Leveraged Lévy processes as models for stock prices

Adopting a constant elasticity of variance formulation in the context of a general Lévy process as the driving uncertainty we show that the presence of the leverage effect? ?One explanation of the documented negative relation between market volatilities and the level of asset prices (the ‘smile’ or ‘skew’), we term the ‘leverage effect’, argues that this negative relation reflects greater risk taking by the management, induced by a fall in the asset price, with a view of maximizing the option value of equity shareholders. in this form has the implication that asset price processes satisfy a scaling hypothesis. We develop forward partial integro-differential equations under a general Markovian setup, and show in two examples (both continuous and pure-jump Lévy) how to use them for option pricing when stock prices follow our leveraged Lévy processes. Using calibrated models we then show an example of simulation-based pricing and report on the adequacy of using leveraged Lévy models to value equity structured products.     

Three centuries of asset pricing

Theory on the pricing of financial assets can be traced back to Bernoulli's famous St Petersburg paper of 1738. Since then, research into asset pricing and derivative valuation has been influenced by a couple of dozen major contributions published during the twentieth century. These seminal works have underpinned the key ideas of mean–variance optimisation, equilibrium analysis and no-arbitrage arguments. This paper presents a historical review of these important contributions to finance.     

How common are common return factors across the NYSE and Nasdaq?

We entertain the possibility of pervasive factors that are not common across two (or more) groups of securities. We propose and implement a general procedure to estimate the space spanned by common and group-specific pervasive factors. In our empirical analysis, we study the factor structure of excess returns on stocks traded on the NYSE and Nasdaq using our methodology. We find that there are only two common pervasive factors that govern the returns for both NYSE and Nasdaq. At the same time, the NYSE and Nasdaq each have one more group-specific factor that is not the same across the two exchanges. Our results point to the absence of complete similarity between the factors driving the returns on these exchanges.     

The characteristics of informed trading: Implications for asset pricing

This paper investigates the linkage of microstructure, accounting, and asset pricing. We determine the relationship between firm characteristics as captured by accounting and market data and a firm's probability of private information-based trade (PIN) as estimated from trade data. This allows us to determine what types of firms have high information risk. We then use these data to create an instrument for PIN, the PPIN, which we can estimate from firm-specific data. We show that PPINs have explanatory power for the cross-section of asset returns in long sample tests. We also investigate whether information risk vitiates the influence of other variables on asset returns. We develop a PPIN factor and show that it dominates the Amihud factor in asset returns. Our results provide strong support for information risk affecting asset returns in long sample tests.     

The impact of exchange rate risk on international asset pricing under various market structures

This article derives international equity pricing relations by taking into account inflationary exchange risk under various forms of market segmentation/integration. In a mean-variance framework, a two-country, two-period, two-goods model is analyzed under three different market structures: segmented, mildly segmented and integrated. It is found that as long as investors are consuming imported goods, in the presence of market frictions, inflationary exchange risk is an important determinant of real equity prices. This is the case because inflationary exchange rate affects the real purchasing power of investors.

Anomalies and financial distress

This paper explores commonalities across asset pricing anomalies. In particular, we assess implications of financial distress for the profitability of anomaly-based trading strategies. Strategies based on price momentum, earnings momentum, credit risk, dispersion, idiosyncratic volatility, and capital investments derive their profitability from taking short positions in high credit risk firms that experience deteriorating credit conditions. In contrast, the value-based strategy derives most of its profitability from taking long positions in high credit risk firms that survive financial distress and subsequently realize high returns. The accruals anomaly is an exception. It is robust among high and low credit risk firms in all credit conditions.     

Asset price bubbles: a survey

Why do asset price bubbles continue to appear in various markets? What types of events give rise to bubbles and why do arbitrage forces fail to quickly burst them? Do bubbles have real economic consequences and should policy makers do more to prevent them? This paper provides an overview of recent literature on bubbles, with significant attention given to behavioral models and rational models with frictions. The latest U.S. real estate bubble is described in the context of this literature.     

