The goal of this work is to examine the PDE approach to the valuation and hedging of defaultable claims in a Markovian model of credit risk. Our approach is based on the previous work by Bielecki et al. [3]. We extend the results in [3] by considering a general credit risk model, in which the...

The problem of term structure of interest rates modelling is considered in a continuous-time framework. The emphasis is on the bond prices, forward bond prices and so-called LIBOR rates, rather than on the instantaneous continuously compounded rates as in most traditional models. Forward and...

The backward induction approach is systematically used to produce various models of forward market rates. These include the lognormal model of forward Libor rates examined by Miltersen et al. and Brace et al., as well as the lognormal model of (fixed-maturity) forward swap rates, which was...

This paper is the first in a series that we devote to studying the problems of valuation and hedging of defaultable game options in general, and convertible corporate bonds in particular. Here, we present mathematical foundations for our overall study. Specifically, we provide several results...

A term structure model proposed by Flesaker and Hughston (1996a,b) is analysed within the general framework of arbitrage-free term structure modelling. Basic valuation formulae for caps and swaptions are presented.

We depart from the usual methods for pricing contracts with the counterparty credit risk found in most of the existing literature. In effect, typically, these models do not account for either systemic effects or at-first-default contagion and postulate that the contract value at default equals...

We introduce a class of financial contracts involving several parties by extending the notion of a two-person game option (see Kifer (2000)) to a contract in which an arbitrary number of parties is involved and each of them is allowed to make a wide array of decisions at any time, not restricted...

A new approach to modeling credit risk, to valuation of defaultable debt and to pricing of credit derivatives is developed. Our approach, based on the Heath, Jarrow, and Morton (1992) methodology, uses the available information about the credit spreads combined with the available information...

The time evolution of a sliding bond is studied in discrete‐ and continuous‐time setups. By definition, a sliding bond represents the price process of a discount bond with a fixed time to maturity. Examples of measure‐valued trading strategies (introduced by Bj"ork et al. 1997a, 1997b) which are...

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...