Valuation of default-sensitive claims under imperfect information

We propose a valuation method for financial assets subject to default risk, where investors cannot observe the state variable triggering the default but observe a correlated price process. The model is sufficiently general to encompass a large class of structural models and can be seen as a generalization of the model of Duffie and Lando (Econometrica 69:633–664, [2001]). In this setting we prove that the default time is totally inaccessible in the market’s filtration and derive the conditional default probabilities and the intensity process. Finally, we provide pricing formulas for default-sensitive claims and illustrate in particular examples the shapes of the credit spreads.      

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.     

The valuation of multivariate contingent claims under transformed trinomial approaches

This study develops a transformed-trinomial approach for the valuation of contingent claims written on multiple underlying assets. Our model is characterized by an extension of the Camara and Chung (J Futur Mark 26: 759–787, 2006) transformed-binomial model for pricing options with one underlying asset, and a discrete-time version of the Schroder (J Finance 59(5): 2375–2401, 2004) model. However, unlike the Schroder model, our model can facilitate straightforward valuation of American-style multivariate contingent claims. The major advantage of our transformed-trinomial approach is that it can easily tackle the volatility skew observed within the markets. We go on to use numerical examples to demonstrate the way in which our transformed-trinomial approach can be utilized for the valuation of multivariate contingent claims, such as binary options.     

Relationship between Treasury bills and Eurodollars: Theoretical and Empirical Analyses

In this paper, we derive an equilibrium relationship between the yields on Eurodollar and Treasury bills based on equivalent martingale results derived by Harrison and Kreps (1979) and Harrison and Pliska (1981, 1983) as well as the corporate debt pricing model developed by Merton (1974). The derived equilibrium relationship incorporates the models used by Booth and Tse (1995) and Shrestha and Welch (2001) as special cases. The equilibrium relationship indicates that the conditional volatility of the yield on Eurodollars explains the variation in the TED spread. We empirically test the equilibrium relationship using a GARCH-M model and the concept of fractional cointegration. We use both the ex ante data implied by the respective futures contracts as well as the ex post spot data with daily, weekly and monthly frequencies. We find empirical support for the Equilibrium relationship.

Marketing Period Risk in a Portfolio Context: Theory and Empirical Estimates from the UK Commercial Real Estate Market

The role of selling (or marketing) period uncertainty in understanding risk associated with property investment is examined in this paper. Using an approach developed by Lin (2004), and Lin and Vandell (2001, 2005), combined with a statistical model of UK commercial property transactions, we show that the ex ante level of risk exposure for a commercial real estate investor is around one and a half times that obtained from historical statistics. The risk related to marketing time uncertainty can be reduced by constructing a portfolio. We find that at least ten properties are necessary to reduce this risk, assuming independence between marketing period risk and price risk. These findings have important implications for mixed-asset portfolio allocation decisions.      

Computation of Multivariate Barrier Crossing Probability and its Applications in Credit Risk Models

Abstract

In this paper we consider computational methods of finding exit probabilities for a class of multivariate diffusion processes. Although there is an abundance of results for one-dimensional diffusion processes, for multivariate processes one has to rely on approximations or simulation methods. We adopt a Large Deviations approach to approximate barrier crossing probabilities of a multivariate Brownian Bridge. We use this approach in conjunction with simulation methods to develop an efficient method of obtaining barrier crossing probabilities of a multivariate Brownian motion. Using numerical examples, we demonstrate that our method works better than other existing methods. We mainly focus on a three-dimensional process, but our framework can be extended to higher dimensions. We present two applications of the proposed method in credit risk modeling. First, we show that we can efficiently estimate the default probabilities of several correlated credit risky entities. Second, we use this method to efficiently price a credit default swap (CDS) with several correlated reference entities. In a conventional approach one normally adopts an arbitrary copula to capture dependency among counterparties. The method we propose allows us to incorporate the instantaneous variance-covariance structure of the underlying process into the CDS prices.     

Using Nonnormal Distributions to Analyze the Relationship Between Stock Returns in Japan and the US

The Pearson distribution system is researched and applied to financial engineering (Nagahara, Financ Eng Jpn Mark 2(2):139–154 in 1995, Financ Eng Jpn Mark 3(2):121–149 in 1996, Stat Prob Lett 43:251–264 in 1999, J Time Ser Anal 24(6):721–738 in 2003, A method of fitting multivariate nonnormal distributions to financial data. Discussion paper of Institute of Social Sciences, F-2006-2, Meiji University in 2006, Asia Pac Financial Markets 15(3–4):175–184 in 2008a). And a method of fitting multivariate nonnormal distributions by using random numbers from the Pearson distribution system was developed (Nagahara, Comput Stat Data Anal 47(1):1–29 in 2004). This method uses the grid search of the parameters for the maximum likelihood. In this paper, we adopt Grid-Computing and its middleware for the parameter sweep in order to reduce the computational time and the workload of this method. In the area of the financial risk management, it is very important to analyze the relationship between stock returns in Japan and the US. We analyze the data based on the same date and the following date because Japanese stock market opens before the US stock market opens in a day. We compare these returns by means of the multivariate nonnormal distributions by using this method. And we test the international transmission of stock markets movement. Furthermore, we obtain the optimal job schedule for our computer system using the middleware in order to reduce the computational time.     

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.     

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.     

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.      

