Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view

We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinu-ous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results

Stochastic grid bundling method for backward stochastic differential equations

In this work, we apply the Stochastic Grid Bundling Method (SGBM) to numerically solve backward stochastic differential equations. The SGBM algorithm is based on conditional expectations approximation by means of bundling of Monte Carlo sample paths and a local regress-later regression within each bundle. The basic algorithm for solving backward stochastic

〈公共交通工具的社會建構及其他〉 : 新詩創作三十首

交通工具是日常生活中不可缺少的事物，除了是人們行走各處的途徑，也是公共空間的一種，其特性在文學作品中也多有表述。這次的創作計劃分三輯共三十首新詩作品，意在用不同角度敘述相關的香港故事，從而反思我們的日常生活，以及當中的歷史、文化論述。 第一輯的詩作回應了一些歷史／社會事件，包括六七暴動、移民潮、保育皇后 碼頭運動等，並用較抽離的視角反思它們對當下社會的影響。第二輯則更注視地方與交通工具的連繫，例如坪州、馬鞍山礦洞等地，除了有回顧歷史及城市變化的地文書寫，也關注當地人們的日常生活。第三輯以宏觀的角度，輔以平日的觀察，思考人與人／人與城市的關係，因而較多哲思及情感抒發，亦思考了汽車等工業產物以外的移動方式。整個創作計劃歷時近一年，希望聚焦在當下的香港故事，用現在的角度審視城市的身世，也並非漁翁撒網式地把所有交通工具都書寫一遍，而專注於主流聲音所忽略的事物

Rabin’s calibration theorem revisited

We simplify and refine the theoretical results behind Rabin’s famous calibration theorem for expected utility preferences and present the resulting tightened versions of his numerical illustrations

An SGBM-XVA demonstrator: A scalable Python tool for pricing XVA

In this work, we developed a Python demonstrator for pricing total valuation adjustment (XVA) based on the stochastic grid bundling method (SGBM). XVA is an advanced risk management concept which became relevant after the recent financial crisis. This work is a follow-up work on Chau and Oosterlee in (Int J Comput Math 96(11):2272–2301, 2019), in which we extended SGBM to numerically solving backward stochastic differential equations (BSDEs). The motivation for this work is basically two-fold. On the application side, by focusing on a particular financial application of BSDEs, we can show the potential of using SGBM on a real-world risk management problem. On the implementation side, we explore the potential of developing a simple yet highly efficient code with SGBM by incorporating CUDA Python into our program

Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view

We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinu-ous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results

Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view

We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear reaction/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinuous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results