The problem of non-confluence and strong comparison of solutions of one-dimensional Itô stochastic differential equations is studied. Sufficient conditions which guarantee these properties in the case of non-degenerate diffusion coefficient are given. In the case of possibly degenerate...

This paper presents a PDE approach in a Markovian setting to hedge defaultable derivatives. The arbitrage price and the hedging strategy for an attainable contingent claim are described in terms of solutions of a pair of coupled PDEs. For some standard examples of defaultable claims, we provide...

The goal of this work is to examine the static replication of path-dependent derivatives such as realized variance swaps, using more standard products such as forward-start binary (i.e. digital) double calls and puts. We first examine, following Carr and Madan (2002), the static replication of...

The present research is motivated by the recent results of Jeanblanc and Song (2011) [10,11]. Our aim is to demonstrate, with the help of multiplicative systems introduced in Meyer (1979) [21], that for any given positive F-submartingale F such that F∞=1, there exists a random time τ on some...

<title>Abstract</title> Foreign exchange options are studied in the Heston stochastic volatility model for the exchange rate combined with the Cox <italic>et al</italic>. dynamics for the domestic and foreign stochastic interest rates. The instantaneous volatility is correlated with the dynamics of the exchange rate return,...

We propose a fairly general framework which allows one to perform Credit Value Adjustment (CVA) computations for a contract with bilateral counterparty risk in the presence of (a) systemic risk and (b) wrong-way or right-way risks. Our methodology focuses on the role of alternative settlement...