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Semi-analytic pricing of American options in some time-dependent jump-diffusion models 时变跳跃-扩散模型下美式期权的半解析定价
arXiv - QuantFin - Pricing of Securities Pub Date : 2023-08-17 DOI: arxiv-2308.08760
Andrey Itkin
{"title":"Semi-analytic pricing of American options in some time-dependent jump-diffusion models","authors":"Andrey Itkin","doi":"arxiv-2308.08760","DOIUrl":"https://doi.org/arxiv-2308.08760","url":null,"abstract":"In this paper we propose a semi-analytic approach to pricing American options\u0000for some time-dependent jump-diffusions models. The idea of the method is to\u0000further generalize our approach developed for pricing barrier, [Itkin et al.,\u00002021], and American, [Carr and Itkin, 2021; Itkin and Muravey, 2023], options\u0000in various time-dependent one factor and even stochastic volatility models. Our\u0000approach i) allows arbitrary dependencies of the model parameters on time; ii)\u0000reduces solution of the pricing problem for American options to a simpler\u0000problem of solving an algebraic nonlinear equation for the exercise boundary\u0000and a linear Fredholm-Volterra equation for the the option price; iii) the\u0000options Greeks solve a similar Fredholm-Volterra linear equation obtained by\u0000just differentiating Eq. (25) by the required parameter.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Insurance pricing on price comparison websites via reinforcement learning 基于强化学习的比价网站保险定价
arXiv - QuantFin - Pricing of Securities Pub Date : 2023-08-14 DOI: arxiv-2308.06935
Tanut Treetanthiploet, Yufei Zhang, Lukasz Szpruch, Isaac Bowers-Barnard, Henrietta Ridley, James Hickey, Chris Pearce
{"title":"Insurance pricing on price comparison websites via reinforcement learning","authors":"Tanut Treetanthiploet, Yufei Zhang, Lukasz Szpruch, Isaac Bowers-Barnard, Henrietta Ridley, James Hickey, Chris Pearce","doi":"arxiv-2308.06935","DOIUrl":"https://doi.org/arxiv-2308.06935","url":null,"abstract":"The emergence of price comparison websites (PCWs) has presented insurers with\u0000unique challenges in formulating effective pricing strategies. Operating on\u0000PCWs requires insurers to strike a delicate balance between competitive\u0000premiums and profitability, amidst obstacles such as low historical conversion\u0000rates, limited visibility of competitors' actions, and a dynamic market\u0000environment. In addition to this, the capital intensive nature of the business\u0000means pricing below the risk levels of customers can result in solvency issues\u0000for the insurer. To address these challenges, this paper introduces\u0000reinforcement learning (RL) framework that learns the optimal pricing policy by\u0000integrating model-based and model-free methods. The model-based component is\u0000used to train agents in an offline setting, avoiding cold-start issues, while\u0000model-free algorithms are then employed in a contextual bandit (CB) manner to\u0000dynamically update the pricing policy to maximise the expected revenue. This\u0000facilitates quick adaptation to evolving market dynamics and enhances algorithm\u0000efficiency and decision interpretability. The paper also highlights the\u0000importance of evaluating pricing policies using an offline dataset in a\u0000consistent fashion and demonstrates the superiority of the proposed methodology\u0000over existing off-the-shelf RL/CB approaches. We validate our methodology using\u0000synthetic data, generated to reflect private commercially available data within\u0000real-world insurers, and compare against 6 other benchmark approaches. Our\u0000hybrid agent outperforms these benchmarks in terms of sample efficiency and\u0000cumulative reward with the exception of an agent that has access to perfect\u0000market information which would not be available in a real-world set-up.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Instabilities of explicit finite difference schemes with ghost points on the diffusion equation 扩散方程上带虚点的显式有限差分格式的不稳定性
arXiv - QuantFin - Pricing of Securities Pub Date : 2023-08-08 DOI: arxiv-2308.04629
Fabien Le Floc'h
