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Option pricing with orthogonal polynomial expansions
Author(s) -
Ackerer Damien,
Filipović Damir
Publication year - 2020
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12226
Subject(s) - stochastic volatility , valuation of options , affine transformation , mathematics , heston model , greeks , polynomial , series (stratigraphy) , extension (predicate logic) , orthogonal polynomials , edgeworth series , volatility (finance) , mathematical economics , econometrics , economics , sabr volatility model , computer science , mathematical analysis , pure mathematics , financial economics , paleontology , biology , programming language
We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein–Stein, and Hull–White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accurately as the Fourier‐transform‐based method in the nested affine cases. We also derive and numerically validate series representations for option Greeks. We depict an extension of our approach to exotic options whose payoffs depend on a finite number of prices.