On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives

This paper analyses the robustness of Least-Squares Monte Carlo, a technique proposed by Longstaff and Schwartz (2001) for pricing American options. This method is based on least-squares regressions in which the explanatory variables are certain polynomial functions. We analyze the impact of different basis functions on option prices. Numerical results for American put options show that this approach is quite robust to the choice of basis functions. For more complex derivatives, this choice can slightly affect option prices. This revised version was published online in June 2006 with corrections to the Cover Date.     

Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models

This paper demonstrates how to value American interest rate options under the jump-extended constant-elasticity-of-variance (CEV) models. We consider both exponential jumps (see Duffie et al., 2000) and lognormal jumps (see Johannes, 2004) in the short rate process. We show how to superimpose recombining multinomial jump trees on the diffusion trees, creating mixed jump-diffusion trees for the CEV models of short rate extended with exponential and lognormal jumps. Our simulations for the special case of jump-extended Cox, Ingersoll, and Ross (CIR) square root model show a significant computational advantage over the Longstaff and Schwartz’s (2001) least-squares regression method (LSM) for pricing American options on zero-coupon bonds.     

Refining the least squares Monte Carlo method by imposing structure

The least squares Monte Carlo method of Longstaff and Schwartz has become a standard numerical method for option pricing with many potential risk factors. An important choice in the method is the number of regressors to use and using too few or too many regressors leads to biased results. This is so particularly when considering multiple risk factors or when simulation is computationally expensive and hence relatively few paths can be used. In this paper we show that by imposing structure in the regression problem we can improve the method by reducing the bias. This holds across different maturities, for different categories of moneyness and for different types of option payoffs and often leads to significantly increased efficiency.     

A UK Test of an Inflation‐Adjusted Ohlson Model

Abstract:   This paper conducts a UK test of a version of the Ohlson (1995) model. We should only expect abnormal earnings to revert to zero if the book value of assets is economically meaningful. In this paper we make use of the property revaluations common in UK accounts, but estimate other asset values and earnings in inflation‐adjusted terms. This, we argue, gives rise to estimates of abnormal earnings that can reasonably be expected to revert to zero. We then test this modified model on UK data using the Dechow, Hutton and Sloan (1999) method. In line with the predictions of the Ohlson model, we find that these modified abnormal earnings appear to mean revert, and that a first order autoregressive process is sufficient to capture the persistence of UK real abnormal earnings. The modified abnormal earnings model in general predicts one year ahead earnings more successfully than an unmodified model. Furthermore, for much of the sample period, one year ahead predictions of abnormal earnings are better for the real model during periods of higher inflation. The undervaluation problem found in prior studies appears to be replaced with an overvaluation problem in the real model which is more acute during periods of high inflation. Last, we show that an estimate of the model based upon an industry level specification appears to perform no better than a market‐wide specification of the model.     

The Dynamics of Short-Term Interest Rate Volatility Reconsidered

In this paper we present and estimate a model of short-term interest rate volatility that encompasses both the level effect of Chan, Karolyi, Longstaff and Sanders (1992) and the conditional heteroskedasticity effect of the GARCH class of models. This flexible specification allows different effects to dominate as the level of the interest rate varies. We also investigate implications for the pricing of bond options. Our findings indicate that the inclusion of a volatility effect reduces the estimate of the level effect, and has option implications that differ significantly from the Chan, Karolyi, Longstaff and Sanders (1992) model.     

Continuous time and nonparametric modelling of U.S. interest rate models

In this paper we compare the forecasting performance of different models of interest rates using parametric and nonparametric estimation methods. In particular, we use three popular nonparametric methods, namely, artificial neural networks (ANN), k-nearest neighbour (k-NN), and local linear regression (LL). These are compared with forecasts obtained from two-factor continuous time interest rate models, namely, Chan, Karolyi, Longstaff, and Sanders [CKLS, J. Finance 47 (1992) 1209]; Cos, Ingersoll, and Ross [CIR, Econometrica 53 (1985) 385]; Brennan and Schwartz [BR-SC, J. Financ. Quant. Anal. 15 (1980) 907]; and Vasicek [J. Financ. Econ. 5 (1977) 177]. We find that while the parametric continuous time method, specifically Vasicek, produces the most successful forecasts, the nonparametric k-NN performed well.     

