2016/08/31 by Michael A. Kouritzin · 9 citations
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Barrier option #Computer science #Econometrics #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Heston model #Jump #Jump diffusion #Mathematical optimization #Mathematics #Monte Carlo method #SABR volatility model #Stochastic differential equation #Stochastic processes and financial applications #Stochastic volatility #Valuation of options #Volatility (finance) #q-fin.PR
paper · pdf · doi:10.1142/s0219024918500061
published in International Journal of Theoretical and Applied Finance 21(01), 1850006 (World Scientific) · 42 pages
openalex publication_date 2018/02/01 · openalex created_date 2018/03/06 · arxiv created 2018/04/12 · arxiv updated 2018/04/13 · openalex updated_date 2026/08/05
New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: (1) stochastic approximation replaces regression in the LSM algorithm; (2) explicit weak solutions to stochastic differential equations are developed and applied to Heston model simulation; and (3) importance sampling expands these explicit solutions. The approach complements Heston [(1993) A closed-form solutions for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies 6, 327–343] and Broadie & Kaya [(2006) Exact simulation of stochastic volatility and other affine jump diffusion processes, Operations Research 54 (2), 217–231] by handling the case of path-dependence in the option’s execution strategy. Numeric comparison against standard Monte Carlo methods demonstrates up to two orders of magnitude speed improvement. The general ideas will extend beyond the important Heston setting.