The critical price for the American put in an exponential Lévy model

This paper considers the behavior of the critical price for the American put in the exponential Lévy model when the underlying stock pays dividends at a continuous rate. We prove the continuity of the free boundary and give a characterization of the critical price at maturity, generalizing a recent result of S.Z. Levendorskiǐ (Int. J. Theor. Appl. Finance 7:303–336, 2004).      

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.     

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.     

Extreme Events and the Copula Pricing of Commercial Mortgage-Backed Securities

Commercial mortgage-backed securities (CMBS), as a portfolio-based financial product, have gained great popularity in financial markets. This paper extends Childs, Ott and Riddiough’s (J Financ Quant Anal, 31(4), 581–603, 1996) model by proposing a copula-based methodology for pricing CMBS bonds. Default on underlying commercial mortgages within a pool is a crucial risk associated with CMBS transactions. Two important issues associated with such default—extreme events and default dependencies among the mortgages—have been identified to play crucial roles in determining credit risk in the pooled commercial mortgage portfolios. This article pays particular attention to these two issues in pricing CMBS bonds. Our results show the usefulness and potential of copula-based models in pricing CMBS bonds, and the ability of such models to correctly price CMBS tranches of different seniorities. It is also important to sufficiently consider complex default dependence structure and the likelihood of extreme events occurring in pricing various CMBS bonds.     

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.     

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.     

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.      

A forward started jump-diffusion model and pricing of cliquet style exotics

In this paper we present an alternative model for pricing exotic options and structured products with forward-starting components. As presented in the recent study by Eberlein and Madan (Quantitative Finance 9(1):27–42, 2009), the pricing of such exotic products (which consist primarily of different variations of locally/globally, capped/floored, arithmetic/geometric etc. cliquets) depends critically on the modeling of the forward–return distributions. Therefore, in our approach, we directly take up the modeling of forward variances corresponding to the tenor structure of the product to be priced. We propose a two factor forward variance market model with jumps in returns and volatility. It allows the model user to directly control the behavior of future smiles and hence properly price forward smile risk of cliquet-style exotic products. The key idea, in order to achieve consistency between the dynamics of forward variance swaps and the underlying stock, is to adopt a forward starting model for the stock dynamics over each reset period of the tenor structure. We also present in detail the calibration steps for our proposed model.     

Dual pricing of multi-exercise options under volume constraints

In this paper, we study the pricing problem of multi-exercise options under volume constraints. The volume constraint is modelled by an adapted process with values in the positive integers, which describes the maximal number of rights to be exercised at a given time. We derive a representation of the marginal value of an additional nth right as a standard single stopping problem with a modified cash-flow process. This representation then leads to a dual pricing formula, which generalizes a result by Meinshausen and Hambly (Math. Finance 14:557–583, 2004) from the standard multi-exercise option (with at most one right per time step) to general constraints. We also state an explicit Monte Carlo algorithm for computing confidence intervals for the price of multi-exercise options under volume constraints and present numerical results for the pricing of a swing contract in an electricity market.     

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.     

Pricing growth-rate risk

We characterize the compensation demanded by investors in equilibrium for incremental exposure to growth-rate risk. Given an underlying Markov diffusion that governs the state variables in the economy, the economic model implies a stochastic discount factor process S. We also consider a reference growth process G that may represent the growth in the payoff of a single asset or of the macroeconomy. Both S and G are modeled conveniently as multiplicative functionals of a multidimensional Brownian motion. We consider the pricing implications of parametrized family of growth processes G ^ε , with G ⁰=G, as ε is made small. This parametrization defines a direction of growth-rate risk exposure that is priced using the stochastic discount factor S. By changing the investment horizon, we trace a term structure of risk prices that shows how the valuation of risky cash flows depends on the investment horizon. Using methods of Hansen and Scheinkman (Econometrica 77:177–234, 2009), we characterize the limiting behavior of the risk prices as the investment horizon is made arbitrarily long.     

Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling

We study, in the framework of Back [Rev. Financial Stud. 5(3), 387–409 (1992)], an equilibrium model for the pricing of a defaultable zero coupon bond issued by a firm. The market consists of a risk-neutral informed agent, noise traders, and a market maker who sets the price using the total order. When the insider does not trade, the default time possesses a default intensity in the market’s view as in reduced-form credit risk models. However, we show that, in equilibrium, the modelling becomes structural in the sense that the default time becomes the first time that some continuous observation process falls below a certain barrier. Interestingly, the firm value is still not observable. We also establish the no expected trade theorem that the insider’s trades are inconspicuous.      

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.      

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].      

Redistributive taxation and social insurance under adverse selection in the insurance market

This paper extends the analysis of optimal income taxation under uncertainty studied by Cremer and Pestieau (International Tax and Public Finance, 3, 281–295, 1996). We introduce asymmetric information in the insurance market whereby private insurance companies cannot identify the risk probability of the agents, and we examine its effect on public policy. We consider the separating equilibrium of Rothschild and Stiglitz (Quarterly Journal of Economics, 90, 629–649, 1976) and Riley (Econometrica, 47, 331–359, 1979) where the low risk agent is only partially insured. The presence of the distortion in the insurance market changes the affinity of labor, and in some cases, we show that the scope of redistribution and the resulting social welfare are higher under asymmetric information than under full information. We also show that the increase in social insurance affects the utility and labor incentive of the low risk type by relaxing the self-selection constraint in the insurance market. The policy implications of the redistributive taxation and social insurance are analytically and numerically examined.      

Heterogeneous Agents and the Indifference Pricing of Property Index Linked Swaps

Swap spreads predicted by the traditional risk-neutral valuation models are much lower than the quoted market spreads for property index linked swaps (Patel and Pereira, Journal of Real Estate Finance and Economics, 36:5–21, 2008). This paper attempts to develop a utility indifference-based model for evaluating the reservation spreads of swap receivers and payers based on the principle of expected wealth utility equivalence rather than the traditional risk-neutral argument. Under the proposed model framework, this paper addresses the determination of the swap spreads. When the incompleteness of real estate markets and heterogeneity of representative agents are taken into consideration, it is shown that the agents’ risk preferences and heterogeneous beliefs about expected future property returns are the remarkable determinants for the swap spreads. Our model also identifies market power and the settlement rules in the event of counterparty default as important factors in determining the swap spreads. Our model provides a possible interpretation for the difference between the spreads predicted by the traditional models and the actual market spreads.     

A remark on static hedging of options written on the last exit time

In this paper, several different static hedges of the option written on the last exit time are given. One of them was originally presented in Akahori et al. (Methodol Comput Appl Probab 11(4): 661–668, 2009). Another one is derived from an expression in Madan et al. (Asia Pac Financ Mark 15(2): 97–115, 2008d). It is remarked in this paper that these static hedges are also obtained by applying a method in Carr and Chou (Hedging complex barrier options, 2001).     

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.     

How well do investors understand loss persistence?

This paper examines investors’ expectations of loss persistence. I develop a model to forecast loss firms’ future earnings based on Joos and Plesko, The Accounting Review 80: 847–870, (2005). This model produces smaller forecast errors than two random walk models and a model that assumes losses are transitory. The results suggest that investors do not fully distinguish the differences in loss persistence captured by the model and instead appear to assume that all losses are transitory. Consequently, investors are surprised by future announcements of negative earnings for firms with predicted persistent losses, and these firms experience significantly negative abnormal returns over the following four quarters. Additional results indicate that the future negative returns of firms with predicted persistent losses are smaller in magnitude when these firms are followed by analysts. The results are robust to controls for various price anomalies and are not driven by short sale constraints.     

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.