Expected Default Probabilities in Structural Models: Empirical Evidence

We apply a set of structural models (Black and Cox 1976; Collin-Dufresne and Goldstein 2001; Ericsson and Reneby 1998; Leland and Toft 1996; Longstaff and Schwartz 1995; Merton 1974) to estimate expected default probabilities (EDPs) for a sample of failed and non-failed UK real estate companies. Results are generally consistent with models’ predictions and estimates of EDPs for different models are closely clustered. The results of z-scores and synthetic ratings misclassify 33% of the total sample in contrast to 8% misclassification by structural models. Further analysis of EDPs based on logistic regressions suggests the observed misclassification of the companies by structural models is due to special company management and/or regulatory circumstances rather than limitations of these models.      

Investigating the leverage effect in commodity markets with a recursive estimation approach

This paper investigates the presence of the leverage effect in commodities, in comparison with financial markets. The EGARCH model with a Mixture of Normals distribution (EGARCH-MN) is used to capture (i) heavy tails and skewness in the conditional returns, and (ii) leverage effects and time-varying long-term component in the volatility specification. Besides, the estimation strategy relies on an innovative recursive (REC) method, which allows disentangling the leverage effect from the unconditional skewness as an empirical result. When applied to a broadly diversified dataset of assets during 1995–2012, the EGARCH-MN models offers state-of-the-art specifications with leverage and fat-tailed skewed densities, that allow to contrast the specific characteristics of commodities with traditional assets (equities, bonds, FX).     

Corporate yield spreads and real interest rates

The effect of inflation on the credit spreads of corporate bonds is investigated utilising real instead of nominal interest rates in extensions of the models proposed by Longstaff and Schwartz (1995) and Collin-Dufresne et al. (2001). Inflation is a critical, non-default, component incorporated in nominal bond yields, whose effect has not been considered by existing credit spread theory. In this sense the only true test of models of credit spread pricing must utilise real rates. To illustrate these requirements the Canadian bond data of Jacoby, Liao, and Batten (2009) is utilised. This Canadian data accommodates callability and the tax effects otherwise present in U.S. bond markets. The relation with historical default rates of both U.S. and Canadian bonds is also investigated since this approach is clean of both callability and tax effects. Overall, the analysis provides additional insights into the theoretical drivers of credit spreads as well as helping to explain observed corporate bond yield behaviour in financial markets.     

A computational definition of financial randomness

The aim of this study is to present an efficient and easy framework for the application of the Least Squares Monte Carlo methodology to the pricing of gas or power facilities as detailed in Boogert and de Jong [J. Derivatives, 2008, 15, 81–91]. As mentioned in the seminal paper by Longstaff and Schwartz [Rev. Financ. Stud. 2001, 113–147], the convergence of the Least Squares Monte Carlo algorithm depends on the convergence of the optimization combined with the convergence of the pure Monte Carlo method. In the context of the energy facilities, the optimization is more complex and its convergence is of fundamental importance in particular for the computation of sensitivities and optimal dispatched quantities. To our knowledge, an extensive study of the convergence, and hence of the reliability of the algorithm, has not been performed yet, in our opinion this is because the apparent infeasibility and complexity uses a very high number of simulations. We present then an easy way to simulate random trajectories by means of diffusion bridges in contrast to Dutt and Welke [J. Derivatives, 2008, 15 (4), 29–47] that considers time-reversal Itô diffusions and subordinated processes. In particular, we show that in the case of Cox-Ingersoll-Ross and Heston models, the bridge approach has the advantage to produce exact simulations even for non-Gaussian processes, in contrast to the time-reversal approach. Our methodology permits performing a backward dynamic programming strategy based on a huge number of simulations without storing the whole simulated trajectory. Generally, in the valuation of energy facilities, one is also interested in the forward recursion. We then design backward and forward recursion algorithms such that one can produce the same random trajectories by the use of multiple independent random streams without storing data at intermediate time steps. Finally, we show the advantages of our methodology for the valuation of virtual hydro power plants and gas storages.     

