This book is intended for readers who are quite familiar with probability and stochastic
processes but know little or nothing about finance. It is written in the definition/theorem/proof …

Markov-modulated models for equity prices have recently been extensively studied in the
literature. In this paper, we apply some old results on the Wiener--Hopf factorization of …

This book is the definitive and most comprehensive guide to modeling derivatives in C++
today. Providing readers with not only the theory and math behind the models, as well as the …

This thesis summarizes most of my recent research in the field of portfolio optimization. The
main topics which I have addressed are portfolio problems with stochastic interest rates and …

This paper studies derivative contracts with payoffs contingent on the amount of time the
underlying asset price spends outside of a pre-specified price range (occupation time) …

We discuss here an alternative interpretation of the familiar binomial lattice approach to
option pricing, illustrating it with reference to pricing of barrier options, one-and two-sided …

This paper examines a class of barrier options, multi‐step barrier options, which can have
any finite number of barriers of any level. We obtain a general, explicit expression for option …

In this paper, we prove the existence of an integral closed-form solution for pricing barrier
options in both Heston and Bates frameworks. The option value depends on time, on the …

This paper considers pricing multi-step double barrier options. The non-crossing probability
for a multi-step double boundary is vital in valuing the options. We extend an explicit formula …

In this work, the Fourier-cosine series (COS) method has been combined with the Boundary
Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its …