Classes of Interest Rate Models under the HJM Framework

Although the HJM term structure model is widely accepted as the mostgeneral, and perhaps the most consistent, framework under which to studyinterest rate derivatives, the earlier models of Vasicek,Cox–Ingersoll–Ross, Hull–White, andBlack–Karasinski remain popular among both academics andpractitioners. It is often stated that these models are special cases ofthe HJM framework, but the precise links have not been fully establishedin the literature. By beginning with certain forward rate volatilityprocesses, it is possible to obtain classes of interest models under theHJM framework that closely resemble the traditional models listed above.Further, greater insight into the dynamics of the interest rate processemerges as a result of natural links being established between the modelparameters and market observed variables.     

Traffic light options

This paper introduces, prices, and analyzes traffic light options. The traffic light option is an innovative structured OTC derivative developed independently by several London-based investment banks to suit the needs of Danish life and pension (L&P) companies, which must comply with the traffic light solvency stress test system introduced by the Danish Financial Supervisory Authority (DFSA) in June 2001. This monitoring system requires L&P companies to submit regular reports documenting the sensitivity of the companies’ base capital to certain pre-defined market shocks – the red and yellow light scenarios. These stress scenarios entail drops in interest rates as well as in stock prices, and traffic light options are thus designed to pay off and preserve sufficient capital when interest rates and stock prices fall simultaneously. Sweden’s FSA implemented a traffic light system in January 2006, and supervisory authorities in many other European countries have implemented similar regulation. Traffic light options are therefore likely to attract the attention of a wider audience of pension fund managers in the future. Focusing on the valuation of the traffic light option we set up a Black–Scholes/Hull–White model to describe stock market and interest rate dynamics, and analyze the traffic light option in this framework.     

Lean Trees—A General Approach for Improving Performance of Lattice Models for Option Pricing

The well-known binomial and trinomial tree models for option pricing are examined from the point of view of numerical efficiency. Common lattices use a large part of time resources for calculations which are almost irrelevant for the solution. To avoid this waste of resources, the tree is reduced to a lean form which yields the same order of convergence, but with a reduction of numerical effort. In numerical tests it is shown that the proposed method leads to a significant improvement in real calculation time without loss of accuracy for a broad class of derivatives.     

Environmental Conditions,Reservation Prices,and Time on the Market for Housing

A general analytical model to describe the impact of environmental disamenities on duration of sales is derived. A statistical technique to recover a sellers reservation price is proposed. An econometric procedure that consistently estimates market duration and a sellers reservation price is described. An application to the impact of highway noise on property values and market duration is presented. The estimation results show that, while highway noise has a significant negative impact on forming reservation prices and predicting sale prices, the noise effect on duration of sales is not statistically significant. Empirical evidence also shows a negative impact of market duration on reservation prices, which indicates an updating process for reservation prices over time.     

Cross-sectional tests of deterministic volatility functions

We study the cross-sectional performance of option pricing models in which the volatility of the underlying stock is a deterministic function of the stock price and time. For each date in our sample of FTSE 100 index option prices, we fit an implied binomial tree to the panel of all European style options with different strike prices and maturities and then examine how well this model prices a corresponding panel of American style options. We find that the implied binomial tree model performs no better than an ad-hoc procedure of smoothing Black–Scholes implied volatilities across strike prices and maturities. Our cross-sectional results complement the time-series findings of Dumas et al. [J. Finance 53 (1998) 2059].     

Pricing and Hedging Discount Bond Options in the Presence of Model Risk

This paper focuses on pricing and hedging options on a zero-coupon bond in a Heath–Jarrow–Morton (1992) framework when the value and/or functional form of forward interest rates volatility is unknown, but is assumed to lie between two fixed values. Due to the link existing between the drift and the diffusion coefficients of the forward rates in the Heath, Jarrow and Morton framework, this is equivalent to hedging and pricing the option when the underlying interest rate model is unknown. We show that a continuous rangeof option prices consistent with no arbitrage exist. This range is bounded by the smallest upper-hedging strategy and the largest lower-hedging strategy prices, which are characterized as the solutions of two non-linear partial differential equations. We also discuss several pricing and hedging illustrations.     