Asymmetric Mean Reversion in European Interest Rates: A Two-factor Model

Abstract

This paper tests for asymmetric mean reversion in European short-term interest rates using a combination of the interest rate models introduced by Longstaff and Schwartz (Longstaff, F.A., Schwarts, E.S. (1992) Interest rate volatility and the ferm structure: A two factor general equilibrium model, Journal of Finance, 48, pp. 1259–1282.) and Bali (Bali, T. (2000) Testing the empirical performance of stochastic volatility models of the short-term interest rates, Journal of Financial and Quantitative Analysis, 35, pp. 191–215.). Using weekly rates for France, Germany and the United Kingdom, it is found that short-term rates follow in all instances asymmetric mean reverting processes. Specifically, interest rates exhibit non-stationary behavior following rate increases, but they are strongly mean reverting following rate decreases. The mean reverting component is statistically and economically stronger thus offsetting non-stationarity. Volatility depends on past innovations past volatility and the level of interest rates. With respect to past innovations volatility is asymmetric rising more in response to positive innovations. This is exactly opposite to the asymmetry found in stock returns.     

Primal–dual quasi-Monte Carlo simulation with dimension reduction for pricing American options

The pricing of American options is one of the most challenging problems in financial engineering due to the involved optimal stopping time problem, which can be solved by using dynamic programming (DP). But applying DP is not always practical, especially when the state space is high dimensional. However, the curse of dimensionality can be overcome by Monte Carlo (MC) simulation. We can get lower and upper bounds by MC to ensure that the true price falls into a valid confidence interval. During the recent decades, progress has been made in using MC simulation to obtain both the lower bound by least-squares Monte Carlo method (LSM) and the upper bound by duality approach. However, there are few works on pricing American options using quasi-Monte Carlo (QMC) methods, especially to compute the upper bound. For comparing the sample variances and standard errors in the numerical experiments, randomized QMC (RQMC) methods are usually used. In this paper, we propose to use RQMC to replace MC simulation to compute both the lower bound (by the LSM) and the upper bound (by the duality approach). Moreover, we propose to use dimension reduction techniques, such as the Brownian bridge, principal component analysis, linear transformation and the gradients based principle component analysis. We perform numerical experiments on American–Asian options and American max-call options under the Black–Scholes model and the variance gamma model, in which the options have the path-dependent feature or are written on multiple underlying assets. We find that RQMC in combination with dimension reduction techniques can significantly increase the efficiency in computing both the lower and upper bounds, resulting in better estimates and tighter confidence intervals of the true price than pure MC simulation.     

The valuation of contingent claims using alternative numerical methods

This study compares the computational accuracy and efficiency of three numerical methods for the valuation of contingent claims written on multiple underlying assets; these are the trinomial tree, original Markov chain and Sobol–Markov chain approaches. The major findings of this study are: (i) the original Duan and Simonato (2001) Markov chain model provides more rapid convergence than the trinomial tree method, particularly in cases where the time to maturity period is less than nine months; (ii) when pricing options with longer maturity periods or with multiple underlying assets, the Sobol–Markov chain model can solve the problem of slow convergence encountered under the original Duan and Simonato (2001) Markov chain method; and (iii) since conditional density is used, as opposed to conditional probability, we can easily extend the Sobol–Markov chain model to the pricing of derivatives which are dependent on more than two underlying assets without dealing with high-dimensional integrals. We also use ‘executive stock options’ (ESOs) as an example to demonstrate that the Sobol–Markov chain method can easily be applied to the valuation of such ESOs.     

An Assessment of Empirical Model Performance When Financial Market Transactions are Observed at Different Data Frequencies: An Application to East Asian Exchange Rates

This paper compares the performance of alternative models of east Asian exchange rates at different data frequencies. Selected models employ different specifications of the conditional variance and the conditional error distribution. Conditional variance specifications include: homoscedasticity, GARCH, LGARCH, and EGARCH. Conditional error distribution specifications include normal and Student t. The best exchange rate model specification is clearly conditional on data frequency. Higher frequency (daily, weekly) data commonly exhibit characteristics that demand more sophisticated estimation methods than analysts commonly employ. These characteristics generally vanish at lower (monthly, quarterly) frequencies. Overall we find significant benefit from accommodating heteroscedasticity and leptokurtic properties of the conditional distribution as data frequency increases. Using a likelihood ratio test we compare the relative gain from addressing heteroscedasticity (through use of GARCH models) versus accommodation of leptokurtosis. This comparison suggests that the gains from correct specification of the conditional distribution dominate those obtained from addressing problems of heteroscedasticity.     

