Model risk and discretisation of locally risk-minimising strategies

详细信息    查看全文

• 作者：Xianming Sun^a ; ^b ; ^{Xianming.Sun@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; Thorsten Schulz^c ; ^{t.schulz@tum.de" class="auth_mail" title="E-mail the corresponding author} ; Asma Khedher^d ; ^{A.Khedher@uva.nl" class="auth_mail" title="E-mail the corresponding author} ; Michè ; le Vanmaele^b ; ^{Michele.Vanmaele@ugent.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Quadratic hedging strategies ; Backward stochastic differential equations ; Jump&ndash ; diffusions
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：38-53
• 全文大小：532 K

文摘

We consider two models for the price process: a time-continuous jump–diffusion and a time-discretisation of it. Then we study the robustness of the related locally risk-minimising strategy to this model choice where we focus mainly on hedging Asian and spread options. Using the discretisation scheme and the convergence results on backward stochastic differential equations as studied in Khedher and Vanmaele (2016), we show that the discrete-time locally risk-minimising strategies converge to the corresponding continuous-time strategies in an class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303211&_mathId=si14.gif&_user=111111111&_pii=S0377042716303211&_rdoc=1&_issn=03770427&md5=4132db32d4a3983b129d564f0e6744d4" title="Click to view the MathML source">L²class="mathContainer hidden">class="mathCode">$L^2$-sense. We present different numerical examples to illustrate our results.