Binomial Option Pricing with Skewed Asset Returns

This research presents a method for estimating the parameters of the binomial option pricing model necessary to appropriately price calls on assets with asymmetric end-of-period return distributions. Parameters of the binomial model are shown to be a function of the mean, variance, and skewness of the underlying return distribution. It is also shown that failure to incorporate skewness results in the mispricing of the call.     

Diagnosing Asset Pricing Models Using the Distribution of Asset Returns

This paper develops a set of diagnostic tests which can shed light on why a particular model is failing and indicate what steps might be taken to make the model consistent with asset returns. Theoretical bounds on the moments of a stochastic discount factor are derived as a function of the moments of observed asset returns. Particular attention is paid to restrictions on moments other than the variance. These bounds can also be used to measure the information about the distribution of the discount factor contained in the moments of various asset returns. As an application of this methodology, bounds on the discount factor are estimated using size-based portfolios, and the results are used to analyze the small firm effect. Empirical results indicate, for the period 1926–1975, that moments of the returns of small firms contain information about the discount factor that is not contained in the moments of the returns of large firms and/or a proxy of the aggregate wealth portfolio. However, this difference disappears when more recent data is included.     

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)     

Comparing Asset Pricing Models

A Bayesian asset pricing test is derived that is easily computed in closed form from the standard F‐statistic. Given a set of candidate traded factors, we develop a related test procedure that permits the computation of model probabilities for the collection of all possible pricing models that are based on subsets of the given factors. We find that the recent models of Hou, Xue, and Zhang (2015a, 2015b) and Fama and French (2015, 2016) are dominated by a variety of models that include a momentum factor, along with value and profitability factors that are updated monthly.     

Multifactor Asset Pricing Models

Since the early 1960s, the mean-variance Capital Asset Pricing Model (CAPM) has been a dominant paradigm in modern finance. Recently, the accumulation of anomalous evidence, and a realisation that empirical tests of the model are tautologically related to the efficiency of the market index, have pushed that paradigm to a point of crisis. This paper reviews alternative asset pricing models which coexisted with the CAPM and may provide plausible substitutes. The major distinguishing feature of these models is that they predict multiple risk factors and, with the exception of the Arbitrage Pricing Theory (APT), are extensions of the CAPM.     

The Valuation of Options When Asset Returns Are Generated by a Binomial Process

This paper values options on assets whose returns, over a finite interval of time, are generated by a binomial process. It shows that a simple valuation relationship, between the option and the underlying stock, obtains if investors have preference functions that belong to a particular class, even if opportunities to hedge do not exist. One particular application of the theory is in the case where the stock price over a finite interval could increase by an amount, fall by the same amount, or stay at the same level. The results in this paper may be viewed as the foundation of the preference-based approaches to obtaining a risk neutral valuation relationship.     

Investing for the Long Run when Returns Are Predictable

We examine how the evidence of predictability in asset returns affects optimal portfolio choice for investors with long horizons. Particular attention is paid to estimation risk, or uncertainty about the true values of model parameters. We find that even after incorporating parameter uncertainty, there is enough predictability in returns to make investors allocate substantially more to stocks, the longer their horizon. Moreover, the weak statistical significance of the evidence for predictability makes it important to take estimation risk into account; a long-horizon investor who ignores it may overallocate to stocks by a sizeable amount.     

On Comparing Asset Pricing Models

Revisiting the framework of (Barillas, Francisco, and Jay Shanken, 2018, Comparing asset pricing models, The Journal of Finance 73, 715–754). BS henceforth, we show that the Bayesian marginal likelihood-based model comparison method in that paper is unsound : the priors on the nuisance parameters across models must satisfy a change of variable property for densities that is violated by the Jeffreys priors used in the BS method. Extensive simulation exercises confirm that the BS method performs unsatisfactorily. We derive a new class of improper priors on the nuisance parameters, starting from a single improper prior, which leads to valid marginal likelihoods and model comparisons. The performance of our marginal likelihoods is significantly better, allowing for reliable Bayesian work on which factors are risk factors in asset pricing models.     

Factor Models for Option Pricing

Options on stocks are priced using information on index options and viewing stocks in a factor model as indirectly holding index risk. The method is particularly suited to developing quotations on stock options when these markets are relatively illiquid and one has a liquid index options market to judge the index risk. The pricing strategy is illustrated on IBM and Sony options viewed as holding SPX and Nikkei risk respectively.     

Some Tests of the Risk-Return Relationship Using Alternative Asset Pricing Models and Observed Expected Returns

This study examines the performance of three asset pricing models: the CAPM, the APT and the UAPT using observed expected returns from a three-phase dividend discount model with Value Line analyst estimates of future company-level earnings, dividends and growth rates. Our study is the first we know of to test the three major asset pricing models using observed expected returns. Our results are similar to prior research using ex post (realized) returns in that we find that the UAPT using macroeconomic factors is the best performing model, followed by the APT and the CAPM. However, our results also suggest that the importance of macroeconomic factors is much greater to expected returns than to realized returns, and the corresponding R2 values for models using expected returns are much higher than for models using realized returns. Combining our results for the UAPT with those of Marston and Harris (1993) for the CAPM suggests that these models are more successful in tests using observed expected returns than in tests using realized returns as proxies for expected returns. Unit root tests suggest that monthly observed expected returns follow the classic random walk without drift model while monthly realized returns do not.     

