Real-World Forward Rate Dynamics With Affine Realizations
Eckhard Platen,Stefan Tappe +1 more
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In this article, the existence of affine realizations for Levy driven interest rate term structure models under the real-world probability measure was investigated under an assumed risk-neutral probability measure.Abstract:
We investigate the existence of affine realizations for Levy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral approach concerning the existence of affine realizations are transferred to the general case. A similar result holds true for models driven by compound Poisson processes with finite jump size distributions. However, in the presence of jumps with infinite activity we obtain severe restrictions on the structure of the market price of risk; typically, it must even be constant.read more
Citations
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Affine multiple yield curve models
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Affine realizations with affine state processes for stochastic partial differential equations
TL;DR: In this paper, the authors clarify when a stochastic partial differential equation with an affine realization admits affine state processes, including a characterization of the set of initial points of the realization.
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Existence of affine realizations for stochastic partial differential equations driven by Lévy processes
TL;DR: In this paper, the authors clarified when a semilinear stochastic partial differential equation driven by Levy processes admits an affine realization and provided several examples arising in natural sciences and economics.
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Invariance of closed convex cones for stochastic partial differential equations
TL;DR: In this article, the authors clarified when a closed convex cone is invariant for a stochastic partial differential equation (SPDE) driven by a Wiener process and a Poisson random measure.
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Affine realizations with affine state processes for stochastic partial differential equations
TL;DR: In this article, the authors clarify when a stochastic partial differential equation with an affine realization admits affine state processes, including a characterization of the set of initial points of the realization.
References
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Jean Jacod,Albert N. Shiryaev +1 more
TL;DR: In this article, the General Theory of Stochastic Processes, Semimartingales, and Stochastically Integrals is discussed and the convergence of Processes with Independent Increments is discussed.
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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.
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Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation'
TL;DR: In this article, the authors present a unifying theory for valuing contingent claims under a stochastic term structure of interest rates, based on the equivalent martingale measure technique.
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A Benchmark Approach to Quantitative Finance
Eckhard Platen,David Heath +1 more
TL;DR: Preliminaries from Probability Theory and Statistical Methods are used in this article to estimate the probability that a stock market will be a buy or sell in the next five years.
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Bond Market Structure in the Presence of Marked Point Processes
TL;DR: In this paper, the authors investigated the term structure of zero coupon bonds when interest rates are driven by a general marked point process as well as by a Wiener process and proved the existence of a time-independent set of basic bonds.