Researches on Asymptotic Expansion Approaches around Non-Gaussian Distributions

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17087
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Money/ Finance
• Research Institution: Tokyo Metropolitan University (2016-2017); University of Tsukuba (2015)
• Principal Investigator: Takehara Kohta 首都大学東京, 社会科学研究科, 准教授 (70611747)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 漸近展開法 / 解析近似解 / オプション価格解 / SABRモデル

Outline of Final Research Achievements

In this research, we analyse "an asymptotic expansion approach," known as a useful tool for practitioners in pricing derivatives or risk managements. Especially, we extend the "original" approach which expands the target process around Normal distribution, to the ours expanding the target around more general stochastic processes whose distributions are available. We also try to analyse the mathematical structures in our expansion.
As a result, the underlying problem for solving the stochastic differential equation is transformed into the problem for solving infinite numbers of ordinary differential equations with hierarchical dependence, via projecting correction terms onto the "central" terms in our expansion.
To confirm usefulness and accuracy of our proposing technique, it is applied to practically important examples, such as an expansion of lamuda-SABR model with mean-reversion around original SABR model, and satisfactory results are observed.

Free Research Field

ファイナンス，金融工学