A Note on Several Alternatives to Numerical Pricing of Options

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F17%3A00006306" target="_blank" >RIV/46747885:24510/17:00006306 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27510/17:10240132

Výsledek na webu

<a href="http://lef.tul.cz/" target="_blank" >http://lef.tul.cz/</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

A Note on Several Alternatives to Numerical Pricing of Options

Popis výsledku v původním jazyce

Option pricing is a popular problem of financial mathematics and optimization due to the non-linearity in the option pay-off function and enormous sensitivity to the selection of underlying processes and input parameters. This aspect differentiates options from other derivatives. Since pricing and hedging of plain vanilla options under the conditions of Gaussian distribution (or a so called Black-Scholes model) is already well documented, it commonly serves as a benchmark for developing of new approaches and methods, which, in fact, aims on options with more complex payoffs (exotic options) and/or probability distributions that fit empirical observations about the market prices better, but for which no analytical formula is available. Obviously, being able to compare the results of the novel model with theoretically correct one is a crucial step of model testing. In this contribution we focuse on numerical pricing of options. We first review well known approaches of Monte Carlo simulation and Lattice models and subsequently we formulate a Black-Scholes-Merton Partial Differential Equation, which serves as a starting point for discretization via two novel approaches, discontinuous Galerkin approach and Fuzzy transform technique. Both approaches seems to be promising especially for complex processes and payoff functions.

Název v anglickém jazyce

A Note on Several Alternatives to Numerical Pricing of Options

Popis výsledku anglicky

Option pricing is a popular problem of financial mathematics and optimization due to the non-linearity in the option pay-off function and enormous sensitivity to the selection of underlying processes and input parameters. This aspect differentiates options from other derivatives. Since pricing and hedging of plain vanilla options under the conditions of Gaussian distribution (or a so called Black-Scholes model) is already well documented, it commonly serves as a benchmark for developing of new approaches and methods, which, in fact, aims on options with more complex payoffs (exotic options) and/or probability distributions that fit empirical observations about the market prices better, but for which no analytical formula is available. Obviously, being able to compare the results of the novel model with theoretically correct one is a crucial step of model testing. In this contribution we focuse on numerical pricing of options. We first review well known approaches of Monte Carlo simulation and Lattice models and subsequently we formulate a Black-Scholes-Merton Partial Differential Equation, which serves as a starting point for discretization via two novel approaches, discontinuous Galerkin approach and Fuzzy transform technique. Both approaches seems to be promising especially for complex processes and payoff functions.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA16-09541S" target="_blank" >GA16-09541S: Robustní numerická schémata pro oceňování vybraných opcí za různých tržních podmínek</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

13th International Conference on Liberec Economic Forum

ISBN

978-80-7494-349-2

ISSN

—

e-ISSN

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Počet stran výsledku

9

Strana od-do

381-389

Název nakladatele

Technical University of Liberec

Místo vydání

Liberec

Místo konání akce

Liberec

Datum konání akce

1. 1. 2017

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000426486500043