Evaluating asset pricing models using the second Hansen-Jagannathan distance

We develop a specification test and a sequence of model selection procedures for non-nested, overlapping, and nested models based on the second Hansen-Jagannathan distance, which requires a good asset pricing model to not only have small pricing errors but also be arbitrage free. Our methods have reasonably good finite sample performances and are more powerful than existing ones in detecting misspecified models with small pricing errors but are not arbitrage-free and in differentiating models that have similar pricing errors of a given set of test assets. Using the Fama and French size and book-to-market portfolios, we reach dramatically different conclusions on model performances based on our approach and existing methods.     

Empirical performance of multifactor term structure models for pricing and hedging Eurodollar futures options

This article compares two one-factor, two two-factor, two three-factor models in the HJM class and Black's [Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3, 167-179.] implied volatility function in terms of their pricing and hedging performance for Eurodollar futures options across strikes and maturities from 1 Jan 2000 to 31 Dec 2002. We find that three-factor models perform the best for 1-day and 1-week prediction, as well as for 5-day and 20-day hedging. The moneyness bias and the maturity bias appear for all models, but the three-factor models produce lower bias. Three-factor models also outperform other models in hedging, in particular for away-from-the-money and long-dated options. Making Black's volatility a square root or exponential function performs similar to one-factor HJM models in pricing, but not in hedging. Correctly specified and calibrated multifactor models are thus important and cannot be replaced by one-factor models in pricing or hedging interest rate contingent claims.     

Model-free hedge ratios and scale-invariant models

A price process is scale-invariant if and only if the returns distribution is independent of the price measurement scale. We show that most stochastic processes used for pricing options on financial assets have this property and that many models not previously recognised as scale-invariant are indeed so. We also prove that price hedge ratios for a wide class of contingent claims under a wide class of pricing models are model-free. In particular, previous results on model-free price hedge ratios of vanilla options based on scale-invariant models are extended to any contingent claim with homogeneous pay-off, including complex, path-dependent options. However, model-free hedge ratios only have the minimum variance property in scale-invariant stochastic volatility models when price–volatility correlation is zero. In other stochastic volatility models and in scale-invariant local volatility models, model-free hedge ratios are not minimum variance ratios and our empirical results demonstrate that they are less efficient than minimum variance hedge ratios.     

Asset pricing with a reference level of consumption: New evidence from the cross-section of stock returns

This paper presents an empirical evaluation of recently proposed asset pricing models which extend the standard preference specification by a reference level of consumption. We motivate an alternative model that accounts for the return on human capital as a determinant of the reference level. Our analysis is based on a broad cross-section of test assets, which provides a level playing field for a comparison to established benchmark models. The reference level model extended by human capital does a good job in explaining size and value premia. Estimated on Fama and French's size and book-to-market sorted portfolios, it outperforms Lettau and Ludvigson's scaled CCAPM and delivers average pricing errors comparable to the Fama-French three-factor model.     

Nonparametric,conditional pricing of higher order multivariate contingent claims

This paper describes and applies a nonparametric model for pricing multivariate contingent claims. Multivariate contingent claims are contracts whose payoffs depend on the future prices of more than one underlying variable. The pricing however of these kinds of contracts represents a challenge. All known models are adaptations of earlier ones that have been introduced to price plain vanilla calls and puts. They are imposing strong assumptions on the distributional properties of the underlying variables. In contrast, this study adopts a methodology that relaxes such restrictions. Following [Barone-Adesi, G., Bourgoin, F., Giannopoulos, K., 1998. Don’t Look Back, Risk 11 (August), 100–104; Barone-Adesi, G., Engle, R., Mancini, L., 2004. GARCH Options in Incomplete Markets, mimeo, University of Applied Sciences of Southern Switzerland; Long, X., 2004. Semiparametric Multivariate GARCH Model, mimeo, University of California, Riverside], multivariate pathways for a set of underlying variables are constructed before the option payoffs are computed. This enables the covariances, in addition to the means and variances, to be modelled in a dynamic and nonparametric manner. The model is particular suitable for options whose payoffs depend on variables that are characterised by high nonlinearities and extremes and on higher order multivariate options whose underlying variables are more unlikely to conform to a common theoretical distribution.     

Asset pricing: A tale of two days

We show that asset prices behave very differently on days when important macroeconomic news is scheduled for announcement. In addition to significantly higher average returns for risky assets on announcement days, return patterns are much easier to reconcile with standard asset pricing theories, both cross-sectionally and over time. On such days, stock market beta is strongly related to average returns. This positive relation holds for individual stocks, for various test portfolios, and even for bonds and currencies, suggesting that beta is after all an important measure of systematic risk. Furthermore, a robust risk–return trade-off exists on announcement days. Expected variance is positively related to future aggregated quarterly announcement day returns, but not to aggregated non-announcement day returns. We explore the implications of our findings in the context of various asset pricing models.     

