Asset pricing with Second-Order Esscher Transforms

The purpose of the paper is to introduce, in a discrete-time no-arbitrage pricing context, a bridge between the historical and the risk-neutral state vector dynamics which is wider than the one implied by a classical exponential-affine stochastic discount factor (SDF) and to preserve, at the same time, the tractability and flexibility of the associated asset pricing model. This goal is achieved by introducing the notion of exponential-quadratic SDF or, equivalently, the notion of Second-Order Esscher Transform. The log-pricing kernel is specified as a quadratic function of the factor and the associated sources of risk are priced by means of possibly non-linear stochastic first-order and second-order risk-correction coefficients. Focusing on security market models, this approach is developed in the multivariate conditionally Gaussian framework and its usefulness is testified by the specification and calibration of what we name the Second-Order GARCH Option Pricing Model. The associated European Call option pricing formula generates a rich family of implied volatility smiles and skews able to match the typically observed ones.     

Asset financing with credit risk

This paper develops a model for the unified valuation of all forms of real asset financing, such as bank loans, leases, securitization vehicles, and credit guarantees, secured by assets that generate a stochastic service flow to the operator, or a rental stream to the lessor, and depreciate over a finite economic life to their scrap value. Examples include mobile equipment, such as aircraft, railroad equipment, ships, trucks and trailers, as well as energy generation assets, heavy factory equipment and construction equipment. In the event of obligor default, after a repossession delay and incurring costs of repossession, maintenance, re-marketing and re-deployment, the lender repossesses the asset and sells it on the secondary market and is, thus, subject to the risk of decline in the market value of the asset. The model we develop in this paper treats all forms of asset financing in a unified fashion as contingent claims on the collateral asset and the credit of the borrower. As an application, we estimate the collateral asset model on historical secondary market data for aircraft values and calibrate the financing model to the Enhanced Equipment Trust Certificates (EETCs) issued in 2007 by Continental Airlines and secured by a fleet of new aircraft. We then apply the calibrated model to value private market financing, including bank loans, leases, and credit guarantees, consistently with the capital market financing, and assess the impact of repossession delays on credit spreads. This analysis leads to a policy insight suggesting that bankruptcy laws limiting asset repossession delays lead to lower costs of asset financing.     

Asset pricing with partial-moments

I bridge the current pricing kernel framework with the early partial-moment pricing models of the beta framework, thereby reconciling and clarifying these bodies of literature. I argue for the inclusion of powers of min and max functions within a generalized kernel, and form a generalized beta model. Polynomial kernels and the kernel underpinning the partial-moment analogue of the Sharpe-Lintner CAPM are nested. I derive the partial-moment analogue to the Black CAPM, thus completing a theoretical parallelism, and compare the kernel-implied and canonical risk-neutral probabilities. A new model involving both lower and upper partial-moments, accommodating various kernel shapes present in the literature, is developed in the context of preference regularity conditions.     

Asset pricing with heterogeneous beliefs and relative performance

We propose an equilibrium asset pricing model in which agents with heterogeneous beliefs care about relative performance. We find that the concern with relative performance leads agents to trade more similarly, a development that has two effects. First, similar trading directly decreases volatility. Second, similar trading decreases the impact of dominant agents. The second effect dominates the first when agents expect large differences between their final performances, and vice versa when agents expect small differences between their final performances. Compared with the case in which agents are unconcerned about relative performance, the stock return volatility is higher when the second effect dominates, and lower when the first effect dominates. This paper also demonstrates that the concern about relative performance influences investors’ holdings, stock prices and risk premia.     