{"title":"Instabilities of explicit finite difference schemes with ghost points on the diffusion equation","authors":"Fabien Le Floc'h","doi":"arxiv-2308.04629","DOIUrl":"https://doi.org/arxiv-2308.04629","url":null,"abstract":"Ghost, or fictitious points allow to capture boundary conditions that are not\u0000located on the finite difference grid discretization. We explore in this paper\u0000the impact of ghost points on the stability of the explicit Euler finite\u0000difference scheme in the context of the diffusion equation. In particular, we\u0000consider the case of a one-touch option under the Black-Scholes model. The\u0000observations and results are however valid for a much wider range of financial\u0000contracts and models.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Path Shadowing Monte-Carlo 路径阴影蒙特卡洛
arXiv - QuantFin - Pricing of Securities Pub Date : 2023-08-03 DOI: arxiv-2308.01486
Rudy Morel, Stéphane Mallat, Jean-Philippe Bouchaud
{"title":"Path Shadowing Monte-Carlo","authors":"Rudy Morel, Stéphane Mallat, Jean-Philippe Bouchaud","doi":"arxiv-2308.01486","DOIUrl":"https://doi.org/arxiv-2308.01486","url":null,"abstract":"We introduce a Path Shadowing Monte-Carlo method, which provides prediction\u0000of future paths, given any generative model. At any given date, it averages\u0000future quantities over generated price paths whose past history matches, or\u0000`shadows', the actual (observed) history. We test our approach using paths\u0000generated from a maximum entropy model of financial prices, based on a recently\u0000proposed multi-scale analogue of the standard skewness and kurtosis called\u0000`Scattering Spectra'. This model promotes diversity of generated paths while\u0000reproducing the main statistical properties of financial prices, including\u0000stylized facts on volatility roughness. Our method yields state-of-the-art\u0000predictions for future realized volatility and allows one to determine\u0000conditional option smiles for the S&P500 that outperform both the current\u0000version of the Path-Dependent Volatility model and the option market itself.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
American Passport options in an exponential Lévy model 美国护照选项在指数lsamvy模型中
arXiv - QuantFin - Pricing of Securities Pub Date : 2023-07-31 DOI: arxiv-2307.16649
Zakaria Marah
{"title":"American Passport options in an exponential Lévy model","authors":"Zakaria Marah","doi":"arxiv-2307.16649","DOIUrl":"https://doi.org/arxiv-2307.16649","url":null,"abstract":"In this paper we examine the problem of valuing an exotic derivative known as\u0000the American passport option where the underlying is driven by a L'evy\u0000process. The passport option is a call option on a trading account. We derive\u0000the pricing equation, using the dynamic programming principle, and prove that\u0000the option value is a viscosity solution of variational inequality. We also\u0000establish the comparison principle, which yields uniqueness and the convexity\u0000of the viscosity solution.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Machine Learning-powered Pricing of the Multidimensional Passport Option 多维护照选项的机器学习定价
arXiv - QuantFin - Pricing of Securities Pub Date : 2023-07-27 DOI: arxiv-2307.14887
Josef Teichmann, Hanna Wutte
{"title":"Machine Learning-powered Pricing of the Multidimensional Passport Option","authors":"Josef Teichmann, Hanna Wutte","doi":"arxiv-2307.14887","DOIUrl":"https://doi.org/arxiv-2307.14887","url":null,"abstract":"Introduced in the late 90s, the passport option gives its holder the right to\u0000trade in a market and receive any positive gain in the resulting traded account\u0000at maturity. Pricing the option amounts to solving a stochastic control problem\u0000that for $d>1$ risky assets remains an open problem. Even in a correlated\u0000Black-Scholes (BS) market with $d=2$ risky assets, no optimal trading strategy\u0000has been derived in closed form. In this paper, we derive a discrete-time\u0000solution for multi-dimensional BS markets with uncorrelated assets. Moreover,\u0000inspired by the success of deep reinforcement learning in, e.g., board games,\u0000we propose two machine learning-powered approaches to pricing general options\u0000on a portfolio value in general markets. These approaches prove to be\u0000successful for pricing the passport option in one-dimensional and\u0000multi-dimensional uncorrelated BS markets.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"119 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Option Smile Volatility and Implied Probabilities: Implications of Concavity in IV Curves 期权微笑波动率和隐含概率:IV曲线凹凸性的含义
arXiv - QuantFin - Pricing of Securities Pub Date : 2023-07-27 DOI: arxiv-2307.15718
Darsh Kachhara, John K. E Markin, Astha Singh
