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TJ Mather - Financial Mathematics Papers
Two-State Markovian Representations of Term Structure Dynamics
Date: January 1998
Abstract:
This paper considers a family of models for pricing interest rate
derivatives where the term structure is Markov with respect to two state
variables.
These models belong to the class of Heath, Jarrow, and Morton models in that
the initial forward rate curve and volatility structures
are inputs to the model. In this family, the forward rate
volatility structure at time t is a function of time, maturity date, the
spot interest rate at time t, and a state variable which captures the
history of the Brownian motion up to time t.
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How does the Interest Rate Volatility depend on the level of the Interest Rate?
Date: May 1998
Abstract:
This paper investigates the dependence of the interest rate volatility
on the level of the interest rate. It considers a class of models
which are Markov with respect to two state variables. In this family,
the interest rate volatility of the form sigma r^gamma.
This paper attempts to find the gamma which best explains a
series of cap prices.
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Does Observed Skewness and Kurtosis Imply a
Stochastic Volatility or Jump Diffusion Model?
Date: May 1999
Abstract:
This paper considers two classes of volatility models, stochastic volatility
and jump-diffusion models. It calculates the
term structure of skewness and kurtosis of the
distributions given by these models and compares that to the
skewness and kurtosis as implied by empirical data.
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Last updated November 9th, 2001
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