Risk-neutral and actual default probabilities with an endogenous bankruptcy jump-diffusion model

This paper focuses on historical and risk-neutral default probabilities in a structural model, when the firm assets dynamics are modeled by a double exponential jump diffusion process. Relying on the Leland [(1994a) Journal of Finance, 49, 1213–1252; (1994b) Bond prices, yield spreads, and optimal capital structure with default risk. Working paper no. 240, IBER, University of California, Berkeley] or Leland and Toft [(1996) Journal of Finance, 51(3), 987–1019] endogenous structural approaches, as formalized by Hilberink and Rogers [(2002) Finance and Stochastics, 6(2), 237–263], this article gives a coherent construction of historical default probabilities. The risk-neutral world where evolve the firm assets, modeled by a class of geometric Lévy processes, is constructed based on the Esscher measure, yielding useful and new analytical relations between historical and risk-neutral probabilities. We do a complete numerical analysis of the predictions of our framework, and compare these predictions with actual data. In particular, this new framework displays an enhanced predictive power w.r.t. current Gaussian endogenous structural models.      

Bankruptcy prediction: the case of Japanese listed companies

This paper investigates if bankruptcy of Japanese listed companies can be predicted using data from 1992 to 2005. We find that the traditional measures, such as Altman’s (J Finance 23:589–609, 1968) Z-score, Ohlson’s (J Accounting Res 18:109–131, 1980) O-score and the option pricing theory-based distance-to-default, previously developed for the U.S. market, are also individually useful for the Japanese market. Moreover, the predictive power is substantially enhanced when these measures are combined. Based on the unique Japanese institutional features of main banks and business groups (known as Keiretsu), we construct a new measure that incorporates bank dependence and Keiretsu dependence. The new measure further improves the ability to predict bankruptcy of Japanese listed companies.     

Can long-term performance plans mitigate the negative effects of stock consideration and high cash for acquirers?

Following Travlos (J Finance 42: 943–963, 1987), Loughran and Vijh (J Finance 52: 1765–1790, 1997), Harford (J Finance 54: 1969–1997, 1999), and Oler (Rev Acc Stud 13: 479–511, 2008), we investigate whether acquisitions involving stock consideration and acquirers with high cash levels are associated with poor performance or not. In addition, we investigate whether including a long-term performance plan in top management’s compensation package can mitigate these negative effects. We find that acquirers with a long-term performance plan are less likely to hold a high cash balance and are less likely to use stock consideration, thus avoiding scenarios that are more likely to be value-destructive. Even if an acquirer with a long-term performance plan carries a high cash balance or uses stock, we find that the plan is associated with improved fundamental performance; however, this relationship does not flow through to improved post-acquisition returns.     

Hedging errors with Leland's option model in the presence of transaction costs

Nonzero transaction costs invalidate the Black–Scholes [1973. Journal of Political Economy 81, 637–654] arbitrage argument based on continuous trading. Leland [1985. Journal of Finance 40, 1283–1301] developed a hedging strategy which modifies the Black–Scholes hedging strategy with a volatility adjusted by the length of the rebalance interval and the rate of the proportional transaction cost. Kabanov and Safarian [1997. Finance and Stochastics 1, 239–250] calculated the limiting hedging error of the Leland strategy and pointed out that it is nonzero for the approximate pricing of an European call option, in contradiction to Leland's claim. As a further contribution, we first identify the mathematical flaw in the argument of Leland's claim and then quantify the expected percentage of hedging losses in terms of the hedging frequency and the level of the option strike price.     

An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model

Under the assumption that the asset value follows a phase-type jump-diffusion, we show that the expected discounted penalty satisfies an ODE and obtain a general form for the expected discounted penalty. In particular, if only downward jumps are allowed, we get an explicit formula in terms of the penalty function and jump distribution. On the other hand, if the downward jump distribution is a mixture of exponential distributions (and upward jumps are determined by a general Lévy measure), we obtain closed-form solutions for the expected discounted penalty. As an application, we work out an example in Leland’s structural model with jumps. For earlier and related results, see Gerber and Landry [Insur. Math. Econ. 22:263–276, 1998], Hilberink and Rogers [Finance Stoch. 6:237–263, 2002], Asmussen et al. [Stoch. Proc. Appl. 109:79–111, 2004], and Kyprianou and Surya [Finance Stoch. 11:131–152, 2007].      

