ONLINE LOCAL VOLATILITY CALIBRATION BY CONVEX REGULARIZATION

Applicable Analysis and Discrete Mathematics

article

Vinicius Albani¹  Jorge P. Zubelli¹ 

[1] Instituto Nacional de Matem´atica Pura e Aplicada

关键词: Local Volatility Calibration;    Convex Regularization;    Online Estimation;    Morozov's Principle;    Convergence Rates;   

DOI  :  10.2298/AADM140811012A

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

We address the inverse problem of local volatility surface calibration frommarket given option prices. We integrate the ever-increasing flow of optionprice information into the well-accepted local volatility model of Dupire. Thisleads to considering both the local volatility surfaces and their correspondingprices as indexed by the observed underlying stock price as time goes by inappropriate function spaces. The resulting parameter to data map is definedin appropriate Bochner-Sobolev spaces. Under this framework, we prove keyregularity properties. This enables us to build a calibration technique thatcombines online methods with convex Tikhonov regularization tools. Suchprocedure is used to solve the inverse problem of local volatility identification. As a result, we prove convergence rates with respect to noise and acorresponding discrepancy-based choice for the regularization parameter. Weconclude by illustrating the theoretical results by means of numerical tests.

【 授权许可】

Unknown