A new approach to unbiased estimation for SDE's

亚洲期权（Asian options）的无偏模拟

Unbiased simulation of Asian options

本研究将 SDE 的无偏模拟方法扩展至亚洲期权相关的路径依赖动力学，解决收益和系数依赖过程加权平均值的数值求解问题，适用于路径依赖 PDE 类的数值求解。

Realized volatility and parametric estimation of Heston SDEs

We present a detailed analysis of \emph{observable} moments based parameter estimators for the Heston SDEs jointly driving the rate of returns $R_t$ and the squared volatilities $V_t$. Since volatilities are not directly observable, our parameter estimators are constructed from empirical moments of realized volatilities $Y_t$, which are of course observable. Realized volatilities are computed over sliding windows of size $\varepsilon$, partitioned into $J(\varepsilon)$ intervals. We establish criteria for the joint selection of $J(\varepsilon)$ and of the sub-sampling frequency of return rates…

Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation

In this paper we introduce a new multilevel Monte Carlo (MLMC) estimator for multi-dimensional SDEs driven by Brownian motions. Giles has previously shown that if we combine a numerical approximation with strong order of convergence $O(Δt)$ with MLMC we can reduce the computational complexity to estimate expected values of functionals of SDE solutions with a root-mean-square error of $ε$ from $O(ε^{-3})$ to $O(ε^{-2})$. However, in general, to obtain a rate of strong convergence higher than $O(Δt^{1/2})$ requires simulation, or approximation, of Lévy areas. In this paper, through the construct…