Pricing credit card loans with default risks: a discrete-time approach

The main purpose of this paper is to modify the Jarrow and van Deventer model by using Das and Sundaram (Manag Sci 46:46–62, 2000) model to extend the Heath–Jarrow–Morton (J Finan Quant Anal 25:419–440, 1990) term-structure model to facilitate the consideration of default risks for pricing credit card loans. Furthermore, we derive closed-form solutions within a continuous-time framework. In addition, we also provide a numerical method for the evaluation of credit card loans within a discrete-time framework. Using the market segmentation argument to describe the characteristics of the credit card industry, our simulation results show that the shapes of the forward rate and forward spread (default risk premium) term structures play extremely important roles in determining the value of credit card loans.     

Re-examining the investment-uncertainty relationship in a real options model

The main purpose of this paper is to re-examine the investment-uncertainty relationship in a real options model, and demonstrates that the Sarkar (J Econ Dyn Control 24:219–225, 2000) model is a special case of our model. This paper uses a general dynamic process, which incorporates mean reversion and jumps in a firm’s project earnings. We further derive a quasi-analytical form solution for the critical investment value and investment probability of a firm’s projects. From the simulation results, we find that an increase in uncertainty can always lead to an increase in the probability of investment, and thus has a positive impact on investment. These results, which differ from the findings of Sarkar (J Econ Dyn Control 24:219–225, 2000), could be explained by the mean-reversion and jump effects on a firm’s earnings.     

Optimal commodity taxation with duty-free shopping

International travellers are frequently offered the opportunity to purchase a certain quantity of goods duty-free. Individuals differ in their opportunities to benefit from duty-free shopping, and we focus on the implications of these differences for optimal commodity taxation within a version of the optimal tax model of Mirrlees (Review of Economic Studies, 38, 175–208, 1971). We show how duty-free alters the constraints on the use of commodity taxes to reduce the distortionary costs of income taxation or to reflect externalities. Beyond characterising optimal taxes in the duty-free regime, we discuss conditions under which allowing duty-free would increase or reduce social welfare.      

The heteroskedasticity-consistent covariance estimator in accounting

The main purpose of this paper is to compare the White (1980) heteroskedasticity-consistent (HC) covariance matrix estimator with alternative estimators. Many regression packages compute the White (1980) heteroskedasticity-consistent (HC) covariance matrix estimator. The common procedure in Accounting and Finance research to deal with the heteroskedasticity problem is based on this estimator, despite its worse finite-samples properties when compared with other consistent estimators. In this paper we compare several HC covariance matrix estimators based on a sample of 3706 European listed companies from Austria, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden and the United Kingdom. We conclude that HC standard errors increase when finite-samples more appropriate estimators are considered and in the most part of countries the Ohlson (1995) model coefficients estimates became statistically insignificant. This can be explained by the high leverage points in the design matrix. To the best of our knowledge it is the first time that these alternative estimators are compared with the one of White (1980) in accounting research.     

Capturing model risk and rating momentum in the estimation of probabilities of default and credit rating migrations

We present two methodologies on the estimation of rating transition probabilities within Markov and non-Markov frameworks. We first estimate a continuous-time Markov chain using discrete (missing) data and derive a simpler expression for the Fisher information matrix, reducing the computational time needed for the Wald confidence interval by a factor of a half. We provide an efficient procedure for transferring such uncertainties from the generator matrix of the Markov chain to the corresponding rating migration probabilities and, crucially, default probabilities. For our second contribution, we assume access to the full (continuous) data set and propose a tractable and parsimonious self-exciting marked point processes model able to capture the non-Markovian effect of rating momentum. Compared to the Markov model, the non-Markov model yields higher probabilities of default in the investment grades, but also lower default probabilities in some speculative grades. Both findings agree with empirical observations and have clear practical implications. We use Moody's proprietary corporate credit rating data set. Parts of our implementation are available in the R package ctmcd.     

A note on portfolio choice for sovereign wealth funds

The current vast account surpluses of commodity-rich nations, combined with record account deficits in developed markets (the United States, Britain) have created a new type of investor. Sovereign wealth funds (SWF) are instrumental in deciding how these surpluses will be invested. We need to better understand the investment problem for an SWF in order to project future investment flows. Extending Gintschel and Scherer (J. Asset Manag. 9(3):215–238, 2008), we apply the portfolio choice problem for a sovereign wealth fund in a Campbell and Viceira (Strategic Asset Allocation, 2002) strategic asset allocation framework. Changing the analysis from a one to a multi-period framework allows us to establish a three-fund separation. We split the optimal portfolio for an SWF into speculative demand as well as hedge demand against oil price shocks and shocks to the short-term risk-free rate. In addition, all terms now depend on the investor’s time horizon. We show that oil-rich countries should hold bonds and that the optimal investment policy for an SWF as a long-term investor is determined by long-run covariance matrices that differ from the correlation inputs that one-period (myopic) investors use.

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.     

A note on the existence of the power investor’s optimizer

Karatzas et al. (SIAM J. Control Optim. 29:707–730, 1991) ensure the existence of the expected utility maximizer for investors with constant relative risk aversion coefficients less than one. In this note, we explain a simple trick that allows us to use this result to provide the existence of utility maximizers for arbitrary coefficients of relative risk aversion. The simplicity of our approach is to be contrasted with the general existence result provided in Kramkov and Schachermayer (Ann. Appl. Probab. 9:904–950, 1999).     

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.     

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].