Asset pricing and foreign exchange risk

According to the International Capital Asset Pricing Model (ICAPM), the covariance of assets with foreign exchange currency returns should be a risk factor that must be priced when the purchasing power parity is violated. The goal of this study is to re-examine the relationship between stock returns and foreign exchange risk. The novelties of this work are: (a) a data set that makes use of daily observations for the measurement of the foreign exchange exposure and volatility of the sample firms and (b) data from a Eurozone country.The methodology we make use in reference to the estimation of the sensitivity of each stock to exchange rate movements is that it allows regressing stock returns against factors controlling for market risk, size, value, momentum, foreign exchange exposure and foreign exchange volatility. Stocks are then classified according to their foreign exchange sensitivity portfolios and the return of a hedge (zero-investment) portfolio is calculated. Next, the abnormal returns of the hedge portfolio are regressed against the return of the factors. Finally, we construct a foreign exchange risk factor in such manner as to obtain a monotonic relation between foreign exchange risk and expected returns.The empirical findings show that the foreign exchange risk is priced in the cross section of the German stock returns over the period 2000-2008. Furthermore, they show that the relationship between returns and foreign exchange sensitivity is nonlinear, but it takes an inverse U-shape and that foreign exchange sensitivity is larger for small size firms and value stocks.     

A tale of two regimes: Theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications

We provide closed-form solutions for a continuous time, Markov-modulated jump diffusion model in a general equilibrium framework for options prices under a variety of jump diffusion specifications. We further demonstrate that the two-state model provides the leptokurtic return features, volatility smile, and volatility clustering observed empirically for the Dow Jones Industrial Average (DJIA) and its component stocks. Using 10 years of stock return data, we confirm the existence of jump intensity switching and clustering, illustrate transition probabilities, and verify superior empirical fit over competing Poisson-style models.     

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 FFT-network for Lévy option pricing

This paper develops a simple network approach to American exotic option valuation under Lévy processes using the fast Fourier transform (FFT). The forward shooting grid (FSG) technique of the lattice approach is then generalized to expand the FFT-network to accommodate path-dependent variables. This network pricing approach is applicable to all Lévy processes for which the characteristic function is readily available. In other words, the log-value of the underlying asset can follow finite-activity or infinite-activity Lévy processes. With the powerful computation of FFT, the proposed network has a negligible additional computational burden compared to the binomial tree approach. The early exercise policy and option values in the continuation region are determined in a way very similar to that of the lattice approach. Numerical examples using American-style barrier, lookback, and Asian options demonstrate that the FFT-network is accurate and efficient.     

Inference in asset pricing models with a low-variance factor

This paper concerns with the effects of including a low-variance factor in an asset pricing model. When a low-variance factor is present, the commonly applied Fama–MacBeth two-pass regression procedure is very likely to yield misleading results. Local asymptotic analysis and simulation evidence indicate that the risk premiums corresponding to all factors are very likely to be unreliably estimated. Moreover, t- and F-statistics are less likely to detect whether the risk premiums are significantly different from zero. We recommend Kleibergen’s (2009)FAR statistic when there is a low-variance factor included in an asset pricing model.     

A generalization of reset options pricing formulae with stochastic interest rates

A generalization of reset call options with predetermined dates is derived in the case of time-dependent volatility and time-dependent interest rate by applying martingale method and change of nume?aire or change of probability measure. An analytical pricing formula for the reset call option is also obtained when the interest rate follows an extended Vasicek’s model. Numerical results show that the correlated coefficient between the stock price and interest rate is almost unacted on the price of reset call option with short maturity and Monte Carlo method is inefficient. Monte Carlo method should be only used if there is no closed-formed solution for option pricing.     

Testing conditional asset pricing models: An emerging market perspective

The CAPM as the benchmark asset pricing model generally performs poorly in both developed and emerging markets. We investigate whether allowing the model parameters to vary improves the performance of the CAPM and the Fama–French model. Conditional asset pricing models scaled by conditioning variables such as Trading Volume and Dividend Yield generally result in small pricing errors. However, a graphical analysis reveals that the predictions of conditional models are generally upward biased. We demonstrate that the bias in prediction may be the consequence of ignoring frequent large variation in asset returns caused by volatile institutional, political and macroeconomic conditions. This is characterised by excess kurtosis. An unconditional Fama–French model augmented with a cubic market factor performs the best among some competing models when local risk factors are employed. Moreover, the conditional models with global risk factors scaled by global conditioning variables perform better than the unconditional models with global risk factors.     

