Option Coskewness and Capital Asset Pricing

This article shows how the market coskewness model of Rubinstein(1973) and Kraus and Litzenberger (1976) is altered when a nonredundantcall option is optimally traded. Owing to the option’snonredundancy, the economy’s stochastic discount factor(SDF) depends not only on the market return and the square ofthe market return but also on the option return, the squareof the option return, and the product of the market and optionreturns. This leads to an asset pricing model in which the expectedreturn on any risky asset depends explicitly on the asset’scoskewness with option returns. The empirical results show thatthe option coskewness model outperforms several competing benchmarkmodels. Furthermore, option coskewness captures some of thesame risks as the Fama–French factors small minus big(SMB) and high minus low (HML). These results suggest that thefactors that drive the pricing of nonredundant options are alsoimportant for pricing risky equities.(JEL G11, G12, D61)     

Approximation and Calibration of Short-Term Implied Volatilities Under Jump-Diffusion Stochastic Volatility

We derive an asymptotic expansion formula for option impliedvolatility under a two-factor jump-diffusion stochastic volatilitymodel when time-to-maturity is small. We further propose a simplecalibration procedure of an arbitrary parametric model to short-termnear-the-money implied volatilities. An important advantageof our approximation is that it is free of the unobserved spotvolatility. Therefore, the model can be calibrated on optiondata pooled across different calendar dates to extract informationfrom the dynamics of the implied volatility smile. An exampleof calibration to a sample of S&P 500 option prices is provided.(JEL G12)     

The Book-to-Market and Size Effects in a General Asset Pricing Model: Evidence from Seven National Markets

The positive relation of returns with Book-to-Market ratio (BE/ME)and their negative relation withMarket Value(MVE) remains strongunder a general stochastic discount function (SDF) that doesnot depend on a specific asset pricing model and avoids potentiallyserious simultaneity biases inherent in the Fama and Frenchthree-factor model. However, we find that SDF_s that includethe equivalent of the HML portfolio do not span all asset sub-spaces,even with additional conditioning information. Finally, macroand financial variables we introduce to the pricing functionsdo not offer an alternative explanation of the BE/ME effect.JEL Classification codes: G10, G12, G15, G30.     

A closed-form GARCH option valuation model

This paper develops a closed-form option valuation formula fora spot asset whose variance follows a GARCH(p, q) process thatcan be correlated with the returns of the spot asset. It providesthe first readily computed option formula for a random volatilitymodel that can be estimated and implemented solely on the basisof observables. The single lag version of this model containsHeston's (1993) stochastic volatility model as a continuous-timelimit. Empirical analysis on S&P500 index options showsthat the out-of-sample valuation errors from the single lagversion of the GARCH model are substantially lower than thead hoc Black-Scholes model of Dumas, Fleming and Whaley (1998)that uses a separate implied volatility for each option to fitto the smirk/smile in implied volatilities. The GARCH modelremains superior even though the parameters of the GARCH modelare held constant and volatility is filtered from the historyof asset prices while the ad hoc Black-Scholes model is updatedevery period. The improvement is largely due to the abilityof the GARCH model to simultaneously capture the correlationof volatility, with spot returns and the path dependence involatility.     

The smirk in the S&P500 futures options prices: a linearized factor analysis

In the S&P500 futures options, we identify three factors, corresponding to movements in the underlying, parallel movements, and tilting of the cross section of implied volatilities (the “smirk factor”). We relate these factors non-linearly to movements in the option prices. They seem to be diffusive in nature, have significant associated risk premia, and can account for an overwhelming part of the option price movements. We interpret the options smirk, which is the notion that out-of-the-money (OTM) puts seem expensive relative to OTM calls, in terms of the prices of these risk factors. Going short OTM puts and long OTM calls, corresponding to the third factor, makes a profit on average, but this corresponds to its risk premium, and does not represent a market inefficiency. Our smirk factor is useful for hedging option portfolios, but seems unrelated to movements in the underlying, and does not fit into the framework of the jump-diffusion models.      

Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978

The tests reported here differ in several ways from those of most other papers testing option pricing models: an extremely large sample of observations of both trades and bid-ask quotes is examined, careful consideration is given to discarding misleading records, nonparametric rather than parametric statistical tests are used, reported results are not sensitive to measurement of stock volatility, special care is taken to incorporate the effects of dividends and early exercise, a simple method is developed to test several option pricing formulas simultaneously, and the statistical significance and consistency across subsamples of the most important reported results are unusually high. The three key results are: (1) short-maturity out-of-the-money calls are priced significantly higher relative to other calls than the Black-Scholes model would predict, (2) striking price biases relative to the Black-Scholes model are also statistically significant but have reversed themselves after long periods of time, and (3) no single option pricing model currently developed seems likely to explain this reversal.     

