Journal ArticleDOI
Bond Market Structure in the Presence of Marked Point Processes
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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.Abstract:
We investigate 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. Developing a theory that allows for measure–valued trading portfolios, we study existence and uniqueness of a martingale measure. We also study completeness and its relation to the uniqueness of a martingale measure. For the case of a finite jump spectrum we give a fairly general completeness result and for a Wiener–Poisson model we prove the existence of a time–independent set of basic bonds. We also give sufficient conditions for the existence of an affine term structure.read more
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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
A Jump-Diffusion Model for Option Pricing
TL;DR: In this article, a double exponential jump-diffusion model is proposed for option pricing, which is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and path dependent options.
Journal ArticleDOI
Affine Processes and Applications in Finance
TL;DR: Regular affine processes as discussed by the authors unify the concepts of continuous state branching processes with immigration and Ornstein-Uhlenbeck type processes, and provide foundations for a wide range of financial applications.
Journal ArticleDOI
The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models
TL;DR: In this paper, the role of jumps in continuous-time short rate models is analyzed and a nonparametric jump-diffusion model is proposed to detect jump-induced misspecification.
Journal ArticleDOI
Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing
TL;DR: In this paper, the authors discussed extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps and derived a forward PIDE (Partial Integro-Differential Equation) and demonstrates how this equation can be used to fit the model to European option prices.
References
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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.
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.
Book
Limit Theorems for Stochastic Processes
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.
Book
Stochastic integration and differential equations
TL;DR: In this article, the authors propose a method for general stochastic integration and local times, which they call Stochastic Differential Equations (SDEs), and expand the expansion of Filtrations.