This paper presents an investigation into a random walk on a cycle graph with restricted forward movement at most $m$ steps, known as the forward jump random walk. The study derives precise formulas for the probability mass function of the arriving state, the hitting time, and its expected value...

The field of financial econometrics has exploded over the last decade. This book represents an integration of theory, methods, and examples using the S-PLUS statistical modeling language and the S+FinMetrics module to facilitate the practice of financial econometrics. This is the first book to...

This article studies the impact of long memory on volatility modelling and option pricing. We propose a general discrete-time pricing framework based on affine multi-component volatility models that admit ARCH(ccc) representations. This not only nests a large variety of option pricing models...

Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with...