Funds of hedge funds: performance, risk and capital formation 2005 to 2010

Using a comprehensive data set of funds-of-hedge funds, we extend the results of Fung et al. (J. Finance 63:1777–1803, 2008) (FHNR) with an augmented version of the Fung and Hsieh (Financ. Anal. J. 60:65–80, 2004a; J. Empir. Finance 18:547–569, 2004b) model to document performance characteristics from January 2005 to December 2010. We find that our sample period is divided into three distinct subperiods: January 2005 to June 2007 (pre-subprime crisis); July 2007 to March 2009; and April 2009 to December 2010 (post-credit crunch) during which the average fund of hedge funds delivered positive alpha only in the first subperiod. We divide the funds of hedge funds sample into those who have alpha and the rest, which we call beta-only. The empirical results show a dramatic decline in the population of alpha producing funds of hedge funds post 2008 compared to the FHNR findings. When we repeat our analysis with a synthetic hedge fund index replicator, we find qualitatively similar results.     

On the calibration of structural credit spread models

Empirical findings are mixed about the performance of structural models for term structure of credit spreads. It is commonly believed that all structural models have equally poor performance after calibration. However, proper calibration is not a trivial issue, especially for highly structural models. This paper proposes a more accurate procedure for calibrating two models: Leland–Toft (J Finance 51:987–1019, 1996) and Collin-Dufresne and Goldstein (J Finance 56:2177–2208, 2001). Using rating-based bond data, we find that the Leland–Toft model has significantly greater explanatory power for credit spreads across rating categories than previously reported. We provide theoretical explanations for these findings, and further extend our empirical analysis to include 286 individual senior bonds. Our findings help clarify the controversies over the performance of structural models in general and that of the Leland–Toft model in particular. In addition, we offer a rigorous procedure that can be used for calibrating other structural models more effectively.      

A pure martingale dual for multiple stopping

In this paper, we present a dual representation for the multiple stopping problem, hence multiple exercise options. As such, it is a natural generalization of the method in Rogers (Math. Finance 12:271–286, 2002) and Haugh and Kogan (Oper. Res. 52:258–270, 2004) for the standard stopping problem for American options. We term this representation a ‘pure martingale’ dual as it is solely expressed in terms of an infimum over martingales rather than an infimum over martingales and stopping times as in Meinshausen and Hambly (Math. Finance 14:557–583, 2004). For the multiple dual representation, we propose Monte Carlo simulation methods which require only one degree of nesting.     

BOOK REVIEWS

Book reviewed in this article: Aggregate Theory and Policy: Modern Capital Theory. By Donald Dewey . Aggregate Theory and Policy: Readings in Macroeconomics. Edited by M. G. Mueller . Aggregate Theory and Policy: National Economic Policy. By James Tobin . Business Finance and Investments: Business Finance: Theory and Management. By Stephen H. Archer and Charles A. D'Ambrosio . Business Finance and Investments: The Economics of Corporate Finance. By Seymour Friedland . Business Finance and Investments: Efficiency of Investment in a Socialist Economy. Edited by Mieczystaw Rakowski . Financial Institutions and Markets: Money and Finance: Readings in Theory, Policy, & Institutions. Edited by Deane Carson . Financial Institutions and Markets: Commercial Bank Behavior and Economic Activity: A Structural Study of Monetary Policy in the Postwar United States. By Stephen M. Goldfeld . International Finance: Financing African Development. Edited by Tom J. Farer . International Finance: Central Banking in the Commonwealth. By J. Obasanmi Olakanpo . International Finance: International Monetary Relations: Theory, History, and Policy. By Leland B. Yeager . Public Finance: Federal Budget Projections. By Gerhard Colm and Peter Wagner .     

Optimal portfolio positioning within generalized Johnson distributions

Many empirical studies have shown that financial asset returns do not always exhibit Gaussian distributions, for example hedge fund returns. The introduction of the family of Johnson distributions allows a better fit to empirical financial data. Additionally, this class can be extended to a quite general family of distributions by considering all possible regular transformations of the standard Gaussian distribution. In this framework, we consider the portfolio optimal positioning problem, which has been first addressed by Brennan and Solanki [J. Financial Quant. Anal., 1981, 16, 279–300], Leland [J. Finance, 1980, 35, 581–594] and further developed by Carr and Madan [Quant. Finance, 2001, 1, 9–37] and Prigent [Generalized option based portfolio insurance. Working Paper, THEMA, University of Cergy-Pontoise, 2006]. As a by-product, we introduce the notion of Johnson stochastic processes. We determine and analyse the optimal portfolio for log return having Johnson distributions. The solution is characterized for arbitrary utility functions and illustrated in particular for a CRRA utility. Our findings show how the profiles of financial structured products must be selected when taking account of non Gaussian log-returns.     