An empirical comparison of GARCH option pricing models

Recent empirical studies have shown that GARCH models can be successfully used to describe option prices. Pricing such contracts requires knowledge of the risk neutral cumulative return distribution. Since the analytical forms of these distributions are generally unknown, computationally intensive numerical schemes are required for pricing to proceed. Heston and Nandi (2000) consider a particular GARCH structure that permits analytical solutions for pricing European options and they provide empirical support for their model. The analytical tractability comes at a potential cost of realism in the underlying GARCH dynamics. In particular, their model falls in the affine family, whereas most GARCH models that have been examined fall in the non-affine family. This article takes a closer look at this model with the objective of establishing whether there is a cost to restricting focus to models in the affine family. We confirm Heston and Nandi's findings, namely that their model can explain a significant portion of the volatility smile. However, we show that a simple non affine NGARCH option model is superior in removing biases from pricing residuals for all moneyness and maturity categories especially for out-the-money contracts. The implications of this finding are examined. JEL Classification G13     

Stock Return Predictability: Is it There?

We examine the predictive power of the dividend yields for forecastingexcess returns, cash flows, and interest rates. Dividend yieldspredict excess returns only at short horizons together withthe short rate and do not have any long-horizon predictive power.At short horizons, the short rate strongly negatively predictsreturns. These results are robust in international data andare not due to lack of power. A present value model that matchesthe data shows that discount rate and short rate movements playa large role in explaining the variation in dividend yields.Finally, we find that earnings yields significantly predictfuture cash flows. (JEL C12, C51, C52, E49, F30, G12)     

Portfolio Selection in Stochastic Environments

In this article, I explicitly solve dynamic portfolio choiceproblems, up to the solution of an ordinary differential equation(ODE), when the asset returns are quadratic and the agent hasa constant relative risk aversion (CRRA) coefficient. My solutionincludes as special cases many existing explicit solutions ofdynamic portfolio choice problems. I also present three applicationsthat are not in the literature. Application 1 is the bond portfolioselection problem when bond returns are described by "quadraticterm structure models." Application 2 is the stock portfolioselection problem when stock return volatility is stochasticas in Heston model. Application 3 is a bond and stock portfolioselection problem when the interest rate is stochastic and stockreturns display stochastic volatility. (JEL G11)     

Pricing Interest Rate Derivatives: A General Approach

The relationship between affine stochastic processes and bondpricing equations in exponential term structure models has beenwell established. We connect this result to the pricing of interestrate derivatives. If the term structure model is exponentialaffine, then there is a linkage between the bond pricing solutionand the prices of many widely traded interest rate derivativesecurities. Our results apply to m-factor processes with n diffusionsand l jump processes. The pricing solutions require at mosta single numerical integral, making the model easy to implement.We discuss many options that yield solutions using the methodsof the article.     

The benefits of option use by mutual funds

Based on comprehensive regulatory data on equity mutual fund option use from the SEC's N-SAR filings, we are the first to present consistent evidence that equity funds' option use generates higher risk-adjusted performance. We further show that this is a direct effect of option use and not an indirect effect of other fund characteristics. Option use also directly results in lower systematic risk, as funds show significantly lower market betas during periods of options usage. Finally, mutual funds use options mainly for hedging as they primarily use protective puts and covered calls. These results are independent of known phenomena, such as the low beta anomaly, and robust to tests for endogeneity and a novel 5-factor model including an investable option strategy factor (IOS). Overall, our findings show that mutual fund option use is beneficial to investors and does not pose risk to the financial system as feared by the SEC. Our results are thus important for investors as well as regulators.     

Consumer Confidence and Asset Prices: Some Empirical Evidence

We explore the time-series relationship between investor sentimentand the small-stock premium using consumer confidence as a measureof investor optimism. We estimate the components of consumerconfidence related to economic fundamentals and investor sentiment.After controlling for the time variation of beta, we study thetime-series variation of the pricing error with sentiment. Overthe last 25 years, investor sentiment measured using consumerconfidence forecasts the returns of small stocks and stockswith low institutional ownership in a manner consistent withthe predictions of models based on noise-trader sentiment. Sentimentdoes not appear to forecast time-series variation in the valueand momentum premiums. (JEL G10, G12, G14)     

Option Prices Under Generalized Pricing Kernels

In this paper analytical solutions for European option prices are derived for a class of rather general asset specific pricing kernels (ASPKs) and distributions of the underlying asset. Special cases include underlying assets that are lognormally or log-gamma distributed at expiration date T. These special cases are generalizations of the Black and Scholes (1973) option pricing formula and the Heston (1993) option pricing formula for non-constant elasticity of the ASPK. Analytical solutions for a normally distributed and a uniformly distributed underlying are also derived for the class of general ASPKs. The shape of the implied volatility is analyzed to provide further understanding of the relationship between the shape of the ASPK, the underlying subjective distribution and option prices. The properties of this class of ASPKs are also compared to approaches used in previous empirical studies. JEL Classification: G12, G13, C65 Erik Lüders is an assistant professor at Laval University and a visiting scholar at the Stern School of Business, New York University.     

