A robust numerical method for pricing American options under Kou’s jump-diffusion models based on penalty method

Gan, Xiaoting; Yang, Ying; Zhang, Kun

doi:10.1007/s12190-019-01270-1

Cited by 7 publications

(9 citation statements)

References 22 publications

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“…. , N }, m ∈ N the random variable Ξ n m can be used to hold suitable first and second moment estimates (see (42) and (43) in Section 5 below for the concrete specification of these functions implementing the Adam optimization algorithm).…”

Section: Description Of the Proposed Approximation Methods In The Gen...mentioning

confidence: 99%

“…In finance, non-local PDEs are used, e.g., in jump-diffusion models for the pricing of derivatives where the dynamics of stock prices are described by stochastic processes experiencing large jumps [74,22,65,1,15,90,28,26]. Penalty methods for pricing American put options such as in Kou's jump-diffusion model [58,42], considering large investors where the agent policy affects the assets prices [5,1], or considering default risks [83,55] can further introduce nonlinear terms in non-local PDEs. In economics, non-local nonlinear PDEs appear, e.g., in evolutionary game theory with the so-called replicator-mutator equation capturing continuous strategy spaces [79,62,50,3,4] or in growth models where consumption is nonlocal [6].…”

Section: Introductionmentioning

confidence: 99%

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Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

Boussange¹,

Becker²,

Jentzen³

et al. 2022

Preprint

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Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately account for certain non-local phenomena such as, e.g., interactions at a distance. In order to properly capture these phenomena non-local nonlinear PDE models are frequently employed in the literature. In this article we propose two numerical methods based on machine learning and on Picard iterations, respectively, to approximately solve non-local nonlinear PDEs. The proposed machine learning-based method is an extended variant of a deep learning-based splitting-up type approximation method previously introduced in the literature and utilizes neural networks to provide approximate solutions on a subset of the spatial domain of the solution. The Picard iterations-based method is an extended variant of the so-called full history recursive multilevel Picard approximation scheme previously introduced in the literature and provides an approximate solution for a single point of the domain. Both methods are mesh-free and allow non-local nonlinear PDEs with Neumann boundary conditions to be solved in high dimensions.In the two methods, the numerical difficulties arising due to the dimensionality of the PDEs are avoided by (i) using the correspondence between the expected trajectory of reflected stochastic processes and the solution of PDEs (given by the Feynman-Kac formula) and by (ii) using a plain vanilla Monte Carlo integration to handle the nonlocal term. We evaluate the performance of the two methods on five different PDEs arising in physics and biology. In all cases, the methods yield good results in up to 10 dimensions with short run times. Our work extends recently developed methods to overcome the curse of dimensionality in solving PDEs.

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Section: Description Of the Proposed Approximation Methods In The Gen...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

Boussange¹,

Becker²,

Jentzen³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…For banks, their operating costs are lower, and the main cost is interest costs, so there is greater interest price elasticity. The key to pricing is to determine the starting point for opening an account to make up for operating costs and determine the interest rate difference [24,25].…”

Section: Enterprise Financial Asset Risk Measurementmentioning

confidence: 99%

Enterprise Financial Asset Risk Measurement Based on Embedded Microprocessor Security Analysis

Wang

2022

Wireless Communications and Mobile Computing

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As the volatility of financial markets continues to increase, the risk structure involved in financial derivatives has become more and more complex. The harmful effects of financial risks can put the company in trouble. Only by understanding the correlation between financial assets can we more accurately measure the risk of a company’s financial assets. This article is aimed at studying the company’s financial asset risk measurement method based on integrated microprocessor security analysis, so that enterprises can effectively manage the risk of financial assets. This paper randomly selects 10 variables related to demographic characteristics, customer needs, and consumption characteristics of 850 customers from the historical customer data of a bank that has been abandoned for customer market segmentation research. Based on the theoretical basis of customer value evaluation, the factor analysis method refers to a multivariate statistical analysis method that starts from the internal dependence relationship of the research index correlation matrix and reduces some variables with overlapping information and intricate relationships into a few unrelated comprehensive factors. The basic idea is to group variables according to the size of the correlation, so that the correlation between the variables in the same group is higher, but the variables of different groups are not correlated or correlated, and each group of variables represents a basic structure—the common factor. This paper uses the factor analysis model in statistical principles to analyze the main factors affecting the pricing of deposit products, and we can obtain three quantitative common factors: customers related to the customer’s willingness to pay demand value, customer loyalty factor, and customer cost factor. Then, the variance contribution rate of the three factors to all observable variables is weighted and converted into the net customer relationship value, at the same time, the embedded microprocessor evolved from the CPU in the general-purpose computer. Its characteristic is that it has a 32-bit or more processor and has high performance. In actual embedded applications, it only retains closeness to embedded applications. Related functional hardware, removing other redundant functional parts so that the special requirements of embedded applications can be realized with the lowest power consumption and resources. Before constructing the structural equation model, it is necessary to test the reliability and validity of the sample data. The data selected in this paper are panel data. In order to judge whether the data is stable, the panel unit root test should be carried out. This article chooses LLC to verify the stability of the panel data. Individual fixed effects and linear time trends are added to the test, and the lag order of the difference lag is 0. Among the intermediary business income of joint-stock commercial banks, bank card fee income accounts for the largest proportion, with China Everbright Bank accounting for 70.12% and China CITIC Bank accounting for 54.16%. The research results show that with the continuous increase of Internet penetration rate, the impact of corporate finance on commercial banks shows phased characteristics. The corporate financial risk measurement method studied in this paper can provide effective help for risk monitoring and early warning. Risk measurement is a management activity that uses certain methods to determine and quantify the possibility of a company’s future financial results deviating from expected financial goals due to various uncertain factors. In practice, it is generally analyzed by a combination of qualitative and quantitative, subjective, and objective methods.

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“…Such model has two main approaches, the linear complementarity problem (LCP) formulation and the front-fixing method [6]. Probably the most used approaches are the LCP with the penalty term [7,8,9], and the operator splitting method [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…FD scheme for RBF method is proposed in [22] for Merton and Kou's models. Penalty approach together with RBF method is used in [9], where for the full discretization a fitted finite volume method is employed.…”

Section: Introductionmentioning

confidence: 99%

A front-fixing ETD numerical method for solving jump–diffusion American option pricing problems

Egorova

Jódar

2021

Mathematics and Computers in Simulation

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A robust numerical method for pricing American options under Kou’s jump-diffusion models based on penalty method

Cited by 7 publications

References 22 publications

Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

Enterprise Financial Asset Risk Measurement Based on Embedded Microprocessor Security Analysis

A front-fixing ETD numerical method for solving jump–diffusion American option pricing problems

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