In this paper we study stochastic models for electricity, gas and temperature markets' contracts with delay and jumps. The basic products in these markets are spot, futures and forward contracts, swaps and options written on these. We concentrate our study on pricing of these kind of contracts....

In this paper, we study financial markets with stochastic volatilities driven by fractional Brownian motion with Hurst index H1/2. Our models include fractional versions of Ornstein-Uhlenbeck, Vasicek, geometric Brownian motion and continuous-time GARCH models. We price variance and volatility...

The valuation of the variance swaps for local Levy based stochastic volatility with delay (LLBSVD) is discussed in this paper. We provide some analytical closed forms for the expectation of the realized variance for the LLBSVD. As applications of our analytical solutions, we fit our model to 10...

In this paper, we show numerically how to calculate the price of bond options, swaps, caps and floors for Levy one-factor stochastic interest rate models via partial integro-differential equations (PIDE). These models include, in particular, Ornshtein-Uhlenbeck (1930), Vasicek (1977),...

In this paper, we model financial markets with semi-Markov volatilities and price covarinace and correlation swaps for this markets. Numerical evaluations of varinace, volatility, covarinace and correlations swaps with semi-Markov volatility are presented as well. The novelty of the paper lies...

Some commodity prices, like oil and gas, exhibit the mean reversion, unlike stock price. It means that they tend over time to return to some long-term mean.In this paper we consider a risky asset S_t following the mean-reverting stochastic process. The aim of this paper is to obtain an explicit...

The complexity of pricing variance, volatility, covariance, correlation swaps involves how to determine the dynamics of stochastic processes for underlying assets and their volatilities. In this way, sometimes it is simpler to consider of swaps pricing involving the so-called pseudo- statistics,...

In this paper, we consider pricing of European options and spread options for Hawkes-based model for the limit order book. We introduce multivariate Hawkes process and the multivariable general compound Hawkes process. Exponential multivariate general compound Hawkes processes and limit theorems...

The valuation of the variance swaps for local stochastic volatility with delay and jumps is discussed in this paper. We provide some analytical closed forms for the expectation of the realized variance for the stochastic volatility with delay and jumps. Besides, we also present a lower bound for...

The jumps in stock market volatility are found to be so active that this discredits many recently proposed stochastic volatility models without jumps (Bollerslev et al (2008)). The most convincing evidence comes from recent nonparametric work using high-frequency data as in Barndorff-Nielsen and...