{"title":"Option Smile Volatility and Implied Probabilities: Implications of Concavity in IV Curves","authors":"Darsh Kachhara, John K. E Markin, Astha Singh","doi":"arxiv-2307.15718","DOIUrl":"https://doi.org/arxiv-2307.15718","url":null,"abstract":"Earnings announcements (EADs) are corporate events that provide investors\u0000with fundamentally important information. The prospect of stock price rises may\u0000also contribute to EADs increased volatility. Using data on extremely short\u0000term options, we study that bimodality in the risk neutral distribution and\u0000concavity in the IV smiles are ubiquitous characteristics before an earnings\u0000announcement day. This study compares the returns between concave and non\u0000concave IV smiles to see if the concavity in the IV curve leads to any\u0000information about the risk in the market and showcases how investors hedge\u0000against extreme volatility during earnings announcements. In fact, our paper\u0000shows in the presence of concave IV smiles; investors pay a significant premium\u0000to hedge against the uncertainty caused by the forthcoming announcement.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interest rate convexity in a Gaussian framework 高斯框架下的利率凸性
arXiv - QuantFin - Pricing of Securities Pub Date : 2023-07-26 DOI: arxiv-2307.14218
Antoine Jacquier, Mugad Oumgari
{"title":"Interest rate convexity in a Gaussian framework","authors":"Antoine Jacquier, Mugad Oumgari","doi":"arxiv-2307.14218","DOIUrl":"https://doi.org/arxiv-2307.14218","url":null,"abstract":"The contributions of this paper are twofold: we define and investigate the\u0000properties of a short rate model driven by a general Gaussian Volterra process\u0000and, after defining precisely a notion of convexity adjustment, derive explicit\u0000formulae for it.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
American options in time-dependent one-factor models: Semi-analytic pricing, numerical methods and ML support 时变单因素模型中的美式期权:半解析定价、数值方法和ML支持
arXiv - QuantFin - Pricing of Securities Pub Date : 2023-07-26 DOI: arxiv-2307.13870
Andrey Itkin, Dmitry Muravey
{"title":"American options in time-dependent one-factor models: Semi-analytic pricing, numerical methods and ML support","authors":"Andrey Itkin, Dmitry Muravey","doi":"arxiv-2307.13870","DOIUrl":"https://doi.org/arxiv-2307.13870","url":null,"abstract":"Semi-analytical pricing of American options in a time-dependent\u0000Ornstein-Uhlenbeck model was presented in [Carr, Itkin, 2020]. It was shown\u0000that to obtain these prices one needs to solve (numerically) a nonlinear\u0000Volterra integral equation of the second kind to find the exercise boundary\u0000(which is a function of the time only). Once this is done, the option prices\u0000follow. It was also shown that computationally this method is as efficient as\u0000the forward finite difference solver while providing better accuracy and\u0000stability. Later this approach called \"the Generalized Integral transform\"\u0000method has been significantly extended by the authors (also, in cooperation\u0000with Peter Carr and Alex Lipton) to various time-dependent one factor, and\u0000stochastic volatility models as applied to pricing barrier options. However,\u0000for American options, despite possible, this was not explicitly reported\u0000anywhere. In this paper our goal is to fill this gap and also discuss which\u0000numerical method (including those in machine learning) could be efficient to\u0000solve the corresponding Volterra integral equations.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
American Exchange option driven by a Lévy process 美国交易所期权由一个lsamvy过程驱动
arXiv - QuantFin - Pricing of Securities Pub Date : 2023-07-20 DOI: arxiv-2307.10900
Zakaria Marah
{"title":"American Exchange option driven by a Lévy process","authors":"Zakaria Marah","doi":"arxiv-2307.10900","DOIUrl":"https://doi.org/arxiv-2307.10900","url":null,"abstract":"We consider the problem of pricing American Exchange options driven by a\u0000L'evy process. We study the properties of American Exchange options, we\u0000represented it as the sum of the price of the corresponding European exchange\u0000option price and an early exercise premium. Secondly, we show some properties\u0000of the free boundary and give an approximative formula of an American Exchange\u0000option.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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