The investment fund replication techniques and related financial product have been developed in recent years. It is understood that investing in the replicated fund can help investors gain similar returns without suffering drawbacks of the target fund. However, it is difficult to produce...

In March 2020 the U.S. equity market is suffering large losses. This is primarily due to COVID-19, which probably also caused a drop in the shale oil price. US market indices are fluctuating this month much more than any time in history. In this short note, we are using two high frequency market...

This paper presents a new financial market simulator that may be used as a tool in both industry and academia for research in market micro-structure. It allows multiple automated traders and/or researchers to simultaneously connect to an exchange-like environment, where they are able to...

In a recent study, we present a tree methodology to evaluate the expected generalized realized variance in a general stochastic volatility model. This provides an efficient way of calculating the fair value of the strike for variance swaps. In this article, we expand the methodology to price...

In this paper, we propose an approach to modeling the jump component of a jump-diffusion model using a log mixture of normals distribution. We define explicitly theproperties of the distribution and use it to create an analytic formula for Europeanoption price. Numerous examples of applications...

Liquidity is one of the crucial factors in economy which reflects smooth operation of the markets. In a liquid market, traders are able to transact large quantities of security quickly with minimal trading cost and price impact. Many researchers have investigated the relationship between market...

A new valuation and calibration method for VIX futures and VIX options is proposed. The method is based on a closed-form Hermite series expansion for a stochastic volatility model with the stochastic variance process driven by an affine drift term. We implement the methodology for the Heston and...

Long term memory effects in stock market indices that represent internationally diversified stocks are analyzed in this paper and the results are compared with the S&P 500 index. The Hurst exponent and the Detrended fluctuation analysis (DFA) technique are the tools used for this analysis. The...

We study an integro-differential parabolic problem modelling a process with jumps and stochastic volatility in financial mathematics. Under suitable conditions, we prove the existence of solutions in a general domain using the method of upper and lower solutions and a diagonal argument