An analysis of option pricing under systematic consumption risk using GARCH

An issue in the pricing of contingent claims is whether to account for consumption risk. This is relevant for contingent claims on stock indices, such as the FTSE 100 share price index, as investor’s desire for smooth consumption is often used to explain risk premiums on stock market portfolios, but is not used to explain risk premiums on contingent claims themselves. This paper addresses this fundamental question by allowing for consumption in an economy to be correlated with returns. Daily data on the FTSE 100 share price index are used to compare three option pricing models: the Black–Scholes option pricing model, a GARCH (1, 1) model priced under a risk-neutral framework, and a GARCH (1, 1) model priced under systematic consumption risk. The findings are that accounting for systematic consumption risk only provides improved accuracy for in-the-money call options. When the correlation between consumption and returns increases, the model that accounts for consumption risk will produce lower call option prices than observed prices for in-the-money call options. These results combined imply that the potential consumption-related premium in the market for contingent claims is constant in the case of FTSE 100 index options.     

A general closed-form spread option pricing formula

We propose a new accurate method for pricing European spread options by extending the lower bound approximation of Bjerksund and Stensland (2011) beyond the classical Black–Scholes framework. This is possible via a procedure requiring a univariate Fourier inversion. In addition, we are also able to obtain a new tight upper bound. Our method provides also an exact closed form solution via Fourier inversion of the exchange option price, generalizing the Margrabe (1978) formula. The method is applicable to models in which the joint characteristic function of the underlying assets forming the spread is known analytically. We test the performance of these new pricing algorithms performing numerical experiments on different stochastic dynamic models.     

Asset Pricing Specification Errorsand Performance Evaluation

Many evaluation techniques typically measure performance as deviations of average returns on actively managed funds from those predicted by some asset pricing model. Empirical evidence, however,has so far suggested that all asset pricing models lack empiricalsupport, implying that the models contain mis-specification errors tovarious degrees. Evaluating mutual fund performance relative to any of these models thus becomes problematic.In this paper, we propose an approach to performancemeasurement that emphasizes minimizing explicitly the pricing error associated with an asset pricing function which isemployed to compute performance measures. This approachis henceforth called the minimum specification-error (MSE) method. We also discuss the statistical properties for implementing MSE performance measures.To demonstrate the significance of the pricing errorconfounded in evaluation measurement, we contrast our methodology with the Grinblatt and Titman (1989) period weighting approach and with the empirical implementation of Chen and Knez(1996). We find that the greater the pricing error ofpassive assets, the larger the performance measures. Given the average pricing error generated from a collection of 163 diverse passive portfolios used in this analysis, the performance values assigned to a large number of the funds become statistically and economically insignificant.     

Asset pricing with unforeseen contingencies

We investigate an economy of heterogeneous agents that cannot specify all exogenous welfare-relevant events and consequently view the impact of unforeseen contingencies as utility shocks. In this setting we characterize an appropriate market equilibrium concept when securities can trade only on demand- and price-contingent events. We establish the existence of an equilibrium for a class of parametric models in which aggregating taste shocks across agents can lead to nonconsumption pricing factors. To fit the stylized facts, (i) non consumption factors must dominate the pricing kernel and contribute to the variation of the wealth-consumption ratio, (ii) markets must be incomplete and the set of claims that are traded endogenously determined, (iii) agents’ preferences with respect to unforeseen contingencies must be non-expected utility, and, (iv) although non-consumption pricing factors can be conditionally uncorrelated with aggregate consumption shocks, they must be correlated with shocks to expected consumption growth.     

Testing market efficiency with the pricing kernel

Market efficiency and the pricing kernel are closely related. A non-monotonic decreasing pricing kernel implies the existence of a trading strategy in contingent claims that stochastically dominates a direct investment in the market. Moreover, a market is assumed to be efficient only if no dominating strategies exist. Empirically, many studies of the pricing kernel find non-monotonicity, apparently ruling out market efficiency. However, these results are often unreliable, because the pricing measures of the pricing kernel are estimated using differing filtration sets. We show this effect both theoretically and empirically, and we discuss recent approaches in the literature for achieving more reliable estimates of the pricing kernel, potentially leading to better tests of market efficiency.     

The performance of cross-sectional regression tests of the CAPM with non-zero pricing errors

We show that in the presence of non-zero pricing errors, the Fama–MacBeth (FM) cross-sectional regression test is very likely to either reject the Capital Asset Pricing Model (CAPM) when it (almost) holds or accept the model when it grossly fails. We investigate the case when pricing errors are correlated with betas and demonstrate that the test performance depends crucially on the correlation, cross-sectional distribution of betas, and several other parameter values. Even when the CAPM holds exactly (pricing errors are zero) the FM test is equally likely to either reject or accept the model when typical sample sizes are used.     

