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Fractal Fract
Special Issues
Fractional Calculus in Economics and Finance
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Fractional Calculus in Economics and Finance

A special issue of Fractal and Fractional (ISSN 2504-3110).

Deadline for manuscript submissions: closed (28 February 2018) | Viewed by 10858

Special Issue Editor

Prof. Dr. Vasily E. Tarasov

E-Mail Website
Guest Editor
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Interests: fractional calculus; fractional dynamics; mathematical economics; quantum theory; theoretical physics; processes with memory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Economic and financial processes with memory and nonlocality have been actively studied in recent years. Fractional calculus and fractional differential equations are powerful mathematical tools to describe systems and processes with nonlocality and memory, which are characterized by power-law fading. At present, it is especially important to take into account long- and short-term memory in economic and financial models, since economic agents remember the stories of changes of exogenous and endogenous variables (factors and indicators) that characterize the economic process. The agents may take these changes into account in making economic decisions. The continuous-time description of economic processes with a power-law fading memory can be based on fractional derivatives and integrals of non-integer orders. The inclusion of the effect of memory and nonlocality into the economic and finance models can lead to qualitatively new effects, phenomena, and results despite the same the parameters and initial conditions.

Prof. Dr. Vasily Tarasov
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractional derivatives
  • fractional integrals
  • fractional calculus
  • dynamic memory
  • state-space
  • economics
  • finance
  • continuous-time finance

Published Papers (2 papers)

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Research

16 pages, 1392 KiB  
Article
Option Pricing Models Driven by the Space-Time Fractional Diffusion: Series Representation and Applications
by Jean-Philippe Aguilar and Jan Korbel
Fractal Fract. 2018, 2(1), 15; https://doi.org/10.3390/fractalfract2010015 - 16 Mar 2018
Cited by 12 | Viewed by 4593
Abstract
In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these results to the data from [...] Read more.
In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these results to the data from real markets. We focus on estimation of model parameters from the market data and estimation of implied volatility within the space-time fractional option pricing models. Full article
(This article belongs to the Special Issue Fractional Calculus in Economics and Finance)
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679 KiB  
Article
A Solution to the Time-Scale Fractional Puzzle in the Implied Volatility
by Hideharu Funahashi and Masaaki Kijima
Fractal Fract. 2017, 1(1), 14; https://doi.org/10.3390/fractalfract1010014 - 25 Nov 2017
Cited by 9 | Viewed by 4869
Abstract
In the option pricing literature, it is well known that (i) the decrease in the smile amplitude is much slower than the standard stochastic volatility models and (ii) the term structure of the at-the-money volatility skew is approximated by a power-law function with [...] Read more.
In the option pricing literature, it is well known that (i) the decrease in the smile amplitude is much slower than the standard stochastic volatility models and (ii) the term structure of the at-the-money volatility skew is approximated by a power-law function with the exponent close to zero. These stylized facts cannot be captured by standard models, and while (i) has been explained by using a fractional volatility model with Hurst index H > 1 / 2 , (ii) is proven to be satisfied by a rough volatility model with H < 1 / 2 under a risk-neutral measure. This paper provides a solution to this fractional puzzle in the implied volatility. Namely, we construct a two-factor fractional volatility model and develop an approximation formula for European option prices. It is shown through numerical examples that our model can resolve the fractional puzzle, when the correlations between the underlying asset process and the factors of rough volatility and persistence belong to a certain range. More specifically, depending on the three correlation values, the implied volatility surface is classified into four types: (1) the roughness exists, but the persistence does not; (2) the persistence exists, but the roughness does not; (3) both the roughness and the persistence exist; and (4) neither the roughness nor the persistence exist. Full article
(This article belongs to the Special Issue Fractional Calculus in Economics and Finance)
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