzzles, but contradictory findings have yielded no conclusions.

This paper first uncovers the vital yet understudied role of jumps in volatility in pricing options and stocks. Previous literature shows that though stochastic volatility and jumps in returns improve the fit of options data, the models based on both factors are still misspecified. The most biased parameter is the volatility of volatility, which is biased upward to match high kurtosis and skewness of the volatility process. This paper shows that introducing jumps in volatility can significantly reduce the bias. Jumps in volatility, stochastic volatility, and jumps in returns are all indispensable factors in determining S&P 500 index returns and option prices. All three of the above factors are incorporated into the double jump model and can explain the option pricing puzzles with reasonable risk premiums. In-sample and out-of-sample options pricing errors from the double jump model are less than the bid-ask spreads and much smaller than those from the commonly used models. The absolute pricing errors are more than 80%, 60% and 40% less than these from the Black-Scholes model, the stochastic volatility model, and the stochastic volatility model with jumps in returns, respectively.

One challenge to estimate option pricing models is that volatilities are not directly observable. Current literature often uses implied volatilities as a proxy of the latent volatilities. However, implied volatilities can be very different from instantaneous volatility defined in the models. For example, implied volatility often increases when there is an earning announcement in two weeks but instantaneous volatility does not necessarily increase. This paper develops a new way to estimate the latent volatility model without need to use the proxy. The volatility is directly deduced and endogenously consistent with the models. I construct an MLE method, which is more efficient than the GMM method currently used in the literature. The most challenging part is to calculate the likelihood function conditional upon past history of stock returns. This paper gets the closed-form solution of the likelihood function. Simulation tests show that this estimation method is very accurate and generates much smaller estimation errors than other methods.

Chapter 2: Can Individual Investors Beat the Market: Answer from the Option Market? (Joint with Charles Cao and Ning Zhu)

Current literature generally agrees individual investors cannot consistently beat the market. However all the results are only based on individual equity trading data. If investors have inside information or superior investment skills, they tend to realize advantageous information/skills through options markets rather than equity markets because of leverage in options markets. Particularly, individual investors are more likely to be constrained by limited investment money so that those with profitable information/skills should be more inclined to invest in options markets.

Using the individual investors’ trading record coming from a large discount brokerage firm between January, 1991 and November, 1996, this paper is the first paper to show that individual option investors perform much better than the stock index and individual nonoption traders. The value-weighted raw and net daily option trading returns are 88 and 46 basis points, respectively. These are more than 10 times higher than returns that individuals attain by investing in the equity market. Furthermore, the higher option trading returns are not due to higher risk in options market. While the standard deviation of the delta-adjusted option returns is a little less than that of the equity index return, the delta-adjusted option trading returns are 40% higher than the equity index return. We also show that the underlying stocks are not confined to the well-known profitable strategies such as size, value, or momentum strategies.

To understand why individual option traders achieve better than the market and other individual traders and whether the excess trading profits are due to inside information, we further test 1) whether option traders have same equity trading skills as nonoption traders; 2) whether those profitable option transactions are highly related to corporate events; 3) whether naked option trades (i.e., without hedging with underlying stocks or options) earn higher than nonnaked option trades; 4) whether the stocks underlying to the naked option trades perform better than other stocks. The answers to above questions are all YES. We are inclined to conclude individual option investors trade on inside information.

Chapter 3: Asset Pricing and Financing Constraints: A Firm-level Study

Based on evidence from the aggregate-level study from the manufacturing firms, current literature generally concludes that financial constraint is not a risk factor in determining expected returns. However, non-financially-constrained firms make up more than 90% of the sample. The conclusion from the aggregate-level studies is overwhelmed by the nonfinancially-constrained firms. This paper improves the existing research on financial constraints and proposes a new approach to test the hypothesis in both aggregate and the firm level.

This paper first builds up a production-based dynamic asset pricing model by maximizing the firm’s profit over time subject to external financing constraints. The investment return discounted by the market stochastic discount factor is equal to one. The financial constraint is captured by the shadow price of dividends. Then, all the manufacturing firms are grouped into financially-constrained and non-financially-constrained firms according to the Kaplan and Zingales (1997) index. I construct the aggregate investment rate, the financially-constrained investment rate, and the non-financially-constrained investment rate. Using GMM, I find that although financing frictions do not significantly affect the cross-sectional returns in the aggregate level, at the firm level, financing frictions significantly influence the cross-sectional returns for financially-constrained firms.