Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for the discounted foreign exchange rate. Using these values of the parameters we find a risk-neural measure and provide...

We derived similar to Bo et al. (2010) results but in the case when the dynamics of the FX rate is driven by a general Merton jump-diffusion process. The main results of our paper are as follows: 1) formulas for the Esscher transform parameters which ensure that the martingale condition for the...

The analogue of Black–Scholes formula for vanilla call option price in conditions of (B,S)-securities market with delayed response is derived. A special case of continuous-time version of GARCH is considered. The results are compared with the results of Black and Scholes.

The Markov-modulated (B; S)-securities market is a (B; S)-security market, consisting of riskless asset, bond B; and risky asset, stock S; in random media X; or (B; S)-security market driven by a Markov process xt 2 X: We study the pricing options for Markovmodulated fractional Brownian (B;...

In this paper, we consider hidden semi-Markov chain filters having possible applications in areas such as genomics, statistical studies of earthquakes, reliability, etc.