Estimating the term structures of corporate debt

This paper investigates the corporate bond market by estimating monthly interest rate term structures for investment grade credit classes using both S&P's and Moody's ratings. Term structures are modeled by a piecewise constant forward rate curve and estimated on noncallable coupon paying bonds issued by industrial firms. The iterative estimation algorithm minimizes the sum of squared errors between market prices and model prices while identifying and removing outliers from the sample. Although the forward rate model is successful at pricing corporate debt, additional factors are found to be significant at explaining the residual price error that remains after the forward rate model is fit to market prices. Six necessary no-arbitrage conditions are derived for the term structures of risky and risk-free debt. Occasionally, some of these no-arbitrage conditions are violated and a few violations are asymptotically statistically significant. Finally, trading strategies that capture mispricing in the corporate debt market and violations of no-arbitrage bounds are discussed.This paper was adapted from my dissertation, completed at Cornell University. An earlier version of this paper was titled The Term Structures of Corporate Debt. Thanks to participants at the Cornell University finance workshop, Warren Bailey, Peter Carr, Antoine Giannetti, and especially Robert Jarrow for their helpful comments.     

Theory of Storage and the Pricing of Commodity Claims

We extend the literature on commodity pricing by incorporating a link between the spread of forward prices and spot price volatility suggested by the theory of storage. Our model has closed form solutions that are generalizations of the two-factor model of Gibson–Schwartz (1990). We estimate the model on daily copper spot and forward prices using the Kalman filter methodology. Our findings confirm the link between the forward spread and volatility, but also show that the Gibson–Schwartz (1990) model prices forward contracts almost as well. In the pricing of option contracts, however, there are significant differences between the models.     

Efficient option pricing on stocks paying discrete or path-dependent dividends with the stair tree

Pricing options on a stock that pays discrete dividends has not been satisfactorily settled because of the conflicting demands of computational tractability and realistic modelling of the stock price process. Many papers assume that the stock price minus the present value of future dividends or the stock price plus the forward value of future dividends follows a lognormal diffusion process; however, these assumptions might produce unreasonable prices for some exotic options and American options. It is more realistic to assume that the stock price decreases by the amount of the dividend payout at the ex-dividend date and follows a lognormal diffusion process between adjacent ex-dividend dates, but analytical pricing formulas and efficient numerical methods are hard to develop. This paper introduces a new tree, the stair tree, that faithfully implements the aforementioned dividend model without approximations. The stair tree uses extra nodes only when it needs to simulate the price jumps due to dividend payouts and return to a more economical, simple structure at all other times. Thus it is simple to construct, easy to understand, and efficient. Numerous numerical calculations confirm the stair tree's superior performance to existing methods in terms of accuracy, speed, and/or generality. Besides, the stair tree can be extended to more general cases when future dividends are completely determined by past stock prices and dividends, making the stair tree able to model sophisticated dividend processes.     

An empirical investigation of asset pricing models under divergent lending and borrowing rates

Asset pricing theory implies that the estimate of the zero-beta rate should fall between divergent lending and borrowing rates. This paper proposes a formal test of this restriction using the difference between the prime loan rate and the 1-month Treasury bill rate as a proxy for the difference between borrowing and lending rates. Based on simulations, this paper shows that in the ordinary least squares case, the Fama and MacBeth (J Pol Econ 81:607–636, 1973) t-statistic has high power against a general alternative, which is not true of the Shanken (Rev Financ Stud 5:1–33, 1992) and Kan et al. (J Financ doi:10.1111/jofi.12035, 2013) t-statistics. In the generalized least squares case, all three t-statistics have high power. The empirical investigation highlights that only the intertemporal capital asset pricing model reasonably prices the zero-beta portfolio. Other models, such as the Fama and French (J Financ Econ 33:3–56, 1993) model, do not assign the correct value to the zero-beta rate.     

