Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F19%3A00334283" target="_blank" >RIV/68407700:21340/19:00334283 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3390/math7090796" target="_blank" >https://doi.org/10.3390/math7090796</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math7090796" target="_blank" >10.3390/math7090796</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations

Popis výsledku v původním jazyce

In this article, we first provide a survey of the exponential option pricing models and show that in the framework of the risk-neutral approach, they are governed by the space-fractional diffusion equation. Then, we introduce a more general class of models based on the space-time-fractional diffusion equation and recall some recent results in this field concerning the European option pricing and the risk-neutral parameter. We proceed with an extension of these results to the class of exotic options. In particular, we show that the call and put prices can be expressed in the form of simple power series in terms of the log-forward moneyness and the risk-neutral parameter. Finally, we provide the closed-form formulas for the first and second order risk sensitivities and study the dependencies of the portfolio hedging and profit-and-loss calculations upon the model parameters.

Název v anglickém jazyce

Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations

Popis výsledku anglicky

In this article, we first provide a survey of the exponential option pricing models and show that in the framework of the risk-neutral approach, they are governed by the space-fractional diffusion equation. Then, we introduce a more general class of models based on the space-time-fractional diffusion equation and recall some recent results in this field concerning the European option pricing and the risk-neutral parameter. We proceed with an extension of these results to the class of exotic options. In particular, we show that the call and put prices can be expressed in the form of simple power series in terms of the log-forward moneyness and the risk-neutral parameter. Finally, we provide the closed-form formulas for the first and second order risk sensitivities and study the dependencies of the portfolio hedging and profit-and-loss calculations upon the model parameters.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA19-16066S" target="_blank" >GA19-16066S: Nelineární interakce a přenos informace v komplexních systémech s extrémními událostmi</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

2227-7390

Svazek periodika

7

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

23

Strana od-do

—

Kód UT WoS článku

000487953700044

EID výsledku v databázi Scopus

2-s2.0-85072324812