Singular risk-neutral valuation equations

Many risk-neutral pricing problems proposed in the finance literature do not admit closed-form expressions and have to be dealt with by solving the corresponding partial integro-differential equation. Often, these PIDEs have singular diffusion matrices and coefficients that are not Lipschitz-continuous up to the boundary. In addition, in general, boundary conditions are not specified. In this paper, we prove existence and uniqueness of (continuous) viscosity solutions for linear PIDEs with all the above features, under a Lyapunov-type condition. Our results apply to European and Asian option pricing, in jump-diffusion stochastic volatility and path-dependent volatility models. We verify our Lyapunov-type condition in several examples, including the arithmetic Asian option in the Heston model.     

Good Stewards, Cheap Talkers, or Family Men? The Impact of Mutual Fund Closures on Fund Managers, Flows, Fees, and Performance

We examine a sample of 125 equity mutual funds that closed tonew investment between 1993 and 2004. We find that funds closefollowing a period of superior performance and abnormal fundinflows. Fund managers raise their fees when they close to compensatemanagers for losses in income due to the restrictions in sizeimposed by the fund closure decision. Managers reopen when fundsize declines. However, they do not earn superior returns afterreopening, suggesting that the fund closure decision does notprovide information about superior fund managers. (JEL G14,G23)     

Price Informativeness and Investment Sensitivity to Stock Price

The article shows that two measures of the amount of privateinformation in stock price—price nonsynchronicity andprobability of informed trading (PIN)—have a strong positiveeffect on the sensitivity of corporate investment to stock price.Moreover, the effect is robust to the inclusion of controlsfor managerial information and for other information-relatedvariables. The results suggest that firm managers learn fromthe private information in stock price about their own firms’fundamentals and incorporate this information in the corporateinvestment decisions. We relate our findings to an alternativeexplanation for the investment-to-price sensitivity, namelythat it is generated by capital constraints, and show that boththe learning channel and the alternative channel contributeto this sensitivity. (JEL G14, G31)     

Transactions Accounts and Loan Monitoring

We show that transactions accounts, by providing ongoing dataon borrowers’ activities, help financial intermediariesmonitor borrowers. This information is most readily availableto commercial banks, which offer these accounts and lendingtogether. We find that (1) monthly changes in accounts receivableare reflected in transactions accounts; (2) borrowings in excessof collateral predict credit downgrades and loan write-downs;and (3) the lender intensifies monitoring in response. Thisis evidence on a key issue in financial intermediation—thereis an advantage to providing deposit-taking and lending jointly.But this advantage may have fallen as the cost of communicationhas declined. (JEL G10, G20, G21)     

Options on Leveraged Equity: Theory and Empirical Tests

We develop an option pricing model for calls and puts written on leveraged equity in an economy with corporate taxes and bankruptcy costs. The model explains implied Black-Scholes volatility biases by relating them to the firm's structural characteristics such as leverage and debt covenants. We test the model by comparing predicted pricing biases with biases observed in a large cross-section of firms with liquid exchange traded option contracts. Our empirical study detects leverage related pricing biases. The magnitudes of these biases correspond to those predicted by our model. We also find significant pricing biases for firms financed primarily by short-term debt. This supports our model because short-term debt introduces net-worth hurdles similar to net-worth covenants.     

DIVIDENDS, DIVIDEND POLICY AND OPTION VALUATION: A NEW PERSPECTIVE

This paper develops a model which explicitly incorporates the impact of the payment of dividends on the underlying stock into the valuation of both American and European calls and puts. Unlike earlier models, what we call the Dividend Adjustment Merton (DAM) model neither assumes arbitrary continuous dividends nor uses ad hoc methods to adjust for discrete dividend payments. Instead, it assumes the existence of a Miller and Modigliani (1961) valuation neutral dividend policy and adjusts Merton's constant proportional dividend model to incorporate any known schedule of discrete cash dividends of this type. The DAM model produces results which are equal to or superior to those of the separate models now used to value American calls (the Roll-Geske-Whaley model) and American puts (the Geske-Johnson model) on dividend paying stocks. It has the virtue of being internally consistent in that the same model can be used to value both calls and puts. In developing the DAM model, the paper clarifies the role of dividends and dividend policy in determining option values. It also produces significantly tightened boundary conditions for option values.     

Pricing and hedging American options: a recursive investigation method

In this article we present a new method for pricing and hedgingAmerican options along with an efficient implementation procedure.The proposed method is efficient and accurate in computing bothoption values and various option hedge parameters. We demonstratethe computational accuracy and efficiency of this numericalprocedure in relation to other competing approaches. We alsosuggest how the method can be applied to the case of any Americanoption for which a closed-form solution exists for the correspondingEuropean options.