Evaluation of linear asset pricing models by implied portfolio performance

We present a theoretical perspective that motivates the use of the Generalized Least Squares R-Square, prominently advocated by Lewellen et al. [Lewellen, J., Nagel, S., Shanken, J., forthcoming. A skeptical appraisal of asset-pricing tests. Journal of Financial Economics], as an evaluation measure for multivariate linear asset pricing models. Adapting results from Shanken [Shanken, J., 1985. Multivariate tests of the zero-beta CAPM. Journal of Financial Economics 14, 327–348] and Kandel and Stambaugh [Kandel, S., Stambaugh, R.F., 1995. Portfolio inefficiency and the cross-section of expected returns. Journal of Finance 50, 157–184], we provide various interpretations and a graphical account in mean-variance space of this measure, facilitating a better understanding of its properties. We furthermore relate it to another leading evaluation metric, the HJ-distance of Hansen and Jagannathan [Hansen, L.P., Jagannathan, R., 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52, 557–590]. Additionally, we present a comparison between these evaluation measures using mean-variance mathematics in risk-return space, and we provide a simple formula for calculating both model evaluation measures that involves only the parameters of the mean-variance asset and factor frontiers.     

Can position limits restrain ‘rogue’ trading?

This paper studies the imposition of position limits on commodity futures from the perspective of curbing excessive speculation and thus manipulation. We present a simple general equilibrium model in a static rational expectations framework and agent heterogeneity to illustrate that excessive speculation serves to enrich other agents at the expense of the speculator. Position limits, on the contrary, are not only superfluous, but also counter-productive, as they exacerbate market power and lead to a deterioration in efficiency. Position limits not only reduce social welfare but also cannot restrain market manipulation.     

Decomposing swap spreads

We analyze a six-factor model for Treasury bonds, corporate bonds, and swap rates and decompose swap spreads into three components: a convenience yield from holding Treasuries, a credit risk element from the underlying LIBOR rate, and a factor specific to the swap market. The convenience yield is by far the largest component of spreads. There is a discernible contribution from credit risk as well as from a swap-specific factor with higher variability which in certain periods is related to hedging activity in the mortgage-backed security market. The model also sheds light on the relation between AA hazard rates and the spread between LIBOR rates and General Collateral repo rates and on the level of the riskless rate compared to swap and Treasury rates.     

Monetary policy regimes: Implications for the yield curve and bond pricing

We develop a multivariate dynamic term structure model, which takes into account the nonlinear (time-varying) relation between interest rates and the state of the economy. In contrast to the classical term structure literature, in which nonlinearities are captured by increasing the number of latent state variables or by latent regime shifts, in our no-arbitrage framework the regimes are governed by thresholds and are directly linked to economic fundamentals. Specifically, starting from a simple monetary policy model for the short rate, we introduce a parsimonious and tractable model for the yield curve, which takes into account the possibility of regime shifts in the behavior of the Federal Reserve. In our empirical analysis, we show the merit of our approach three dimensions: interpretable bond dynamics, accurate short end yield curve pricing, and yield curve implications.     

The intertemporal relation between expected returns and risk

This paper explores the time-series relation between expected returns and risk for a large cross section of industry and size/book-to-market portfolios. I use a bivariate generalized autoregressive conditional heteroskedasticity (GARCH) model to estimate a portfolio's conditional covariance with the market and then test whether the conditional covariance predicts time–variation in the portfolio's expected return. Restricting the slope to be the same across assets, the risk-return coefficient is highly significant with a risk–aversion coefficient (slope) between one and five. The results are robust to different portfolio formations, alternative GARCH specifications, additional state variables, and small sample biases. When conditional covariances are replaced by conditional betas, the risk premium on beta is estimated to be in the range of 3% to 5% per annum and is statistically significant.     

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.     

Stock market momentum, business conditions, and GARCH option pricing models

This paper examines the forecasting performance of GARCH option pricing models from a market momentum perspective, and the possible impacts of financial crises and business conditions are also examined. The empirical results demonstrate that market momentum impacts the forecasting performance of GARCH option pricing models. The EGARCH model performs better under downward market momentum, while the standard GARCH performs better under upward market momentum. In addition, parsimonious models generally outperform richly parameterized ones. The above findings are robust to financial crises, and the results further demonstrate that business conditions influence the forecasting performance of GARCH option pricing models.