The role of time-varying jump risk premia in pricing stock index options

This paper examines out-of-sample option pricing performances for the affine jump diffusion (AJD) models by using the S&P 500 stock index and its associated option contracts. In particular, we investigate the role of time-varying jump risk premia in the AJD specifications. Our empirical analysis shows strong evidence in favor of time-varying jump risk premia in pricing cross-sectional options. We also find that, during a period of low volatility, the role of jump risk premia becomes less pronounced, making the differences across pricing performances of the AJD models not as substantial as during a period of high volatility. This finding can possibly explain poor pricing perfomances of the sophisticated AJD models in some previous studies whose sample periods can be characterized by low volatility.     

A skeptical appraisal of asset pricing tests

It has become standard practice in the cross-sectional asset pricing literature to evaluate models based on how well they explain average returns on size-B/M portfolios, something many models seem to do remarkably well. In this paper, we review and critique the empirical methods used in the literature. We argue that asset pricing tests are often highly misleading, in the sense that apparently strong explanatory power (high cross-sectional R²s and small pricing errors) can provide quite weak support for a model. We offer a number of suggestions for improving empirical tests and evidence that several proposed models do not work as well as originally advertised.     

Comparing the performance of market-based and accounting-based bankruptcy prediction models

Recently developed corporate bankruptcy prediction models adopt a contingent claims valuation approach. However, despite their theoretical appeal, tests of their performance compared with traditional simple accounting-ratio-based approaches are limited in the literature. We find the two approaches capture different aspects of bankruptcy risk, and while there is little difference in their predictive ability in the UK, the z-score approach leads to significantly greater bank profitability in conditions of differential decision error costs and competitive pricing regime.     

An unobserved component model of asset pricing across financial markets

Our research focuses on multifactor asset pricing models that investigate the importance of economic factors in the pricing of assets beyond the scope of the stock market. We present a Bayesian learning model of asset pricing across financial markets in which unobserved components are estimated using a Kalman filter (KF). Economic factors serve to drive the pricing of risk in the market, and agents update expectations recursively, as new information becomes available. We generally find that the Kalman filter provides superior performance and that economic factors like industrial production and unanticipated inflation provide consistent implications across financial markets.     

Valuing Flexibility as a Complex Option

This paper develops an approach for valuing flexible production systems using contingent claims pricing. Demand curves for our model's underlying assets (output products) may be downward sloping, in contrast with the standard option pricing assumption. Also, our marginal production(exercise) costs may be increasing. In addition, we allow for multiple products and a production capacity constraint. These elements of the model result in complex exercise decisions for the contingent claims which comprise the production system's value. We illustrate our approach by valuing a flexible system that produces two products which have profit margin functions with stochastic parameters.     

Conditional beta pricing models: A nonparametric approach

We propose a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of asset betas and market prices of risk (MPR). First, conditional betas are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and betas. We prove the consistency and asymptotic normality of the estimators. We also perform Monte Carlo simulations for the conditional version of the three-factor model of Fama and French (1993) and show that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that the nonparametric procedure produces a better fit of the three-factor model to the data, less biased estimates of MPR and lower pricing errors than the Fama–MacBeth procedure with betas estimated under several alternative parametric specifications.     

Option pricing for GARCH-type models with generalized hyperbolic innovations

In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. Given the historical measure, the dynamics of assets being modeled by Garch-type models with generalized hyperbolic innovations and the pricing kernel is an exponential affine function of the state variables, we show that the risk-neutral distribution is unique and again implies a generalized hyperbolic dynamics with changed parameters. We provide an empirical test for our pricing methodology on two data sets of options, respectively written on the French CAC 40 and the American SP 500. Then, using our theoretical result associated with Monte Carlo simulations, we compare this approach with natural competitors in order to test its efficiency. More generally, our empirical investigations analyse the ability of specific parametric innovations to reproduce market prices in the context of an exponential affine specification of the stochastic discount factor.     

VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation

This study integrates CBOE VIX Term Structure and VIX futures to simplify VIX option pricing in multifactor models. Exponential and hump volatility functions with one- to three-factor models of the VIX evolution are used to examine their pricing for VIX options across strikes and maturities. The results show that using exponential volatility functions presents an effective choice as pricing models for VIX calls, whereas hump volatility functions provide efficient out-of-sample valuation for most VIX puts, in particular with deep in-the-money and deep out-of-the-money. Pricing errors for calls can be further reduced with a two-factor model.