DEFAULTABLE TERM STRUCTURES DRIVEN BY SEMIMARTINGALES

Term Structures of Defaultable Bonds

In this essay we introduce three types of credit pricing models: first and second generation structural-form models and reduced-form models with relative papers and their main results. This paper mainly focuses on the reduced-form credit pricing model by explaining Duffie and Singleton’s paper Modeling Term Structure of Defaultable Bonds (1999). A detailed explanation of the paper’s deductions ...

Finite Dimensional Realizations for Term Structure Models driven by Semimartingales

Let f(t, T ) be a term structure model of Heath-Jarrow-Morton type df(t, T ) = α(t, T )dt+ σ(t, T )dXt, driven by a multidimensional semimartingaleX. Our objective is to study the existence of finite dimensional realizations for equations of this kind. Choosing the class of Grigelionis processes (including in particular Lévy processes) as driving processes, we approach this problem from two dif...

Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales

ASYMPTOTIC ERROR FOR THE MILSTEIN SCHEME FOR SDEs DRIVEN BY CONTINUOUS SEMIMARTINGALES

A Milstein-type scheme was proposed to improve the rate of convergence of its approximation of the solution to a stochastic differential equation driven by a vector of continuous semimartingales. A necessary and sufficient condition was provided for this rate to be 1/n when the SDE is driven by a vector of continuous local martingales, or continuous semimartingales under an additional assumptio...

Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite dimensional semimartingales

Let H be a separable Banach space. We considered the sequence of stochastic integrals {Xn− · Yn} where {Yn} is a sequence of infinite dimesnional H semimartingales and Xn are H valued cadlag processes. Assuming that {(Xn, Yn)} satisfies large deviation principle, a uniform exponential tightness condition is described under which large deviation principle holds for {(Xn, Yn, Xn− · Yn)}. When H i...