The effect of corporate social responsibility on stock performance: new evidence for the USA and Europe

This paper provides new empirical evidence for the effect of corporate social responsibility on corporate financial performance. In contrast to former studies, we examine two different regions, namely the USA and Europe, and disentangle firm and sector specific impacts. Our econometric analysis shows that environmental and social activities of a firm compared with other firms within the industry are valued by financial markets in both regions. However, the respective positive effects on average monthly stock returns between 2003 and 2006 are more robust in the USA and, in addition, non-linear. Our analysis furthermore points to biased parameter estimates if incorrectly specified econometric models are applied: the seemingly significantly negative effect of environmental and social performance of the industry to which a firm belongs strongly declines and mostly becomes insignificant if the explanation of stock performance is based on the Fama–French three-factor or the Carhart four-factor models instead of the simple Capital Asset Pricing Model.     

The other January effect: International, style, and subperiod evidence

We report international, style, and subperiod evidence for the other January effect (OJE) documented in Cooper et al. [2006. The other January effect. Journal of Financial Economics 82, 315–341]. When examining the OJE in 22 countries starting as early as 1801, we find that the spread between 11-month returns following positive and negative Januarys does tend to be positive. However, the spreads are rarely statistically significant and the returns of other calendar months exhibit similar subsequent 11-month return spreads. Further, the international OJE spreads and the OJE spreads in disaggregate U.S.-style portfolios are more related to the U.S. market-level January return, rather than the respective country-specific or portfolio-specific January return. Finally, the OJE is weaker over the 1975–2006 post-discovery period than over the 1940–1974 pre-discovery period. Our evidence indicates that the OJE is primarily a U.S. market-level-based phenomenon that has diminished over time, which suggests a ‘temporary anomaly’ interpretation.     

An intertemporal capital asset pricing model with bank credit growth as a state variable

An ICAPM which includes bank credit growth as a state variable explains 94% of the cross-sectional variation in the average returns on the 25 Fama–French portfolios. We find compelling evidence that bank credit growth is priced in the cross-section of expected stock returns, even after controlling for well-documented asset pricing factors. These results are robust to the inclusion of industry portfolios in the set of test assets. They are also robust to the addition of firm characteristics and lagged instruments in the factor model. Bank credit growth is important because of its ability to predict business cycle variables as well as future labor income growth. These findings underscore the relevance of bank credit growth in stock pricing.     

The other side of value: The gross profitability premium

Profitability, measured by gross profits-to-assets, has roughly the same power as book-to-market predicting the cross section of average returns. Profitable firms generate significantly higher returns than unprofitable firms, despite having significantly higher valuation ratios. Controlling for profitability also dramatically increases the performance of value strategies, especially among the largest, most liquid stocks. These results are difficult to reconcile with popular explanations of the value premium, as profitable firms are less prone to distress, have longer cash flow durations, and have lower levels of operating leverage. Controlling for gross profitability explains most earnings related anomalies and a wide range of seemingly unrelated profitable trading strategies.     

A perturbative approach to Bermudan options pricing with applications

In this paper we address the problem of the valuation of Bermudan option derivatives in the framework of multi-factor interest rate models. We propose a solution in which the exercise decision entails a properly defined series expansion. The method allows for the fast computation of both a lower and an upper bound for the option price, and a tight control of its accuracy, for a generic Markovian interest rate model. In particular, we show detailed computations in the case of the Bond Market Model. As examples we consider the case of a zero coupon Bermudan option and a coupon bearing Bermudan option; in order to demonstrate the wide applicability of the proposed methodology we also consider the case of a last generation payoff, a Bermudan option on a CMS spread bond.     

Market integration and currency risk in Asian emerging markets

Most of the Asian emerging stock markets started to liberalize their markets in 1990s. In this paper, I examine whether those markets have become integrated with world stock market since the 1990s by estimating and testing a dynamic version of international CAPM (ICAPM) in the absence of purchasing power parity (PPP) using a parsimonious multivariate GARCH-in-Mean (MGARCH-M) approach. I also investigate to what extent the liberalization process has affected the cost of capital and price volatility for each market. The empirical results show that Philippines was segmented from the world stock market before its liberalization date, but no evidence of market segmentation is found for the other five markets (India, Korea, Malaysia, Taiwan, and Thailand) before their liberalization dates. However, all six markets have become integrated after opening up their markets to foreign investors. In addition, the estimated risk premia are lower after the liberalization, indicating that the liberalization process has reduced the cost of capital for their domestic firms. Moreover, there is no evidence of extra market volatility introduced by capital market liberalization, and on the contrary, the markets have become more stabilized through the liberalization process.     