Can Asset Pricing Models Price Idiosyncratic Risk in U.K. Stock Returns?

I examine how well different linear factor models and consumption‐based asset pricing models price idiosyncratic risk in U.K. stock returns. Correctly pricing idiosyncratic risk is a significant challenge for many of the models I consider. For some consumption‐based models, there is a clear tradeoff in the performance of the models between correctly pricing systematic risk and idiosyncratic risk. Linear factor models do a better job in most cases in pricing systematic risk than consumption‐based models but the reverse is true for idiosyncratic risk.     

Are Stock Returns Predictable? A Test Using Markov Chains

This paper uses a Markov chain model to test the random walk hypothesis of stock prices. Given a time series of returns, a Markov chain is defined by letting one state represent high returns and the other represent low returns. The random walk hypothesis restricts the transition probabilities of the Markov chain to be equal irrespective of the prior years. Annual real returns are shown to exhibit significant nonrandom walk behavior in the sense that low (high) returns tend to follow runs of high (low) returns in the postwar period.     

Examination of Conditional Asset Pricing in UK Stock Returns

I examine the empirical performance of various specifications of the capital asset pricing model (CAPM) in UK stock returns, using the stochastic discount framework. When the proxy for the market portfolio includes a proxy for labor income growth in addition to the stock market index, the performance of the CAPM improves. The improvement in performance shows in the magnitude and significance of the pricing errors and in the reduced impact of asset characteristics and other factors in the pricing of assets. There is further improvement when I use conditional versions of the models.     

Pricing Options on an Asset with Bernoulli Jump-Diffusion Returns

The price movements of certain assets can be modeled by stochastic processes that combine continuous diffusion with discrete jumps. This paper compares values of options on assets with no jumps, jumps of fixed size, and jumps drawn from a lognormal distribution. It is shown that not only the magnitude but also the direction of the mispricing of the Black-Scholes model relative to jump models can vary with the distribution family of the jump component. This paper also discusses a methodology for the numerical valuation, via a backward induction algorithm, of American options on a jump-diffusion asset whose early exercise may be profitable. These cannot, in general, be accurately priced using analytic models. The procedure has the further advantage of being easily adaptable to nonanalytic, empirical distributions of period returns and to nonstationarity in the underlying diffusion process.     

Portfolio Selection and Asset Pricing Models

Finance theory can be used to form informative prior beliefs in financial decision making. This paper approaches portfolio selection in a Bayesian framework that incorporates a prior degree of belief in an asset pricing model. Sample evidence on home bias and value and size effects is evaluated from an asset-allocation perspective. U.S. investors' belief in the domestic CAPM must be very strong to justify the home bias observed in their equity holdings. The same strong prior belief results in large and stable optimal positions in the Fama–French book-to-market portfolio in combination with the market since the 1940s.     

Asset Pricing Models and Financial Market Anomalies

This article develops a framework that applies to single securitiesto test whether asset pricing models can explain the size, value,and momentum anomalies. Stock level beta is allowed to varywith firm-level size and book-to-market as well as with macroeconomicvariables. With constant beta, none of the models examined captureany of the market anomalies. When beta is allowed to vary, thesize and value effects are often explained, but the explanatorypower of past return remains robust. The past return effectis captured by model mispricing that varies with macroeconomicvariables.     

Option Pricing Under Autoregressive Random Variance Models

Abstract

The autoregressive random variance (ARV) model introduced by Taylor (1980, 1982, 1986) is a popular version of stochastic volatility (SV) models and a discrete-time simplification of the continuous-time diffusion SV models. This paper introduces a valuation model for options under a discrete-time ARV model with general stock and volatility innovations. It employs the discretetime version of the Esscher transform to determine an equivalent martingale measure under an incomplete market. Various parametric cases of the ARV models, are considered, namely, the log-normal ARV models, the jump-type Poisson ARV models, and the gamma ARV models, and more explicit pricing formulas of a European call option under these parametric cases are provided. A Monte Carlo experiment for some parametric cases is also conducted.     

Using Expectations to Test Asset Pricing Models

Asset pricing models generate predictions relating assets' expected rates of return and their risk attributes. Most tests of these models have employed realized rates of return as a proxy for expected return. We use analysts' expected rates of return to examine the relation between these expectations and firm attributes. By assuming that analysts' expectations are unbiased estimates of market-wide expected rates of return, we can circumvent the use of realized rates of return and provide evidence on the predictions emanating from traditional asset pricing models. We find a positive, robust relation between expected return and market beta and a negative relation between expected return and firm size, consistent with the notion that these are risk factors. We do not find that high book-to-market firms are expected to earn higher returns than low book-to-market firms, inconsistent with the notion that book-to-market is a risk factor.     

Stock Return Predictability and Asset Pricing Models

This article develops an asset allocation framework that incorporatesprior beliefs about the extent of stock return predictabilityexplained by asset pricing models. We find that when prior beliefsallow even minor deviations from pricing model implications,the resulting asset allocations depart considerably from andsubstantially outperform allocations dictated by either theunderlying models or the sample evidence on return predictability.Under a wide range of beliefs about model pricing abilities,asset allocations based on conditional models outperform theirunconditional counterparts that exclude return predictability.