Is information risk priced for NASDAQ-listed stocks?

Easley et al. (J Finance 57:2185–2221, 2002), building upon the asset pricing model of Fama and French (J Finance 47:427–465, 1992), show that the probability of informed trading (PIN) is a determinant of asset returns for NYSE-listed securities. We extend this work by examining whether the PIN is a predictive factor for NASDAQ stocks, as many studies document significant differences between NYSE and NASDAQ listed securities. In the process we examine whether the use of PIN is appropriate for NASDAQ-listed securities. We find that PIN and certain stock characteristics correlate differently for our sample of NASDAQ stocks than that of Easley et al. sample of NYSE stocks. We also determine that the risk of informed trading is only weakly priced for NASDAQ stocks. Contrary to Easley et al. we do not find evidence that excess returns increases as PIN increases.     

Dynamic optimal capital structure with regime switching

We investigate the optimal capital structure of a corporate when the dynamics of the assets (both growth rate and volatility) change following different states of the economy. Two structural models are examined in the paper. The first considers the case when the firm is not facing tax benefit and bankruptcy costs with a regime switching dynamics. This model extends the Black and Cox (J Financ 31:351–367, 1976) model to allow for regime switching risk. The second model incorporates both tax benefit and bankruptcy costs with a regime switching dynamics. This is is more realistic, and is an extension of the Leland (J Financ 49(4):1213–1252, 1994) model with regime switching risk. We obtain closed-form analytic solutions for the optimal capital structure and default barrier for both models.     

Analytical approximations for the critical stock prices of American options: a performance comparison

Many efficient and accurate analytical methods for pricing American options now exist. However, while they can produce accurate option prices, they often do not give accurate critical stock prices. In this paper, we propose two new analytical approximations for American options based on the quadratic approximation. We compare our methods with existing analytical methods including the quadratic approximations in Barone-Adesi and Whaley (J Finance 42:301–320, 1987) and Barone-Adesi and Elliott (Stoch Anal Appl 9(2):115–131, 1991), the lower bound approximation in Broadie and Detemple (Rev Financial Stud 9:1211–1250, 1996), the tangent approximation in Bunch and Johnson (J Finance 55(5):2333–2356, 2000), the Laplace inversion method in Zhu (Int J Theor Appl Finance 9(7):1141–1177, 2006b), and the interpolation method in Li (Working paper, 2008). Both of our methods give much more accurate critical stock prices than all the existing methods above.     

Optimal consumption policies in illiquid markets

We investigate optimal consumption policies in the liquidity risk model introduced by Pham and Tankov (Math. Finance 18:613–627, 2008). Our main result is to derive smoothness C ¹ results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second-order ODE. Finally, numerical illustrations of the behavior of optimal consumption strategies between two trading dates are given.     

Optimal Incentive Contracts When Agents Can Save, Borrow, and Default

The standard Principal–Agent (PA) model assumes that the principal can control the agent's consumption profile. In an intertemporal setting, however, Rogerson (1985, Econometrica53, 69–76) shows that given the optimal PA contract, the agent has an unmet precautionary demand for savings. Thus the standard PA model is invalid if the agent has access to credit markets. In this paper we generalize the standard PA model to allow for saving and borrowing by the agent. We show that the impact of such access critically depends upon the treatment of default. If default is not permitted, efficiency is strictly reduced by the introduction of credit markets, and the equilibrium level of borrowing or saving is indeterminate in the model. If default is allowed, however, the optimal contract depends upon the level of bankruptcy protection in the economy, which is described by a minimum level of wage income. We show that there is an optimal intermediate range of bankruptcy protection. Within this range, allowing default increases efficiency in the economy relative to the case of no default. Also, the model predicts specific levels of consumer debt, interest rates, and default rates as functions of the level of bankruptcy protection level. Journal of Economic Literature Classification Numbers: D80, G21, G28, J30.     

