Financial Mathematics and Financial Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E5: Financial Mathematics".

Deadline for manuscript submissions: closed (31 December 2024) | Viewed by 913

Special Issue Editor


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Guest Editor
Department of Business, Jiangnan University, Wuxi 214100, China
Interests: financial mathematics; financial engineering

Special Issue Information

Dear Colleagues,

It is well-known that financial instruments designed to serve the needs of mature capital markets and established trading forums need to be adapted for application in new markets and evolving trading platforms. The development of new financial products and trading methodologies has also led to new challenges, for both institutions and regulatory bodies. These challenges include the development of sophisticated mathematical models based on the principles of modern finance theory, the calibration of these models with market data, the simulation of such models using efficient computational algorithms, updating these models in line with evolving market developments, and the adaptation of these models by industry practitioners.

Mathematical analysis is usually a crucial step in solving those challenges. Indeed, with mathematical tools, the development of financial mathematics and financial engineering can be improved.

This Special Issue aims to support the development of financial mathematics and financial engineering. Topics of interest for submission to this issue include but are not limited to: the applications of modern probability theory and stochastic analysis in finance; the applications of stochastic optimization, stochastic control and stochastic filtering in finance; computational and numerical methods in finance; calibration, stress-testing and the institutional implementation of financial models; modelling issues arising in emerging markets and new products; mathematical models for systemic risk in financial markets; mathematical models for algorithmic trading and high-frequency trading.

Prof. Dr. Wenting Chen
Guest Editor

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Keywords

  • stochastic process
  • derivatives’ pricing
  • stochastic control
  • portfolio selection problem
  • model calibration
  • risk management
  • algorithmic trading, computational finance

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Published Papers (1 paper)

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Research

14 pages, 283 KiB  
Article
Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options
by Guillaume Leduc
Mathematics 2025, 13(2), 213; https://doi.org/10.3390/math13020213 - 10 Jan 2025
Viewed by 466
Abstract
American options have long received considerable attention in the literature, with numerous publications dedicated to their pricing. Bermudan and randomized Bermudan options are broadly used to estimate their prices efficiently. Notably, the penalty method yields option prices that coincide with those of randomized [...] Read more.
American options have long received considerable attention in the literature, with numerous publications dedicated to their pricing. Bermudan and randomized Bermudan options are broadly used to estimate their prices efficiently. Notably, the penalty method yields option prices that coincide with those of randomized Bermudan options. However, theoretical results regarding the speed of convergence of these approximations to the American option price remain scarce. In this paper, we address this gap by establishing a general result on the convergence speed of Bermudan and randomized Bermudan option prices to their American limits. We prove that for convex payoff functions, the convergence speed is linear; that is, of order 1/n, where n denotes the number of exercisable opportunities in the Bermudan case and serves as the intensity parameter of the underlying Poisson process in the randomized Bermudan case. Our framework is quite general, encompassing Lévy models, stochastic volatility models, and nearly any risk-neutral model that can be incorporated within a strong Markov framework. We extend our analysis to Canadian options, showing under mild conditions a convergence rate of 1/n to their American limits. To our knowledge, this is the first study addressing the speed of convergence in Canadian option pricing. Full article
(This article belongs to the Special Issue Financial Mathematics and Financial Engineering)
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