The interest rate sensitivity of equity prices with respect to systematic risk and leverage

This study extends the previous empirical research into the sensitibity of equity prices to include interest rates. Specifically, the null hypothesis that the interest rate sensitivity of equity prices is independent of the level of systematic risk and financial leverage is tested. The hypothesis is tested using a short-term and long-term interest rate index. The results show that the interest rate sensitivity of equity prices is independent of the amount of financial leverage but not independent of the level of systematic risk.     

A two‐mean reverting‐factor model of the term structure of interest rates

This article presents a two‐factor model of the term structure of interest rates. It is assumed that default‐free discount bond prices are determined by the time to maturity and two factors, the long‐term interest rate, and the spread (i.e., the difference) between the short‐term (instantaneous) risk‐free rate of interest and the long‐term rate. Assuming that both factors follow a joint Ornstein‐Uhlenbeck process, a general bond pricing equation is derived. Closed‐form expressions for prices of bonds and interest rate derivatives are obtained. The analytical formula for derivatives is applied to price European options on discount bonds and more complex types of options. Finally, empirical evidence of the model's performance in comparison with an alternative two‐factor (Vasicek‐CIR) model is presented. The findings show that both models exhibit a similar behavior for the shortest maturities. However, importantly, the results demonstrate that modeling the volatility in the long‐term rate process can help to fit the observed data, and can improve the prediction of the future movements in medium‐ and long‐term interest rates. So it is not so clear which is the best model to be used. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23: 1075–1105, 2003     

PRICE‐ADMISSIBILITY CONDITIONS FOR ARBITRAGE‐FREE LINEAR PRICE FUNCTION MODELS FOR THE TERM STRUCTURE OF INTEREST RATES

To assure price admissibility—that all bond prices, yields, and forward rates remain positive—we show how to control the state variables within the class of arbitrage‐free linear price function models for the evolution of interest rate yield curves over time. Price admissibility is necessary to preclude cash‐and‐carry arbitrage, a market imperfection that can happen even with a risk‐neutral diffusion process and positive bond prices. We assure price admissibility by (i) defining the state variables to be scaled partial sums of weighted coefficients of the exponential terms in the bond pricing function, (ii) identifying a simplex within which these state variables remain price admissible, and (iii) choosing a general functional form for the diffusion that selectively diminishes near the simplex boundary. By assuring that prices, yields, and forward rates remain positive with tractable diffusions for the physical and risk‐neutral measures, an obstacle is removed from the wider acceptance of interest rate methods that are linear in prices.     

Pricing Stock Options in a Jump‐Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods

Fast closed form solutions for prices on European stock options are developed in a jump‐diffusion model with stochastic volatility and stochastic interest rates. The probability functions in the solutions are computed by using the Fourier inversion formula for distribution functions. The model is calibrated for the S and P 500 and is used to analyze several effects on option prices, including interest rate variability, the negative correlation between stock returns and volatility, and the negative correlation between stock returns and interest rates.     

A YIELD-FACTOR MODEL OF INTEREST RATES

This paper presents a consistent and arbitrage-free multifactor model of the term structure of interest rates in which yields at selected fixed maturities follow a parametric muitivariate Markov diffusion process with "stochastic volatility." the yield of any zero-coupon bond is taken to be a maturity-dependent affine combination of the selected "basis" set of yields. We provide necessary and sufficient conditions on the stochastic model for this affine representation. We include numerical techniques for solving the model, as well as numerical techniques for calculating the prices of term-structure derivative prices. the case of jump diffusions is also considered.     

Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates

Black's (1995) model of interest rates as options assumes that there is a shadow instantaneous interest rate that can become negative, while the nominal instantaneous interest rate is a positive part of the shadow rate due to the option to convert to currency. As a result of this currency option, all term rates are strictly positive. A similar model was independently discussed by Rogers (1995) . When the shadow rate is modeled as a diffusion, we interpret the zero-coupon bond as a Laplace transform of the area functional of the underlying shadow rate diffusion (evaluated at the unit value of the transform parameter). Using the method of eigenfunction expansions, we derive analytical solutions for zero-coupon bonds and bond options under the Vasicek and shifted CIR processes for the shadow rate. This class of models can be used to model low interest rate regimes. As an illustration, we calibrate the model with the Vasicek shadow rate to the Japanese Government Bond data and show that the model provides an excellent fit to the Japanese term structure. The current implied value of the instantaneous shadow rate in Japan is negative.     

