arXiv subjects

Mishari Al-Foraih

Publications and source records attributed to Mishari Al-Foraih.

3 recordsLinked to original sources

arXiv2025

Computation of Greeks under rough Volterra stochastic volatility models using the Malliavin calculus approach

Using Malliavin calculus techniques, we obtain formulas for computing Greeks under different rough Volterra stochastic volatility models. Due to the fact that underlying prices are not always square integrable, we extend the classical integration by parts formula to integrable but not necessarily square integrable functionals. First of all, we obtain formulas for general stochastic volatility (SV) models, concretely the Greeks Delta, Gamma, Rho, Vega and we introduce the Greek with respect to the roughness parameter. Then, the particular case of rough Volterra SV models is analyzed. Finally, three examples are treated in detail: the family of alpha-RFSV models, that includes rough versions of SABR and Bergomi models, a mixed alpha-RFSV model with two different Hurst parameters representing short (roughness) and long memory, and the rough Stein-Stein model. For different models and Greeks we show a numerical convergence of our formulas in Monte Carlo simulations and depict for example a dependence of the Greeks on the roughness parameter.

q-fin.MF↗

arXiv2022

Wasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency

This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denoted $θ$, for a Ornstein-Uhlenbeck process $X \coloneqq \{X_t,t\geq0\}$ observed at high frequency. We provide an Approximate minimum contrast estimator and an approximate maximum likelihood estimator of $θ$, namely $\widetildeθ_{n}\coloneqq {1}/{\left(\frac{2}{n} \sum_{i=1}^{n}X_{t_{i}}^{2}\right)}$, and $\widehatθ_{n}\coloneqq -{\sum_{i=1}^{n} X_{t_{i-1}}\left(X_{t_{i}}-X_{t_{i-1}}\right)}/{\left(Δ_{n} \sum_{i=1}^{n} X_{t_{i-1}}^{2}\right)}$, respectively, where $ t_{i} = i Δ_{n}$, $ i=0,1,\ldots, n $, $Δ_{n}\rightarrow 0$. We provide Wasserstein bounds in central limit theorem for $\widetildeθ_{n}$ and $\widehatθ_{n}$.

math.ST↗

arXiv2020

Least squares estimation for non-ergodic weighted fractional Ornstein-Uhlenbeck process of general parameters

Let $B^{a,b}:=\{B_t^{a,b},t\geq0\}$ be a weighted fractional Brownian motion of parameters $a>-1$, $|b|<1$, $|b| 0$ of the weighted fractional Ornstein-Uhlenbeck process $X:=\{X_t,t\geq0\}$ defined by $X_0=0; \ dX_t=θX_tdt+dB_t^{a,b}$. In this work, we provide least squares-type estimators for $θ$ based continuous-time and discrete-time observations of $X$. The strong consistency and the asymptotic behavior in distribution of the estimators are studied for all $(a,b)$ such that $a>-1$, $|b|<1$, $|b|<a+1$. Here we extend the results of \cite{SYY2,SYY} (resp. \cite{CSC}), where the strong consistency and the asymptotic distribution of the estimators are proved for $-\frac12<a<0$, $-a<b<a+1$ (resp. $-1<a<0$, $-a<b<a+1$).

math.PR↗