On the Quantitative Properties of Some Market Models Involving Fractional Derivatives

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00355833" target="_blank" >RIV/68407700:21340/21:00355833 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3390/math9243198" target="_blank" >https://doi.org/10.3390/math9243198</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math9243198" target="_blank" >10.3390/math9243198</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Quantitative Properties of Some Market Models Involving Fractional Derivatives

Popis výsledku v původním jazyce

We review and discuss the properties of various models that are used to describe the behavior of stock returns and are related in a way or another to fractional pseudo-differential operators in the space variable; we compare their main features and discuss what behaviors they are able to capture. Then, we extend the discussion by showing how the pricing of contingent claims can be integrated into the framework of a model featuring a fractional derivative in both time and space, recall some recently obtained formulas in this context, and derive new ones for some commonly traded instruments and a model involving a Riesz temporal derivative and a particular case of Riesz-Feller space derivative. Finally, we provide formulas for implied volatility and first- and second-order market sensitivities in this model, discuss hedging and profit and loss policies, and compare with other fractional (Caputo) or non-fractional models.

Název v anglickém jazyce

On the Quantitative Properties of Some Market Models Involving Fractional Derivatives

Popis výsledku anglicky

We review and discuss the properties of various models that are used to describe the behavior of stock returns and are related in a way or another to fractional pseudo-differential operators in the space variable; we compare their main features and discuss what behaviors they are able to capture. Then, we extend the discussion by showing how the pricing of contingent claims can be integrated into the framework of a model featuring a fractional derivative in both time and space, recall some recently obtained formulas in this context, and derive new ones for some commonly traded instruments and a model involving a Riesz temporal derivative and a particular case of Riesz-Feller space derivative. Finally, we provide formulas for implied volatility and first- and second-order market sensitivities in this model, discuss hedging and profit and loss policies, and compare with other fractional (Caputo) or non-fractional models.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure 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

2021

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

9

Číslo periodika v rámci svazku

24

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

24

Strana od-do

—

Kód UT WoS článku

000735474300001

EID výsledku v databázi Scopus

2-s2.0-85121300904