The 1999 Small Employer Retirement Survey

Abstract

In this article we examine to what extent policyholders buying a certain class of participating contracts (in which they are entitled to receive dividends from the insurer) can be described as standard bondholders. Our analysis extends the ideas of Biihlmann and sequences the fundamental advances of Merton, Longstaff and Schwartz, and Briys and de Varenne. In particular, we develop a setup where these participating policies are comparable to hybrid bonds but not to standard risky bonds (as done in most papers dealing with the pricing of participating contracts). In this mixed framework, policyholders are only partly protected against default consequences. Continuous and discrete protections are also studied in an early default Black and Cox-type setting. A comparative analysis of the impact of various protection schemes on ruin probabilities and severities of a life insurance company that sells only this class of contracts concludes this work.     

Are female CEOs associated with lower insolvency risk? Evidence from the US property-casualty insurance industry

This paper investigates the relationship between female CEOs and insolvency risk of US property-casualty insurance companies. We show that female CEOs are associated with lower insurer insolvency propensity, higher z-score, and lower standard deviation of return on assets. These findings are robust to alternative econometric specifications to address potential endogeneity concerns and self-selection issues, including propensity score matching, the instrumental variable approach, and the difference-in-difference approach. Furthermore, we find that the impact of female CEOs on insurer insolvency risk is moderated by firm capitalization, the presence of female directors, and political conservatism of insurers' home states.     

Further analysis of the expectations hypothesis using very short-term rates

Longstaff [Longstaff, F., 2000. The term structure of very short-term rates: new evidence for the expectations hypothesis. Journal of Financial Economics 58, 397–415] finds support for the expectations hypothesis at the very short end of the repurchase agreement (repo) term structure while other studies find calendar-time-based regularities cause rejection of the expectations hypothesis. Using Longstaff’s methods on a sample of repo rates that pre-dates Longstaff’s sample, we reject the expectations hypothesis for every maturity. The pre-Longstaff-sample repo data comes from a time period where the behavior of short-term interest rates is similar to the long-run average behavior of short-term interest rates. Our results imply that expectations hold when rates are less volatile and/or that we may be entering a period of lower volatility.     

Valuation and incentive effects of hurdle rate executive stock options

Traditional executive stock options are often criticized for inherently weak links between pay and performance. Hurdle rate executive stock options represent a viable improvement. However, valuing these options presents extraordinary analytic difficulties. With a constant dividend yield the strike price becomes a path-dependent function of the stock price and exact analytic valuation is intractable. To solve this problem, we apply the Monte Carlo valuation approach developed by Longstaff and Schwartz (Rev Financ Stud 4:113–147, 2001) to estimate the value of path-dependent American options. We also extend the methodology to incorporate the theoretical framework by Ingersoll (J Bus 79:453–487, 2006) to permit subjective valuation influenced by an executive’s risk aversion.

Mutual fund risk and market share-adjusted fund flows

Several papers use a fractional specification (net inflow/ assets under management) to infer a convex relation between flow and past performance. However, heterogeneous linear response functions combined with the pooled analysis commonly used in these studies can yield false convexity estimates. We show that such heterogeneity obtains in practice. Along these same lines, the paper also finds that several previously unexamined implications of a convex flow-performance relation fail to hold. Moreover, convexity with fractional flows (which we confirm) largely disappears in a conditional analysis that controls for heterogeneity. Market shares offer an alternative specification for flow that is more resilient to heterogeneity. Using this alternative specification, we again find no evidence of convexity in the flow-performance relation. We conclude that the widely held belief that the flow response function is convex is due solely to misspecification of the empirical model. The flow-return relation is linear.