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Pricing Bermudan Options Using Regression Trees/Random Forests 使用回归树/随机森林为百慕大期权定价
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-10-19 DOI: 10.1137/21m1460648
Zineb El Filali Ech-Chafiq, Pierre Henry Labordère, Jérôme Lelong
{"title":"Pricing Bermudan Options Using Regression Trees/Random Forests","authors":"Zineb El Filali Ech-Chafiq, Pierre Henry Labordère, Jérôme Lelong","doi":"10.1137/21m1460648","DOIUrl":"https://doi.org/10.1137/21m1460648","url":null,"abstract":"","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135666711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Mean-Field Game of Market-Making against Strategic Traders 对策略交易者做市的平均场博弈
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-10-18 DOI: 10.1137/22m1486492
Bastien Baldacci, Philippe Bergault, Dylan Possamaï
{"title":"A Mean-Field Game of Market-Making against Strategic Traders","authors":"Bastien Baldacci, Philippe Bergault, Dylan Possamaï","doi":"10.1137/22m1486492","DOIUrl":"https://doi.org/10.1137/22m1486492","url":null,"abstract":"We design a market-making model à la Avellaneda and Stoikov [Quant. Finance, 8 (2008), pp. 217–224] in which the market-takers act strategically, in the sense that they design their trading strategy based on an exogenous trading signal. The market-maker chooses her quotes based on the average market-takers’ behavior, modelled through a mean-field interaction. We derive, up to the resolution of a coupled HJB-Fokker–Planck system, the optimal controls of the market-maker and the representative market-taker. This approach is flexible enough to incorporate different behaviors for the market-takers and takes into account the impact of their strategies on the price process.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Short Communication: Is a Sophisticated Agent Always a Wise One? 简短的交流:老练的特工总是明智的吗?
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-10-17 DOI: 10.1137/23m1569137
Jianfeng Zhang
{"title":"Short Communication: Is a Sophisticated Agent Always a Wise One?","authors":"Jianfeng Zhang","doi":"10.1137/23m1569137","DOIUrl":"https://doi.org/10.1137/23m1569137","url":null,"abstract":"For time-inconsistent optimal control problems, a quite popular approach is the equilibrium approach, taken by sophisticated agents. In this short note, we construct a deterministic continuous-time example where the unique equilibrium is dominated by another control. Therefore, in this situation, it may not be wise to take the equilibrium strategy.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136033197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interest Rates Term Structure Models Driven by Hawkes Processes 霍克斯过程驱动的利率期限结构模型
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-10-17 DOI: 10.1137/22m1502604
Guillaume Bernis, Matthieu Garcin, Simone Scotti, Carlo Sgarra
{"title":"Interest Rates Term Structure Models Driven by Hawkes Processes","authors":"Guillaume Bernis, Matthieu Garcin, Simone Scotti, Carlo Sgarra","doi":"10.1137/22m1502604","DOIUrl":"https://doi.org/10.1137/22m1502604","url":null,"abstract":"","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"278 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136033493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Neural Network Approach to High-Dimensional Optimal Switching Problems with Jumps in Energy Markets 能源市场中具有跳跃的高维最优切换问题的神经网络方法
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-10-16 DOI: 10.1137/22m1527246
Erhan Bayraktar, Asaf Cohen, April Nellis
{"title":"A Neural Network Approach to High-Dimensional Optimal Switching Problems with Jumps in Energy Markets","authors":"Erhan Bayraktar, Asaf Cohen, April Nellis","doi":"10.1137/22m1527246","DOIUrl":"https://doi.org/10.1137/22m1527246","url":null,"abstract":"We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then apply this algorithm to a variety of energy scheduling problems, including novel high-dimensional energy production problems. Our experimental results demonstrate that the algorithm performs with accuracy and experiences linear to sublinear slowdowns as dimension increases, demonstrating the value of the algorithm for solving high-dimensional switching problems.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136115606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders 用变分自编码器生成无套利隐含波动面
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-10-11 DOI: 10.1137/21m1443546
Brian Ning, Sebastian Jaimungal, Xiaorong Zhang, Maxime Bergeron
{"title":"Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders","authors":"Brian Ning, Sebastian Jaimungal, Xiaorong Zhang, Maxime Bergeron","doi":"10.1137/21m1443546","DOIUrl":"https://doi.org/10.1137/21m1443546","url":null,"abstract":"We propose a hybrid method for generating arbitrage-free implied volatility (IV) surfaces consistent with historical data by combining model-free variational autoencoders (VAEs) with continuous time stochastic differential equation (SDE) driven models. We focus on two classes of SDE models: regime switching models and Lévy additive processes. By projecting historical surfaces onto the space of SDE model parameters, we obtain a distribution on the parameter subspace faithful to the data on which we then train a VAE. Arbitrage-free IV surfaces are then generated by sampling from the posterior distribution on the latent space, decoding to obtain SDE model parameters, and finally mapping those parameters to IV surfaces. We further refine the VAE model by including conditional features and demonstrate its superior generative out-of-sample performance. Finally, we showcase how our method can be used as a data augmentation tool to help practitioners manage the tail risk of option portfolios.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136058237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Cubature Method for Stochastic Volterra Integral Equations 随机Volterra积分方程的建立方法
