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- Title
An eigenfunction expansion approach for the derivation of asymptotic expansions in financial valuation problems.
- Authors
Manabu Miyamoto; Keiichi Tanaka
- Abstract
This study examines whether an alternative calculation approach exists for the asymptotic expansion of the probability density function of risky asset prices. We focus on the partial differential equation by using an eigenfunction expansion related to Hermite polynomials. We show that the expansion coefficients can be obtained by solving ordinary differential equations recursively and which order of Hermite polynomials appear in asymptotic expansion explicitly.
- Subjects
EIGENFUNCTION expansions; EIGENVALUE equations; PARTIAL differential equations; HERMITE polynomials; PROBABILITY density function
- Publication
JSIAM Letters (Online), 2022, p25
- ISSN
1883-0617
- Publication type
Article
- DOI
10.14495/jsiaml.14.25