A general characterization of one factor affine term structure models

We give a complete characterization of affine term structure models based on a general nonnegative Markov short rate process. This applies to the classical CIR model but includes as well short rate processes with jumps. We provide a link to the theory of branching processes and show how CBI-processes naturally enter the field of term structure modelling. Using Markov semigroup theory we exploit the full structure behind an affine term structure model and provide a deeper understanding of some well-known properties of the CIR model. Based on these fundamental results we construct a new short rate model with jumps, which extends the CIR model and still gives closed form expressions for bond options. Manusript received: June 2000, final version received: October 2000     

Convexity theory for the term structure equation

We study the convexity and model parameter monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide sharp conditions on the model parameters under which the convexity of the price in the short rate is guaranteed. Under these conditions, the price is decreasing in the drift and increasing in the volatility of the short rate. We also study the convexity properties of the logarithm of the price and find simple conditions on the coefficients that guarantee that the price is log-convex or log-concave.      

Fractals in trade duration: capturing long-range dependence and heavy tailedness in modeling trade duration

Several studies that have investigated a few stocks have found that the spacing between consecutive financial transactions (referred to as trade duration) tend to exhibit long-range dependence, heavy tailedness, and clustering. In this study, we empirically investigate whether a larger sample of stocks exhibit those characteristics. We do so by comparing goodness of fit in modeling trade duration data for stable distribution and fractional stable noise based on a procedure applying bootstrap methods developed by the authors with several alternative distributional assumptions in modeling trade duration data. The empirical results suggest that the autoregressive conditional duration model with stable distribution fits better than other combinations, while fractional stable noise itself fits better for the time series of trade duration. Our result is consistent with the general findings in the literature that trade duration is informative and that short trade durations move prices more than long trade duration. In addition, our result confirms the advantage of fractal models in the study of roughness in trade duration and provides some evidence for duration dependence. S. Rachev’s research was supported by grants from the Division of Mathematical, Life and Physical Science, College of Letters and Science, University of California, Santa Barbara, and the Deutschen Forschungsgemeinschaft. W. Sun’s research was supported by grants from the Deutschen Forschungsgemeinschaft. P.S. Kalev’s research was supported with a NCG grant from the Faculty of Business and Economics, Monash University. Data are supplied by Securities Industry Research Center of Asia-Pacific (SIRCA) on behalf of Reuters. The first draft of this paper was presented at the International Conference on High Frequency Finance 2006; the authors would like to thank the conference participants for their valuable comments.     

An analysis of asymmetry in foreign currency exposure of the Australian equities market

Using both daily and monthly data, the authors: (a) analyse the extra-market component of foreign exchange exposure of the Australian equities market using the Australian/US exchange rate factor return in an augmented market model; and (b) use a dummy variable specification to model the potential asymmetric effect induced by non-linear hedging strategies, such as using currency options, for the period 1988–1996. Overall, the results are mixed. The following are found: (i) stronger evidence of foreign exchange exposure in the analysis employing daily data; (ii) when using daily data, a stronger lagged response than a contemporaneous response is observed; (iii) some evidence of asymmetry; and (iv) evidence of significant exchange rate exposures of the predicted sign in several industries. Further, the findings using monthly data are less significant than those using daily data.     

THE SURVIVAL ZONE FOR A BOND WITH BOTH CALL AND PUT OPTIONS EMBEDDED

We present a numerical method to price bonds that have multiple embedded options with an emphasis on the case with both long call and short put options. The valuation framework is a one-factor model for the term structure of interest rates, where the instantaneous interest rate is allowed to follow a fairly general stochastic process. The equilibrium interest rates that define the free boundaries for the embedded call and put options are given. We demonstrate the survival zone within which a bond with both long call and short put options remains afloat. We show that even moderate levels of transaction costs can have a significant effect on exercise of options.     

A link between complete models with stochastic volatility and ARCH models

In this paper, we propose a heteroskedastic model in discrete time which converges, when the sampling interval goes to zero, towards the complete model with stochastic volatility in continuous time described in Hobson and Rogers (1998). Then, we study its stationarity and moment properties. In particular, we exhibit a specific model which shares many properties with the GARCH(1,1) model, establishing a clear link between the two approaches. We also prove the consistency of the pseudo conditional likelihood maximum estimates for this specific model.Received: December 2002Mathematics Subject Classification: 90A09, 60J60, 62M05JEL Classification: C32This work was supported in part by Dynstoch European network. Thanks to David Hobson for introducing me to these models, and to Valentine Genon-Catalot for numerous and very fruitful discussion on this work. The author is also grateful to Uwe Kuchler for various helpful suggestions, and to two referees and an associate editor for their comments and suggestions.     

