Journal ArticleDOI
Squared Bessel Processes and Their Applications to the Square Root Interest Rate Model
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In this article, the Bessel process with time-varying dimension is generalized to the extended Cox-Ingersoll-Ross model with time varying parameters, and a special class of extended CIR models is studied.Abstract:
We study the Bessel processes withtime-varying dimension and their applications to the extended Cox-Ingersoll-Rossmodel with time-varying parameters. It is known that the classical CIR model is amodified Bessel process with deterministic time and scale change. We show thatthis relation can be generalized for the extended CIR model with time-varyingparameters, if we consider Bessel process with time-varying dimension. Thisenables us to evaluate the arbitrage free prices of discounted bonds and theircontingent claims applying the basic properties of Bessel processes. Furthermorewe study a special class of extended CIR models which not only enables us to fitevery arbitrage free initial term structure, but also to give the extended CIRcall option pricing formula.read more
Citations
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Journal ArticleDOI
A survey and some generalizations of Bessel processes
Anja Göing-Jaeschke,Marc Yor +1 more
TL;DR: In this article, the first hitting times of squared Bessel processes and radial Ornstein-Uhlenbeck processes with negative dimensions or negative starting points are studied. But the authors focus on the first time a Bessel process hits a given barrier.
Journal ArticleDOI
Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility
TL;DR: In this article, the authors present a verification result for portfolio problems with stochastic volatility, showing that only under a specific condition on the model parameters does the problem possess a unique solution leading to a partial equilibrium.
Book ChapterDOI
A Minimal Financial Market Model
TL;DR: In this paper, an advanced financial market model should be analytically tractable and must reflect with a minimal number of factors essential stylised empirical facts, and it must work equally well for derivative pricing and hedging as well as for risk measurement and portfolio management.
Journal ArticleDOI
On the pricing of forward starting options in Heston’s model on stochastic volatility
Susanne Kruse,Ulrich Nögel +1 more
TL;DR: A new and more suitable formula is developed that allows to cover the smile effects observed in a Black-Scholes environment, in which the extreme exposure of forward starting options to volatility changes is ignored.
Journal ArticleDOI
Pricing catastrophe risk bonds: A mixed approximation method
Zonggang Ma,Chaoqun Ma +1 more
TL;DR: In this paper, a contingent claim model similar to the one described by Lee and Yu (2002) for pricing catastrophe risk bonds was presented, and a bond pricing formula was derived in a stochastic interest rates environment with the losses following a compound nonhomogeneous Poisson process.
References
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Book
Brownian Motion and Stochastic Calculus
TL;DR: In this paper, the authors present a characterization of continuous local martingales with respect to Brownian motion in terms of Markov properties, including the strong Markov property, and a generalized version of the Ito rule.
Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Book
Continuous martingales and Brownian motion
Daniel Revuz,Marc Yor +1 more
TL;DR: In this article, the authors present a comprehensive survey of the literature on limit theorems in distribution in function spaces, including Girsanov's Theorem, Bessel Processes, and Ray-Knight Theorem.
Journal ArticleDOI
A Theory of the Term Structure of Interest Rates.
TL;DR: In this paper, the authors use an intertemporal general equilibrium asset pricing model to study the term structure of interest rates and find that anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices.