We develop a systematic approach to Markovian projection onto an effective displaced diffusion, and work out a set of computationally efficient formulas valid for a large class of non-Markovian underlying processes. The generic derivation is followed by applications, including the calculation of...

We revisit the cross-currency LIBOR Market Model armed with the technique of Markovian projection. We derive an efficient approximation for FX options and show how the FX skew can be modeled consistently with the interest rate skew in a common multifactor model

This paper presents a discrete framework on event time grid, for a cross-currency term structure modelling. The discrete model is generic, in the sense that it can link together any single currency model to form a multi-factor cross currency model, provided that it is known (analytically or...

Markovian Projection is an optimal approximation of a complex underlying process with a simpler one, keeping essential properties of the initial process. The Heston process, as the Markovian Projection target, is an example.In this article, we generalize the results of Markovian Projection onto...

In this paper, we develop a series of approximations for a fast analytical pricing of European constant maturity swap (CMS) products, such as CMS swaps, CMS caps/floors, and CMS spread options, for the LIBOR Market Model (LMM) with stochastic volatility. The derived formulas can also be used for...

We present the SPA framework, a novel approach to the modeling of the dynamics of portfolio default losses. In this framework, models are specified by a two-layer process. The first layer models the dynamics of portfolio loss distributions in the absence of information about default times. This...

Let (Xn) be a strictly stationary random sequence and Mn=max{X1,...,Xn}. Suppose that some of the random variables X1,X2,... can be observed and denote by the maximum of observed random variables from the set {X1,...,Xn}. We determine the limiting distribution of random vector under some...

Let (Xn) be a sequence of possibly dependent random variables with the same marginal distribution function F, such that 1-F(x)=x-[alpha]L(x), [alpha]0, where L(x) is a slowly varying function. In this paper the Hill estimator of the exponent of regular variation based on a sample with missing...