Static hedging and pricing American knock-in put options

This paper extends the static hedging portfolio (SHP) approach of  and  to price and hedge American knock-in put options under the Black–Scholes model and the constant elasticity of variance (CEV) model. We use standard European calls (puts) to construct the SHPs for American up-and-in (down-and-in) puts. We also use theta-matching condition to improve the performance of the SHP approach. Numerical results indicate that the hedging effectiveness of a bi-monthly SHP is far less risky than that of a delta-hedging portfolio with daily rebalance. The numerical accuracy of the proposed method is comparable to the trinomial tree methods of  and . Furthermore, the recalculation time (the term is explained in Section 1) of the option prices is much easier and quicker than the tree method when the stock price and/or time to maturity are changed.     

The capital asset pricing model as a general equilibrium with incomplete markets

We recast the capital asset pricing model (CAPM) in the broader context of general equilibrium with incomplete markets (GEI). In this setting we give proofs of three properties of CAPM equilibria: they are efficient, asset prices lie on a security market line, and all agents hold the same two mutual funds. The first property requires a riskless asset, the latter two do not. We show that across all GEI only one of these three properties of equilibrium is generally valid: asset prices depend on covariances, not variances. We extend CAPM to many consumption goods in such a way that all three properties hold. But now the definition of a riskless asset depends on preferences and endowments, and so cannot be specifieda priori.We wish to acknowledge assistance of NSF Grant No. 88-12051, and a referee's comments. We are grateful for conversations with H. Polemarchakis, especially concerning Section II.4.     

Bid-ask bounce and speads in the foreign exchange futures market

This paper examines the intraday bid-ask bounce in Deutschemark and Japanese yen futures prices. The intraday Markovian bid-ask bounce process, which leads to a desirable equilibrium condition of reaching a bid or an ask transaction type with equal chances, is identified. A second-order Markov chain transition matrix model is used to derive a generalized estimator of bid-ask spreads in the foreign exchange futures market. It incorporates the conditional probabilities of a subsequent transaction being the same type as the current transaction's () and that of the next transaction being the same as the current type but different from the previous type (). The specification is {-Cov(P _t ,P _t+1 )/[(1–)(–)]}^1/2. The empirical results show that the average implied bid-ask spread is about $10, which is less than one tick's value of $12.50. It is also found that spreads are higher at the beginning and end of the trading day than the rest of the day, reflecting the uncertainty due to information flows and overnight inventory carrying costs, respectively.     

Accounting-Based Valuation with Changing Interest Rates

This paper generalizes Ohlsons [Contemporary Accounting Research Vol. 11 No. 2. 661–687 (1995)] equity valuation framework to allow for stochastic interest rates. Much of this analysis initially deals with the specialized setting in which earnings suffice for cum-dividend value. In such a case, the beginning-of-period (lagged) rate determines the capitalization factor, not the current rate. The underlying earnings dynamic modifies the traditional random walk model via an additional term, namely current earnings multiplied by the percentage change in interest rates. The general model retains these basic aspects of the earnings-sufficiency setting. Empirical implications bear on the returns-to-earnings regression: The earnings-response coefficient decreases as the beginning-of-period rate increases.JEL Classification: M41, G12     

The Halloween Effect and Japanese Equity Prices: Myth or Exploitable Anomaly

Bouman and Jacobsen (American Economic Review 92(5), 1618–1635, 2002) examine monthly stock returns for major world stock markets and conclude that returns are significantly lower during the May–October periods versus the November–April periods in 36 of 37 markets examined. They argue that, in general, the Halloween strategy outperforms the buy and hold strategy thereby casting doubt on the validity of the efficient market paradigm. More recently, Maberly and Pierce (Econ Journal Watch 1(1), 29–46, 2004) re-examine the evidence for U.S. equity prices and conclude that Bouman and Jacobsen’s results are not robust to alternative model specifications. Extending prior research, this paper examines the robustness of the Halloween strategy to alternative model specifications for Japanese equity prices. The Halloween effect is concentrated in the period prior to the introduction of Nikkei 225 index futures in September 1986. After the internationalization of Japanese financial markets in the mid-1980s, the Halloween effect disappears.JEL classification: G14, G15