Fast and accurate pricing of barrier options under Lévy processes

We suggest two new fast and accurate methods, the fast Wiener–Hopf (FWH) method and the iterative Wiener–Hopf (IWH) method, for pricing barrier options for a wide class of Lévy processes. Both methods use the Wiener–Hopf factorization and the fast Fourier transform algorithm. We demonstrate the accuracy and fast convergence of both methods using Monte Carlo simulations and an accurate finite difference scheme, compare our results with those obtained by the Cont–Voltchkova method, and explain the differences in prices near the barrier. The first author is supported, in part, by grant RFBR 09-01-00781.     

Fair (intra-bank transfer) prices for credits with stochastic recovery

In a discrete time stationary setting we derive explicit formulas for the value of a coupon paying defaultable credit contract with stochastic recovery. The pricing method is based on a perfect replication argument using simple 1-period insurance contracts. This work was financially supported by the Christian Doppler Research Association (CDG). The author gratefully acknowledges a fruitful collaboration and continued support by Bank Austria through CDG.     

Investment under uncertainty and time-inconsistent preferences

While standard real options models assume that agents possess a constant rate of time preference, there is substantial evidence that agents are impatient about choices in the short term but are patient when choosing between long-term alternatives. We extend the real options framework to model the investment-timing decisions of entrepreneurs with time-inconsistent preferences. The impact on investment-timing depends on such factors as whether entrepreneurs are sophisticated or naive in their expectations regarding their future time-inconsistent behavior, and whether the payoff from investment occurs all at once or over time. The model is extended to the case of a competitive equilibrium.     

THE PROPOSED INTRODUCTION OF FUTURES‐STYLE MARGINING IN THE UNITED STATES: AN AUSTRALIAN COMPARISON

We extend the quadratic approximation method to examine American‐style options traded using futures‐style margining and show that an early exercise premium can exist when the cost of carry is negative. Empirical results based on a reduced form of the model using futures‐style call options traded on the Australian All Ordinaries Share Price Index are consistent with previous research: call option early exercise premiums are economically zero. Full option prices are examined by comparing observed futures‐style with theoretical stock‐style values. We find futures‐style values exceed stock‐style values and argue that the increase results from improvements in liquidity. The findings are particularly relevant given the pending decision at the Commodity Futures Trading Commission to introduce a futures‐style system in the United States. JEL classification: G13, C13     

A jump to default extended CEV model: an application of Bessel processes

We develop a flexible and analytically tractable framework which unifies the valuation of corporate liabilities, credit derivatives, and equity derivatives. We assume that the stock price follows a diffusion, punctuated by a possible jump to zero (default). To capture the positive link between default and equity volatility, we assume that the hazard rate of default is an increasing affine function of the instantaneous variance of returns on the underlying stock. To capture the negative link between volatility and stock price, we assume a constant elasticity of variance (CEV) specification for the instantaneous stock volatility prior to default. We show that deterministic changes of time and scale reduce our stock price process to a standard Bessel process with killing. This reduction permits the development of completely explicit closed form solutions for risk-neutral survival probabilities, CDS spreads, corporate bond values, and European-style equity options. Furthermore, our valuation model is sufficiently flexible so that it can be calibrated to exactly match arbitrarily given term structures of CDS spreads, interest rates, dividend yields, and at-the-money implied volatilities.     

Pricing of Defaultable Bonds with Log-Normal Spread: Development of the Model and an Application to Argentinean and Brazilian Bonds During the Argentine Crisis

In this paper we describe a two-factor model for a defaultable discount bond, assuming log-normal dynamics with bounded volatility for the instantaneous short rate spread. Under some simplified hypothesis, we obtain an explicit barrier-type solution for zero recovery and constant recovery. We also present a numerical application for Argentinean and Brazilian Sovereign Bonds during the default crisis of Argentina.JEL Classification: G 13