An empirical comparison of continuous time models of the short term interest rate

This article tests the performance of a wide variety of well-known continuous time models—with particular emphasis on the Black, Derman, and Toy (1990; henceforth BDT) term structure model—in capturing the stochastic behavior of the short term interest rate volatility. Many popular interest rate models are nested within a more flexible time-varying BDT framework that allows us to compare the models and find the proper specification of the dynamics of short rates. The empirical results indicate that the equilibrium models that do not allow the drift and diffusion parameters to vary over time and parameterize the volatility only as a function of interest rate levels overemphasize the sensitivity of volatility to the level of interest rate and fail to model adequately the serial correlation in conditional variances. On the other hand, the GARCH-based arbitrage-free models with time-dependent parameters in the drift and diffusion functions define the volatility only as a function of unexpected information shocks and fail to capture adequately the relationship between interest rate levels and volatility. This study shows that the most successful models in capturing the dynamics of short term interest rates are those that introduce time-dependent parameters to the short rate process and define the conditional volatility as a function of both the interest rate levels and the last period's unexpected news. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 777–797, 1999     

VASIČEK BEYOND THE NORMAL

A general Ornstein-Uhlenbeck (OU) process is obtained upon replacing the Brownian motion appearing in the defining stochastic differential equation with a general Lévy process. Certain properties of the Brownian ancestor are distribution-free and carry over to the general OU process. Explicit expressions are obtainable for expected values of a number of functionals of interest also in the general case. Special attention is paid here to gamma- and Poisson-driven OU processes. The Brownian, Poisson, and gamma versions of the OU process are compared in various respects; in particular, their aptitude to describe stochastic interest rates is discussed in view of some standard issues in financial and actuarial mathematics: prices of zero-coupon bonds, moments of present values, and probability distributions of present values of perpetuities. The problem of possible negative interest rates finds its resolution in the general setup by taking the driving Lévy process to be nondecreasing.     

Can exchange seat prices predict financial market volatility?

There is considerable evidence that trading volume and volatility are positively related and that exchange seat prices are largely a function of trading volume. This article examines whether changes in seat prices at the Chicago Board of Trade (where stock index and interest rate futures account for the vast majority of trading volume) are useful in predicting changes in interest rate and stock market volatility. Exponential GARCH and transfer function models are used to demonstrate the power of changes in CBOT seat prices in predicting changes in interest rate and stock market volatility. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1206–1221, 2008     

Prices of deep discount bonds and the Revenue Act of 1978: An evaluation of market response

This article explores the market response of deep discount corporate bonds to the reduction in the capital gains tax rate incorporated into the Revenue Act of 1978. Such tax change should have increased the desirability of assets acquired for capital gains potential, such as deep discount bonds. Examining a time series of prices and returns for a sample of deep discount corporate bonds and a control group of comparable duration and credit risk corporate bonds selling at or near par did indeed provide evidence of a market price reaction. Moreover, the price changes for the deep discount bonds occurred well in advance of the implementation of the tax change.     

What risks do corporate bond put features insure against?

Corporate bond prices are known to be influenced by default and term structure risk in addition to non‐default risks such as illiquidity. Putable corporate bonds allow investors to sell their holdings back to the issuer and may thus provide insurance against all of these risks. We first document empirically that embedded put option values are related to proxies for all three. In a second step, we develop a valuation model that simultaneously captures default and interest rate risk. We use this model to disentangle the reduction in yield spread enjoyed by putable bonds that can be attributed to each risk. Perhaps surprisingly, the most important reduction is due to mitigated default or spread risk, followed by term structure risk. The reduction in the non‐default component is present but rather small.     

INTENSITY-BASED VALUATION OF RESIDENTIAL MORTGAGES: AN ANALYTICALLY TRACTABLE MODEL

This paper presents an analytically tractable valuation model for residential mortgages. The random mortgage prepayment time is assumed to have an intensity process of the form h _t = h ₀( t ) +γ ( k − r _t )⁺ , where h ₀( t ) is a deterministic function of time, r _t is the short rate, and γ and k are scalar parameters. The first term models exogenous prepayment independent of interest rates (e.g., a multiple of the PSA prepayment function). The second term models refinancing due to declining interest rates and is proportional to the positive part of the distance between a constant threshold level and the current short rate. When the short rate follows a CIR diffusion, we are able to solve the model analytically and find explicit expressions for the present value of the mortgage contract, its principal-only and interest-only parts, as well as their deltas. Mortgage rates at origination are found by solving a non-linear equation. Our solution method is based on explicitly constructing an eigenfunction expansion of the pricing semigroup, a Feynman-Kac semigroup of the CIR diffusion killed at an additive functional that is a linear combination of the integral of the CIR process and an area below a constant threshold and above the process sample path (the so-called area functional). A sensitivity analysis of the term structure of mortgage rates and calibration of the model to market data are presented.     

