Options with discontinuous payoffs are generally traded above their theoretical Black-Scholes prices because of the hedging difficulties created by their large delta and gamma values. A theoretical method for pricing these options is to constrain the hedging portfolio and incorporate this...

In this contribution we analyze two models for the joint probability of defaults of dependent credit risks that are based on a generalisation of Polya urn scheme. In particular we focus our attention on the problems related to the maximum likelihood estimation of the parameters involved, and to...

This paper is devoted to the well known transformations that preserve a large deviation principle (LDP), namely, the contraction principle with approximately continuous maps and the concepts of exponential equivalence and exponential approximations. We generalize these transformations to...

For strongly ergodic discrete time Markov chains we discuss the possible limits as n--[infinity] of probability measures on the path space of the form exp(nH(Ln)) dP/Zn· Ln is the empirical measure (or sojourn measure) of the process, H is a real-valued function (possibly attaining...

In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation...

There is a vast literature on numerical valuation of exotic options using Monte Carlo, binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it can be convenient and more efficient to utilize direct...

Sequential Monte Carlo (SMC) methods have successfully been used in many applications in engineering, statistics and physics. However, these are seldom used in financial option pricing literature and practice. This paper presents SMC method for pricing barrier options with continuous and...

The management of operational risk in the banking industry has undergone significant changes over the last decade due to substantial changes in operational risk environment. Globalization, deregulation, the use of complex financial products and changes in information technology have resulted in...

The Local Volatility model is a well-known extension of the Black-Scholes constant volatility model whereby the volatility is dependent on both time and the underlying asset. This model can be calibrated to provide a perfect fit to a wide range of implied volatility surfaces. The model is easy...