We present a full (to my opinion) set of models for big data in nance, including HFT (e.g., LOB). All these models were introduced, pro-posed, and then studied after investigating many HFT data (see [12, 13, 7, 4]), which supported and justi ed our models. For quantitative and comparative...

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 model financial markets with semi-Markov volatilities and price averaged variance, volatility, covariance and correlation swaps for these markets. Formulas used for the numerical evaluation of averaged variance, volatility, covariance and correlation swaps with semi- Markov...

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...

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 paper overviews our recent results in energy market modelling, including: option pricing formula for a mean-reversion asset; variance and volatility swaps in energy markets; applications of weather derivatives in energy markets; pricing crude oil options using L evy processes; energy...

We show how to solve Merton optimal investment stochastic control problem for Hawkes-based models in finance and insurance, i.e., for a wealth portfolio X(t) consisting of a bond and a stock price described by general compound Hawkes process (GCHP), and for a capital R(t) of an insurance company...

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...

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...