In this paper, we price covariance and correlation swaps for financial markets with Markov-modulated volatilities. As an example, we consider stochastic volatility driven by a two-state continuous Markov chain. In this case, numerical examples are presented for VIX and VXN volatility indices...

We propose a semi-Markov modulated interest rate model. We assume that the switching process is a semi-Markov process with finite state space and the modulated process is a diffusive process. Classical models such as those by Vasicek and CIR are generalized.

<i>Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities</i> is devoted to the modeling and pricing of various kinds of swaps, such as those for variance, volatility, covariance, correlation, for financial and energy markets with different stochastic volatilities,...

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.

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