Optimal hedging strategies and its numerical methods under the incomplete markets

2019 Fiscal Year Final Research Report

• Project/Area Number: 17K13764
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Money/ Finance
• Research Institution: Nishogakusha University (2019); Tokyo Metropolitan University (2018); Waseda University (2017)
• Principal Investigator: Imai Yuto 二松學舍大學, 国際政治経済学部, 講師 (60732229)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Keywords: Local risk minimization / Mean-variance hedging / Fast Fourier transform / Malliavin calculus / Lévy processes

Outline of Final Research Achievements

We study both the mathematical and numerical aspects of optimal hedging strategies and numerical calculations for financial derivative securities under the incomplete markets.
In particular, the following two points were focused on the application of the study to financial practice: (i) mathematically derive a representation of the hedging strategy and express it in a numerically computable form, (ii) actually perform numerical calculations by applying the representations to various models and compare the results with those obtained from mathematically rigorous representations and with those obtained by different methods. The Car-Madan method, which uses a fast Fourier transform, was adopted as a numerical calculation method that is widely applicable not only in research but also in practice.

Free Research Field

数理ファイナンス、数値計算

Academic Significance and Societal Importance of the Research Achievements

本研究により、Local Risk Minimization戦略を採用した場合のEuropean Call optionの数値計算可能な式をいくつかのモデルに対して数学的に導出することができた。従来はMonte Carlo法を用いてのみ計算可能であったが、本研究成果を用いることで高速Fourier変換を用いて計算することが可能となった。これにより、従来に比して極めて高速に計算結果が得られることがわかった。これにより、option価格を高速に計算可能になるのみならず、現実的な時間でパラメータ推定を行うことが可能となった。