On the numerical methods for the Heston model

• Main Author: Teixeira, Fernando Ormonde
• Other Authors: Saporito, Yuri Fahham
• Language: English
• Published: 2017
• Subjects: Heston; Stochastic; Volatility; Black-Scholes; European call; R; Matemática; Análise estocástica; Métodos de simulação; Análise numérica; Volatilidade (Finanças)
• Online Access: http://hdl.handle.net/10438/19486

Submitted by Fernando Teixeira ([e-mail]) on 2017-12-08T15:48:21Z No. of bitstreams: 1 Download File (1).pdf: 1437428 bytes, checksum: d6dfbfe41919a0cdd657900b6784f310 (MD5) === Approved for entry into archive by Janete de Oliveira Feitosa ([e-mail]) on 2017-12-08T16:04:57Z (GMT) No. of bitstreams: 1 Download File (1).pdf: 1437428 bytes, checksum: d6dfbfe41919a0cdd657900b6784f310 (MD5) === Made available in DSpace on 2017-12-22T17:16:31Z (GMT). No. of bitstreams: 1 Download File (1).pdf: 1437428 bytes, checksum: d6dfbfe41919a0cdd657900b6784f310 (MD5) Previous issue date: 2017-09-29 === In this thesis we revisit numerical methods for the simulation of the Heston model’sEuropean call. Specifically, we study the Euler, the Kahl-Jackel an two versions of theexact algorithm schemes. To perform this task, firstly we present a literature reviewwhich brings stochastic calculus, the Black-Scholes (BS) model and its limitations,the stochastic volatility methods and why they resolve the issues of the BS model,and the peculiarities of the numerical methods. We provide recommendations whenwe acknowledge that the reader might need more specifics and might need to divedeeper into a given topic. We introduce the methods aforementioned providing all ourimplementations in R language within a package.