Journal ArticleDOI
The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates
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In this article, it is shown that it is possible to specify the law of the state-price density process directly, which is a positive supermartingale and provides a rich framework for the generation of examples of such things.Abstract:
It is possible to specify a model for interest rates in various ways, by giving the dynamics of the spot rate or of the forward rates, for example. A less well–developed approach is to specify the law of the state–price density process directly. In abstract, the state–price density process is a positive supermartingale, and the theory of Markov processes provides a rich framework for the generation of examples of such things. We show how this can be done, and provide simple examples (some familiar, some new) where prices of derivatives can be computed very easily. One benefit of the potential approach is that it becomes very easy to model the yield curve in many countries at once, together with the exchange rates between them.read more
Citations
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Book
Arbitrage Theory in Continuous Time
TL;DR: In this article, the Martingale Approach to Arbitrage theory is used to model the Binomial Model and the Stochastic Optimal Control (SOC) model for short-term interest rates.
Journal ArticleDOI
The Term Structure of Interest Rates
TL;DR: This article reviewed the term structure of interest rates literature relating to the arbitrage-free pricing and hedging of interest rate derivatives and emphasized term structure theory, including the HJM model, forward and futures contracts, the expectations hypothesis, and pricing of caps/floors.
Journal ArticleDOI
Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk
TL;DR: In this article, the authors make use of the similarities between the force of mortality and interest rates to show how we can model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives.
Journal ArticleDOI
Asset Pricing under the Quadratic Class
Markus Leippold,Liuren Wu +1 more
TL;DR: In this paper, the authors identify and characterize a class of term structure models where bond yields are quadratic functions of the Markov process and provide two general transform methods in pricing a wide variety of fixed income derivatives in closed or semi-closed form.
Journal ArticleDOI
Stochastic risk premiums, stochastic skewness in currency options, and stochastic discount factors in international economies
TL;DR: In this article, the authors developed models of stochastic discount factors in international economies that produce risk premiums and skewness in currency options, using time-series returns and option prices on three currency pairs that form a triangular relation.
References
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Journal ArticleDOI
An equilibrium characterization of the term structure
TL;DR: In this article, the authors derived a general form of the term structure of interest rates and showed that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation.
Posted Content
Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation
TL;DR: In this article, a unifying theory for valuing contingent claims under a stochastic term structure of interest rates is presented, based on the equivalent martingale measure technique.
Journal ArticleDOI
Pricing Interest-Rate-Derivative Securities
John Hull,Alan White +1 more
TL;DR: In this paper, the extended Vasicek model is shown to be very tracta-ble analytically, and option prices are compared with those obtained using a number of other models.
Book
Diffusions, Markov processes, and martingales
TL;DR: In this paper, the second volume follows on from the first, concentrating on stochastic integrals, stochy differential equations, excursion theory and the general theory of processes.
Journal ArticleDOI
Term Structure Movements and Pricing Interest Rate Contingent Claims
Thomas S. Y. Ho,Sang Bin Lee +1 more
TL;DR: In this paper, an arbitrage-free interest rate movements model (AR model) is proposed to price interest rate contingent claims relative to the observed complete term structure of interest rates.