For evaluating a hedging strategy we have to know at every instant the solution of the Cauchy problem for a parabolic equation (the value of the hedging portfolio) and its derivatives (the deltas). We suggest to find these magnitudes by Monte Carlo simulation of the corresponding system of...

We study several approximations for the LIBOR market models presented in Brace, Gatarek, Musiela (1997), Jamshidian (1997) and Schoenmakers, Coffey (1999). Special attention is payed to log-normal approximations and their simulation by using direct simulation methods for log-normal random...

Based on Jamshidians framework a general strategy for the quasi-analytical valuation of large classes of LIBOR derivatives will be developed. As a special case we will address the quasi-analytical approximation formula for swaptions of Brace Gatarek and Musiela and show that a similar formula...

We introduce a new Monte Carlo method for constructing the exercise boundary of an American option in a generalized Black-Scholes framework. Based on a known exercise boundary, it is shown how to price and hedge the American option by Monte Carlo simulation of suitable probabilistic...

The CreditRisk+ model launched by CSFB in 1997 is widely used by practitioners in the banking sector as a simple means for the quantification of credit risk, primarily of the loan book. We present an alternative numerical recursion scheme for CreditRisk+, equivalent to an algorithm recently...

In this paper we consider the optimal stopping problem for general dynamic monetary utility functionals. Sufficient conditions for the Bellman principle and the existence of optimal stopping times are provided. Particular attention is payed to representations which allow for a numerical...