Accounting-based versus market-based cross-sectional models of CDS spreads

Models of financial distress rely primarily on accounting-based information (e.g. [Altman, E., 1968. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance 23, 589–609; Ohlson, J., 1980. Financial ratios and the probabilistic prediction of bankruptcy. Journal of Accounting Research 19, 109–131]) or market-based information (e.g. [Merton, R.C., 1974. On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29, 449–470]). In this paper, we provide evidence on the relative performance of these two classes of models. Using a sample of 2860 quarterly CDS spreads we find that a model of distress using accounting metrics performs comparably to market-based structural models of default. Moreover, a model using both sources of information performs better than either of the two models. Overall, our results suggest that both sources of information (accounting- and market-based) are complementary in pricing distress.     

A Quarterly Transactions-based Index of Institutional Real Estate Investment Performance and Movements in Supply and Demand

This article presents a methodology for producing a quarterly transactions-based index (TBI) of property-level investment performance for U.S. institutional real estate. Indices are presented for investment periodic total returns and capital appreciation (or price-changes) for the major property types included in the NCREIF Property Index. These indices are based on transaction prices to avoid appraisal-based sources of index “smoothing” and lagging bias. In addition to producing variable-liquidity indices, this approach employs the Fisher-Gatzlaff-Geltner-Haurin (Real Estate Econ., 31: 269–303, 2003) methodology to produce separate indices tracking movements on the demand and supply sides of the investment market, including a “constant-liquidity” (demand side) index. Extensions of Bayesian noise filtering techniques developed by Gatzlaff and Geltner (Real Estate Finance, 15: 7–22, 1998) and Geltner and Goetzmann (J. Real Estate Finance Econ., 21: 5–21, 2000) are employed to allow development of quarterly frequency, market segment specific indices. The hedonic price model used in the indices is based on an extension of the Clapp and Giacotto (J. Am. Stat. Assoc., 87: 300–306, 1992) “assessed value method,” using a NCREIF-reported recent appraised value of each transacting property as the composite “hedonic” variable, thus allowing time-dummy coefficients to represent the difference each period between the (lagged) appraisals and the transaction prices. The index could also be used to produce a mass appraisal of the NCREIF property database each quarter, a byproduct of which would be the ability to provide transactions price based “automated valuation model” estimates of property value for each NCREIF property each quarter. Detailed results are available at .     

Asymmetric Information in Fads Models

Fads models were introduced by Shiller (Am Econ Rev 71:421–436, 1981) and Summers (J Finance 41:591–601, 1986) as plausible alternatives to the efficient markets/constant expected returns assumptions. Under these models, logarithms of asset prices embody both a martingale component, with permanent shocks, and a stationary component, with temporary shocks. We study a continuous-time version of these models both from the point of view of informed agents, who observe both fundamental and market values, and from that of uninformed agents, who only observe market prices. We specify the asset price in the larger filtration of the informed agent, and then derive its decomposition in the smaller filtration of the uninformed agent using the Hitsuda representation of Gaussian processes. For uninformed agents we obtain a non-Markovian dynamics, which justifies the use of technical analysis in optimal trading strategies. For both types of agents, we solve the problem of maximization of expected logarithmic utility from terminal wealth, and obtain an explicit formula for the additional logarithmic utility of informed agents. Finally, we apply the decomposition result to the problem of testing the presence of fads from market data. An application to the NYSE-AMEX indices from the CRSP database shows that, if the fads component prevails, then the mean-reversion speed must be slow.     

Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets

We consider the infinite-horizon optimal portfolio liquidation problem for a von Neumann–Morgenstern investor in the liquidity model of Almgren (Appl. Math. Finance 10:1–18, 2003). Using a stochastic control approach, we characterize the value function and the optimal strategy as classical solutions of nonlinear parabolic partial differential equations. We furthermore analyze the sensitivities of the value function and the optimal strategy with respect to the various model parameters. In particular, we find that the optimal strategy is aggressive or passive in-the-money, respectively, if and only if the utility function displays increasing or decreasing risk aversion. Surprisingly, only few further monotonicity relations exist with respect to the other parameters. We point out in particular that the speed by which the remaining asset position is sold can be decreasing in the size of the position but increasing in the liquidity price impact.