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,...

We introduce a new model for a stock price, namely, geometric compound Hawkes process, and show how this model can be applied to solving many problems in finance, including European and American option pricing and Merton portfolio optimization problem. This model is a generalization of some...

We consider multi-factor Levy models based on SDEs driven by alpha-stable Levy processes.Using change of time method for Levy-based stochastic integrals we show how to pricing many of financial and energy derivatives

In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regards to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit...

The Paris agreement in 2016 marks a global effort to limit the increase in temperature. In that spirit, the Federal Government of Canada introduced a carbon tax to reduce greenhouse gas emissions. The main goal of this paper is to define the correct approach to carbon pricing. Following the...

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...

We consider an averaging principle for the endemic SIR model in a semi-Markov random media. Under stationary conditions of a semi- Markov media we show that the perturbed endemic SIR model converges to the classic endemic SIR model with averaged coefficients. Numerical toy examples and their...

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...

In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the Hawkes process. Law of...

R. Cont and A. de Larrard (SIAM J. Financial Mathematics, 2013) introduced a tractable stochastic model for the dynamics of a limit order book, computing various quantities of interest such as the probability of a price increase or the diffusion limit of the price process. As suggested by...