In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation technique and Laplace transform method to evaluate...

In these lectures' notes I would like to introduce forwards, futures and options, and to review some results on Black-Scholes-73 and Black-76 models for positive prices, and also on alternatives models for negative prices for option valuation of futures contracts.I will focus on the first model...

This paper is devoted to the pricing of variance and volatility swaps in energy market. We found explicit variance swap formula and closed form volatility swap formula (using Brockhaus-Long approximation) for energy asset with stochastic volatility that follows continuous-time GARCH (1,1) model...

In this paper, we show how to calculate the price of zero-coupon bonds for many Gaussian and Levy one-factor and multi-factor models of r(t) using change of time method. These models include, in particular, Ornshtein-Uhlenbeck (1930), Vasicek (1977), Cox-Ingersoll-Ross (1985), continuous-time...

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...