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-10-10 DOI: 10.1137/22m146889x
Qi Feng, Jianfeng Zhang
{"title":"Cubature Method for Stochastic Volterra Integral Equations","authors":"Qi Feng, Jianfeng Zhang","doi":"10.1137/22m146889x","DOIUrl":"https://doi.org/10.1137/22m146889x","url":null,"abstract":"In this paper, we introduce the cubature formula for stochastic Volterra integral equations. We first derive the stochastic Taylor expansion in this setting, by utilizing a functional Itô formula, and provide its tail estimates. We then introduce the cubature measure for such equations, and construct it explicitly in some special cases, including a long memory stochastic volatility model. We shall provide the error estimate rigorously. Our numerical examples show that the cubature method is much more efficient than the Euler scheme, provided certain conditions are satisfied.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Short Communication: Exponential Utility Maximization in a Discrete Time Gaussian Framework 短通信:离散时间高斯框架下的指数效用最大化
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-09-05 DOI: 10.1137/23m1576074
Yan Dolinsky, Or Zuk
{"title":"Short Communication: Exponential Utility Maximization in a Discrete Time Gaussian Framework","authors":"Yan Dolinsky, Or Zuk","doi":"10.1137/23m1576074","DOIUrl":"https://doi.org/10.1137/23m1576074","url":null,"abstract":"The aim of this short note is to present a solution to the discrete time exponential utility maximization problem in a case where the underlying asset has a multivariate normal distribution. In addition to the usual setting considered in mathematical finance, we also consider an investor who is informed about the risky asset’s price changes with a delay . Our method of solution is based on the theory developed in [W. Barrett and P. Feinsilver, Linear Algebra Appl., 41 (1981), pp. 111–130] and guessing the optimal portfolio.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135254490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal Execution with Quadratic Variation Inventories 二次变量库存的最优执行
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-07-13 DOI: 10.1137/21m1416564
Rene Carmona, Laura Leal
{"title":"Optimal Execution with Quadratic Variation Inventories","authors":"Rene Carmona, Laura Leal","doi":"10.1137/21m1416564","DOIUrl":"https://doi.org/10.1137/21m1416564","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 14, Issue 3, Page 751-776, September 2023. <br/> Abstract. The first half of the paper is devoted to description and implementation of statistical tests arguing for the presence of a Brownian component in the inventories and wealth processes of individual traders. We use intraday data from the Toronto Stock Exchange to provide empirical evidence of this claim. We work with regularly spaced time intervals, as well as with asynchronously observed data. The tests reveal with high significance the presence of a nonzero Brownian motion component. The second half of the paper is concerned with the analysis of trader behaviors throughout the day. We extend the theoretical analysis of an existing optimal execution model to accommodate the presence of Itô inventory processes, and we compare empirically the optimal behavior of traders in such fitted models to the actual behavior we read off the data.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"138 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal Consumption Under a Habit-Formation Constraint: The Deterministic Case 习惯形成约束下的最优消费:确定性情况
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-05-26 DOI: 10.1137/22m1471560
Bahman Angoshtari, Erhan Bayraktar, Virginia R. Young
{"title":"Optimal Consumption Under a Habit-Formation Constraint: The Deterministic Case","authors":"Bahman Angoshtari, Erhan Bayraktar, Virginia R. Young","doi":"10.1137/22m1471560","DOIUrl":"https://doi.org/10.1137/22m1471560","url":null,"abstract":"We formulate and solve a deterministic optimal consumption problem to maximize the discounted constant relative risk aversion utility of an individual’s consumption-to-habit process assuming they only invest in a riskless market and that they are unwilling to consume at a rate below a certain proportion of their consumption habit. Increasing increases the degree of addictiveness of habit formation, with (respectively, ) corresponding to nonaddictive (respectively, completely addictive) model. We derive the optimal consumption policies explicitly in terms of the solution of a nonlinear free-boundary problem, which we analyze in detail. Impatient individuals (or, equivalently, those with more addictive habits) always consume above the minimum rate; thus, they eventually attain the minimum wealth-to-habit ratio. Patient individuals (or, equivalently, those with less addictive habits) consume at the minimum rate if their wealth-to-habit ratio is below a threshold and above it otherwise. By consuming patiently, these individuals maintain a wealth-to-habit ratio that is greater than the minimum acceptable level. Additionally, we prove that the optimal consumption path is hump-shaped if the initial wealth-to-habit ratio is either (1) larger than a high threshold or (2) below a low threshold and the agent is more risk seeking (that is, less risk averse). Thus, we provide a simple explanation for the consumption hump observed by various empirical studies.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"341 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135996977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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