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Recent Developments in Numerical Methods for Option Pricing
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Recent Developments in Numerical Methods for Option Pricing

A special issue of International Journal of Financial Studies (ISSN 2227-7072).

Deadline for manuscript submissions: closed (30 December 2017) | Viewed by 15729

Special Issue Editor

Prof. Dr. Dennis Belomestny

E-Mail Website
Guest Editor
Professor of Finance and Stochastics, Faculty of Mathematics, Duisburg-Essen University, Thea-Leymann-Str. 9, D-45127 Essen, Germany
Interests: Monte Carlo methods in financial engineering; pricing of American options

Special Issue Information

Dear Colleagues,

In recent years, the complexity of numerical computation in financial theory and practice has increased substantially, putting more demands on computational speed and efficiency. Numerical methods are now widely used for the valuation of securities. The purpose of this Special Issue is to present recent developments in numerical methods for option pricing, based on Black-Scholes processes, pure jump processes, jump diffusion process, and stochastic volatility processes. The main focus of the Special Issue will be on Monte Carlo methods, quasi Monte Carlo methods, and FFT methods. Special attention shall be given to the evaluation of American type and other exotic derivatives by Monte Carlo. The recent literature on option pricing pays an increasing attention to efficiency and numerical complexity of the numerical algorithms and this trend is to be reflected in this Special Issue.

Prof. Dr. Dennis Belomestny
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. International Journal of Financial Studies is an international peer-reviewed open access quarterly 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 1800 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

  • Option pricing

  • FFT

  • Monte Carlo

  • stochastic volatility

  • complexity

Published Papers (4 papers)

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Research

26 pages, 2632 KiB  
Article
Asymptotic Expansion of Risk-Neutral Pricing Density
by Thomas Mazzoni
Int. J. Financial Stud. 2018, 6(1), 30; https://doi.org/10.3390/ijfs6010030 - 12 Mar 2018
Viewed by 3254
Abstract
A new method for pricing contingent claims based on an asymptotic expansion of the dynamics of the pricing density is introduced. The expansion is conducted in a preferred coordinate frame, in which the pricing density looks stationary. The resulting asymptotic Kolmogorov-backward-equation is [...] Read more.
A new method for pricing contingent claims based on an asymptotic expansion of the dynamics of the pricing density is introduced. The expansion is conducted in a preferred coordinate frame, in which the pricing density looks stationary. The resulting asymptotic Kolmogorov-backward-equation is approximated by using a complete set of orthogonal Hermite-polynomials. The derived model is calibrated and tested on a collection of 1075 European-style ‘Deutscher Aktienindex’ (DAX) index options and is shown to generate very precise option prices and a more accurate implied volatility surface than conventional methods. Full article
(This article belongs to the Special Issue Recent Developments in Numerical Methods for Option Pricing)
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15 pages, 278 KiB  
Article
Finite Difference Methods for the BSDEs in Finance
by Guangbao Guo
Int. J. Financial Stud. 2018, 6(1), 26; https://doi.org/10.3390/ijfs6010026 - 05 Mar 2018
Cited by 5 | Viewed by 3629
Abstract
This paper gives a review of numerical methods for solving the BSDEs, especially, finite difference methods. For numerical methods of finite difference, we should divide them into three branches. Distributed method (or parallel method) should now become a hot topic. It is a [...] Read more.
This paper gives a review of numerical methods for solving the BSDEs, especially, finite difference methods. For numerical methods of finite difference, we should divide them into three branches. Distributed method (or parallel method) should now become a hot topic. It is a key reason we present the review. We give a brief survey on the financial problems. The problems include solution and simulation methods for the BSDEs. We first describe the BSDEs, and then outline the main techniques and main results of the BSDEs. In addition, we compare with the errors between these methods and the Euler method on the BSDEs. Full article
(This article belongs to the Special Issue Recent Developments in Numerical Methods for Option Pricing)
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350 KiB  
Article
Numerical Simulation of the Heston Model under Stochastic Correlation
by Long Teng, Matthias Ehrhardt and Michael Günther
Int. J. Financial Stud. 2018, 6(1), 3; https://doi.org/10.3390/ijfs6010003 - 25 Dec 2017
Cited by 7 | Viewed by 4888
Abstract
Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a [...] Read more.
Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations. Full article
(This article belongs to the Special Issue Recent Developments in Numerical Methods for Option Pricing)
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305 KiB  
Article
A Dynamic Programming Approach for Pricing Weather Derivatives under Issuer Default Risk
by Wolfgang Karl Härdle and Maria Osipenko
Int. J. Financial Stud. 2017, 5(4), 23; https://doi.org/10.3390/ijfs5040023 - 20 Oct 2017
Cited by 2 | Viewed by 3402
Abstract
Weather derivatives are contingent claims with payoff based on a pre-specified weather index. Firms exposed to weather risk can transfer it to financial markets via weather derivatives. We develop a utility-based model for pricing baskets of weather derivatives under default risk on the [...] Read more.
Weather derivatives are contingent claims with payoff based on a pre-specified weather index. Firms exposed to weather risk can transfer it to financial markets via weather derivatives. We develop a utility-based model for pricing baskets of weather derivatives under default risk on the issuer side in over-the-counter markets. In our model, agents maximise the expected utility of their terminal wealth, while they dynamically rebalance their weather portfolios over a finite investment horizon. Using dynamic programming approach, we obtain semi-closed forms for the equilibrium prices of weather derivatives and for the optimal strategies of the agents. We give an example on how to price rainfall derivatives on selected stations in China in the universe of a financial investor and a weather exposed crop insurer. Full article
(This article belongs to the Special Issue Recent Developments in Numerical Methods for Option Pricing)
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