arXiv subjects

Marc Mukendi Mpanda

Publications and source records attributed to Marc Mukendi Mpanda.

2 recordsLinked to original sources

arXiv2022

Malliavin differentiability of fractional Heston-type model and applications to option pricing

This paper defines fractional Heston-type (fHt) model as an arbitrage-free financial market model with the infinitesimal return volatility described by the square of a single stochastic equation with respect to fractional Brownian motion with Hurst parameter H in (0, 1). We extend the idea of Alos and [Alos, E., & Ewald, C. O. (2008). Malliavin differentiability of the Heston volatility and applications to option pricing. Advances in Applied Probability, 40(1), 144-162.] to prove that fHt model is Malliavin differentiable and deduce an expression of expected payoff function having discontinuity of any kind. Some simulations of stock price process and option prices are performed.

q-fin.MF↗

arXiv2022

Generalisation of Fractional-Cox-Ingersoll-Ross Process

In this paper, we define a generalised fractional Cox-Ingersoll-Ross process as a square of singular stochastic differential equation with respect to fractional Brownian motion with Hurst parameter H in (0,1) and continuous drift function. Firstly, we show that this differential equation has a unique solution which is continuous and positive up to the time of the first visit to zero. In addition, we prove that it is strictly positive everywhere almost surely for H > 1/2. In the case where H < 1/2, we consider a sequence of increasing functions and we prove that the probability of hitting zero tends to zero as n goes to infinity. These results are illustrated with some simulations using the generalisation of the extended Cox-Ingersoll-Ross process.

math.PR↗