Research Interests

I used to work in physics for many years as both a senior researcher and a lecturer. Later on I moved to ﬁnance preserving the same concept that it is better to teach students if you are an active scientist with a broad state-of- the-art vision of contemporary theoretical ideas and practical problems. I strongly believe that my research activity helps me to be a good lecturer as well and vice versa.

I have a deep background in numerical methods and programming as well as in solving various equations of mathematical physics both analytically and numerically. That seriously affected my area of interest in mathematical ﬁnance. I published various papers on

new methods in computational ﬁnance including peculiarities of FFT for the VG mode
new approach to computing jump integrals with O(n) complexity
new splitting techniques for pricing exotic options under various jump-diffusion and local stochastic volatility models
new ﬁnite-difference schemes which preserve positivity of the solution and provide unconditional stability and second of approximation
credit derivatives models when counterparties have mutual obligations
quanto-CDS models

I also did some research on volatility modeling. This includes building asymptotical expansions for some class of stochastic volatility models, new stochastic volatility model that admits closed form solutions for pricing volatility derivatives (variance and volatility swaps, moment swaps), building no-arbitrage volatility surface, extended version of the Local Variance Gamma model, etc.

I also provided some research for Levy models with stochastic time change. In particular, in our join paper with Peter Carr we used a forward characteristic function approach to price variance and volatility swaps and options on swaps for the discrete observations case. Our analysis reveals a natural small parameter of the problem which allows a general asymptotic method to be developed in order to obtain a closed-form expression for the fair price of the above products. As some examples, we consider the CIR clock change, general affine models of the activity rates and the 3/2 power clock change, and give an analytical expression of the swap price. For the references, please see my list of publications.

Some portion of this research has been published here

To recap, my main expertise and research interest are in:

Computational ﬁnance, (various transforms and ﬁnite difference methods, then optimization methods,
calibration, pricing in non-complete markets, HJB and non-linear equations of mathematical ﬁnance).
This includes:

Stable FD methods (ADI, fractional steps, splitting) for pricing option derivatives, special attention to multi-dimensional case

Analytical and numerical methods for Levy models, including time-changed Levy models;

Efficient extensions of the transform methods including FFT and Laplace transforms as well as transforms with different kernels

Apllying RBF and ML to solving multidimensional problems of mathematical finance

Cross asset derivatives:

Analytical and numerical methods for pricing exotic options (including equity and currency options and credit products)

FD and MC methods for pricing convertible bonds with soft and hard calls

short term interest rates models

Volatility products

Analytical and numerical methods for pricing and hedging Variance and Volatility Swaps, options on quadratic variation,
VIX, VIX options and futures;

Modeling current and forward term structure of variance

Modeling correlation and dispersion swaps

Non-linear problems

Non-linear equations of mathematical ﬁnance

Pricing and hedging in incomplete markets