A new method for generating approximation algorithms for financial mathematics applications

This paper describes a new technique that can be used in financial mathematics for a wide range of situations where the calculation of complicated integrals is required. The numerical schemes proposed here are deterministic in nature but their proof relies on known results from probability theory regarding the weak convergence of probability measures. We adapt those results to unbounded payoffs under certain mild assumptions that are satisfied in finance. Because our approximation schemes avoid repeated simulations and provide computational savings, they can potentially be used when calculating simultaneously the price of several derivatives contingent on the same underlying. We show how to apply the new methods to calculate the price of spread options and American call options on a stock paying a known dividend. The method proves useful for calculations related to the log-Weibull model proposed recently for empirical asset pricing.     

The market price of risk and the equity premium: A legacy of the Great Depression?

By positing learning and a pessimistic initial prior, we build a model that disconnects a representative consumer's subjective attitudes toward risk from the high price of risk that a rational-expectations econometrician would deduce from financial market data. We follow Friedman and Schwartz [1963. A Monetary History of the United States, 1857-1960. Princeton University Press, Princeton, NJ] in hypothesizing that the Great Depression heightened fears of economic instability. We use a robustness calculation to elicit a pessimistic prior for a representative consumer and let him update beliefs via Bayes’ law. Learning eventually erases pessimism, but while it persists, pessimism contributes a volatile multiplicative component to the stochastic discount factor that a rational-expectation econometrician would detect. With sufficient initial pessimism, the model generates substantial values for the market price of risk and equity premium and predicts high Sharpe ratios and forecastable excess stock returns.     

Pricing dynamic binary variables and their derivatives

Many important assets or business ventures have cash flows that are not derivatives of a market security but are nevertheless dependent on some variable that is correlated with market prices. This includes many real option projects. This paper presents a methodology using a binary framework for pricing such assets by projection onto the market space. Under certain conditions, the result has the property that, given this price process, no risk-averse investor would choose to invest in this asset either long or short.     

Disclosure and the Cost of Capital: A Survey of the Theoretical Literature

This article offers a survey of theoretical research on disclosure and the cost of capital. We summarize the current state of the literature and discuss the channels through which information affects the cost of capital. After giving an overview of asset pricing theory, we examine the rationale for an accounting risk factor or an ex‐ante effect of information on the cost of capital. Then, we discuss the role of voluntary disclosure, heterogenous beliefs, investor base, liquidity shocks, earnings management, and agency problems as determinants of the cost of capital. Linkages between productive decisions and the cost of capital, and their implication for investor welfare, are also examined.     

Volatility transmission in the UK equity market

In this study, the three-factor model of Fama and French and the ‘characteristic model’ of Daniel and Titman are tested using the French Stock Market. Stocks are ranked by size and book to market ratio and then by ex-ante β, HML or SMB loadings. Based on average returns, results reject the factor model with ‘characteristic balanced’ portfolios. In contrast, in time-series regressions, results are consistent with the factor pricing model and inconsistent with the characteristic-based pricing model. Because the value premium is small, conclusions must be interpreted carefully. However, size and market premiums allow more powerful tests of the two models.     

Pricing the Chicago Board of Trade T-Bond futures

The aim of this paper is to investigate the pricing of the Chicago Board of Trade (CBOT) Treasury-Bond futures. The difficulty in pricing it arises from its multiple inter-dependent embedded delivery options, which can be exercised at various times and dates during the delivery month. We consider a general Markov diffusion process model for stochastic interest rates and propose a pricing algorithm that can handle all the delivery rules embedded in the CBOT T-Bond futures. Our procedure combines dynamic programming, finite-elements approximation, and fixed-point evaluation. Numerical illustrations are provided under the one-factor Vasicek and Cox–Ingesoll–Ross models, and under the time in-homogeneous Hull–White model.