On approximating deep in‐the‐money Asian options under exponential Lévy processes

This note proposes a new approach of valuing deep in‐the‐money fixed strike and discretely monitoring arithmetic Asian options. This new approach prices Asian options whose underlying asset price evolves according to the exponential of a Lévy process as a weighted sum of European options. Numerical results from experimenting on three different types of Lévy processes—a diffusion process, a jump diffusion process, and a pure jump process—illustrate the accuracy of the approach. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark     

Effect of Energy Prices on Economic Growth in the ECOWAS Sub-Region: Investigating the Channels Using Panel Data

The article empirically examines the effect of energy prices on economic growth within the Economic Community of West African States sub-region by acknowledging that the effect of energy prices on growth is quintessentially indirect and hence can be tracked through some channels. Exploiting the System Generalized Methods of Moments estimation technique for the period spanning 2002–2015, the results indicate that the overall effect of energy prices on economic growth is significantly negative. This effect propagates mainly through government consumption expenditure and investment, albeit its effect through real interest rate is positive. However, its negative effects on government consumption, investment, and exchange rate significantly overwhelm the positive effect from real interest rate.     

On dynamics in a Keynesian model of monetary and fiscal stabilization policy mix with twin debt accumulation

In this paper, a six‐dimensional model of flexible prices with the monetary and fiscal policy mix, describing the development of the firms’ private debt, the output, the expected rate of inflation, the rate of interest, government expenditure, and government bonds are analyzed. The stress put on the “twin debt accumulation” means that in our model both private debt accumulation and the public debt (government bond) accumulation are explicitly introduced. Questions concerning the existence of limit cycles around its normal equilibrium point are investigated. The bifurcation equation is found. The formulae for the calculation of its coefficients are gained. Numerical example illustrating the results attained is presented by means of numerical simulations.     

ASSET PRICES,OUTPUT AND MONETARY POLICY IN A SMALL OPEN ECONOMY

We formulate a macro‐model of a small open economy in order to investigate the relative performance of rules that respond to asset prices and those that do not. Our model consists of three asset prices: the stock price, the long‐term interest rate and the exchange rate. These asset prices interact with nominal wage and price Phillips curves, a law of motion for the labour share, a dynamic IS curve that describes output adjustment and a Taylor‐type interest rate policy rule. Estimations of the model show that policy rules that respond to asset price movements dominate rules that do not.     

A TEST OF A GENERAL EQUILIBRIUM STOCK OPTION PRICING MODEL

An empirical version of the Cox, Ingersoll, and Ross (1985a) call option pricing model is derived, assuming execution price uncertainty in the options market. the pricing restrictions come in the form of moment conditions in the option pricing error. These can be estimated and tested using a version of the method of simulated moments (MSM). Simulation estimates, obtained by discretely approximating the risk-neutral processes of the underlying stock price and the interest rate, are substituted for analytically unknown call prices. the asymptotics and other aspects of the MSM estimator are discussed. the model is tested on transaction prices at 15-minute intervals. It substantially outperforms the Black-Scholes model. the empirical success of the Cox-Ingersoll-Ross model implies that the continuous-time interest rate implicit in synchronous transaction quotes of 90-day Treasury-bill futures contracts is an-albeit noisy-proxy for the instantaneous volatility on common stock. the process of the instantaneous volatility is found to be close to nonstationary. It is well approximated by a heteroskedastic unit-root process. With this approximation, the Cox-Ingersoll-Ross model only slightly overprices long-maturity options.     

Simultaneous option prices and an implied risk-free rate of interest: A test of the Black-Scholes models

Two parameters in the Black-Scholes model, the risk-free rate of interest and standard deviation of stock returns, cannot be directly observed. Nevertheless, it is possible to simultaneously solve for the two parameters by using the prices of two different options written on the same security. If the Black-Scholes model is valid, then the implied interest rate from one repair of options should equal the implied interest rate from another pair of options for a given trading day. The analysis reexamines simultaneous option price data from a previous study using the implied interest rate test, and the results support the validity of the Black-Scholes model if we consider the bid/ask spread of option prices and that options are traded over discrete intervals.     

A GENERAL EQUILIBRIUM MODEL OF A MULTIFIRM MORAL‐HAZARD ECONOMY WITH FINANCIAL MARKETS

We present a general equilibrium model of a moral‐hazard economy with many firms and financial markets, where stocks and bonds are traded. Contrary to the principal‐agent literature, we argue that optimal contracting in an infinite economy is not about a tradeoff between risk sharing and incentives, but it is all about incentives. Even when the economy is finite, optimal contracts do not depend on principals’ risk aversion, but on market prices of risks. We also show that optimal contracting does not require relative performance evaluation, that the second best risk‐free interest rate is lower than that of the first best, and that the second‐best equity premium can be higher or lower than that of the first best. Moral hazard can contribute to the resolution of the risk‐free rate puzzle. Its potential to explain the equity premium puzzle is examined.