We derive the short-maturity asymptotics for Asian option prices in local-stochastic volatility (LSV) models. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. Using large deviations theory methods, the asymptotics for the OTM options are expressed as a rate function which is represented as a two-dimensional variational problem. We develop a novel expansion method for the variational problem by expanding the rate function around the ATM point. In particular, we derive series expansions in log-moneyness for the solution of this variational problem around the ATM point, and obtain explicit results for the first three terms. We give the ATM volatility level, skew and convexity of the implied volatility of an Asian option in a general local-stochastic volatility model, which can be used as an approximation for pricing Asian options with strikes sufficiently close to the ATM point. Using numerical simulations in the SABR, Heston and an LSV model with bounded local volatility, we show good performance of the asymptotic result for Asian options with sufficiently small maturity.
{"title":"Short-maturity Asian options in local-stochastic volatility models","authors":"Dan Pirjol, Lingjiong Zhu","doi":"arxiv-2409.08377","DOIUrl":"https://doi.org/arxiv-2409.08377","url":null,"abstract":"We derive the short-maturity asymptotics for Asian option prices in\u0000local-stochastic volatility (LSV) models. Both out-of-the-money (OTM) and\u0000at-the-money (ATM) asymptotics are considered. Using large deviations theory\u0000methods, the asymptotics for the OTM options are expressed as a rate function\u0000which is represented as a two-dimensional variational problem. We develop a\u0000novel expansion method for the variational problem by expanding the rate\u0000function around the ATM point. In particular, we derive series expansions in\u0000log-moneyness for the solution of this variational problem around the ATM\u0000point, and obtain explicit results for the first three terms. We give the ATM\u0000volatility level, skew and convexity of the implied volatility of an Asian\u0000option in a general local-stochastic volatility model, which can be used as an\u0000approximation for pricing Asian options with strikes sufficiently close to the\u0000ATM point. Using numerical simulations in the SABR, Heston and an LSV model\u0000with bounded local volatility, we show good performance of the asymptotic\u0000result for Asian options with sufficiently small maturity.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142262891","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}
We address the problem of pricing Chinese convertible bonds(CCB) by Monte Carlo simulation and dynamic programming. At each exercising time, we use the state variables of the underlying stock to regress the continuation value, and then we apply standard backward induction to get the coefficients until the moment of time zero, thus the price of the CCB is obtained. We apply the pricing of CCBs by simulation and test the performance of an under-priced strategy: long the 10 most underpriced CCBs and rebalance daily. The result show this strategy significantly outperforms the double-low strategy which is used as a benchmark. In practice, CCB issuers usually use the downward adjustment clause to to avoid financial distress upon put provision. Therefore, we treat the downward adjustment clause as a probabilistic event triggering the put provision. In this way, we combine the downward adjustment clause with put provision in a simple manner.
{"title":"Valuation Model of Chinese Convertible Bonds Based on Monte Carlo Simulation","authors":"Yu Liu, Gongqiu Zhang","doi":"arxiv-2409.06496","DOIUrl":"https://doi.org/arxiv-2409.06496","url":null,"abstract":"We address the problem of pricing Chinese convertible bonds(CCB) by Monte\u0000Carlo simulation and dynamic programming. At each exercising time, we use the\u0000state variables of the underlying stock to regress the continuation value, and\u0000then we apply standard backward induction to get the coefficients until the\u0000moment of time zero, thus the price of the CCB is obtained. We apply the\u0000pricing of CCBs by simulation and test the performance of an under-priced\u0000strategy: long the 10 most underpriced CCBs and rebalance daily. The result\u0000show this strategy significantly outperforms the double-low strategy which is\u0000used as a benchmark. In practice, CCB issuers usually use the downward\u0000adjustment clause to to avoid financial distress upon put provision. Therefore,\u0000we treat the downward adjustment clause as a probabilistic event triggering the\u0000put provision. In this way, we combine the downward adjustment clause with put\u0000provision in a simple manner.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227358","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}
Despite significant progress in deep learning for financial trading, existing models often face instability and high uncertainty, hindering their practical application. Leveraging advancements in Large Language Models (LLMs) and multi-agent architectures, we propose a novel framework for quantitative stock investment in portfolio management and alpha mining. Our framework addresses these issues by integrating LLMs to generate diversified alphas and employing a multi-agent approach to dynamically evaluate market conditions. This paper proposes a framework where large language models (LLMs) mine alpha factors from multimodal financial data, ensuring a comprehensive understanding of market dynamics. The first module extracts predictive signals by integrating numerical data, research papers, and visual charts. The second module uses ensemble learning to construct a diverse pool of trading agents with varying risk preferences, enhancing strategy performance through a broader market analysis. In the third module, a dynamic weight-gating mechanism selects and assigns weights to the most relevant agents based on real-time market conditions, enabling the creation of an adaptive and context-aware composite alpha formula. Extensive experiments on the Chinese stock markets demonstrate that this framework significantly outperforms state-of-the-art baselines across multiple financial metrics. The results underscore the efficacy of combining LLM-generated alphas with a multi-agent architecture to achieve superior trading performance and stability. This work highlights the potential of AI-driven approaches in enhancing quantitative investment strategies and sets a new benchmark for integrating advanced machine learning techniques in financial trading can also be applied on diverse markets.
{"title":"Automate Strategy Finding with LLM in Quant investment","authors":"Zhizhuo Kou, Holam Yu, Jingshu Peng, Lei Chen","doi":"arxiv-2409.06289","DOIUrl":"https://doi.org/arxiv-2409.06289","url":null,"abstract":"Despite significant progress in deep learning for financial trading, existing\u0000models often face instability and high uncertainty, hindering their practical\u0000application. Leveraging advancements in Large Language Models (LLMs) and\u0000multi-agent architectures, we propose a novel framework for quantitative stock\u0000investment in portfolio management and alpha mining. Our framework addresses\u0000these issues by integrating LLMs to generate diversified alphas and employing a\u0000multi-agent approach to dynamically evaluate market conditions. This paper\u0000proposes a framework where large language models (LLMs) mine alpha factors from\u0000multimodal financial data, ensuring a comprehensive understanding of market\u0000dynamics. The first module extracts predictive signals by integrating numerical\u0000data, research papers, and visual charts. The second module uses ensemble\u0000learning to construct a diverse pool of trading agents with varying risk\u0000preferences, enhancing strategy performance through a broader market analysis.\u0000In the third module, a dynamic weight-gating mechanism selects and assigns\u0000weights to the most relevant agents based on real-time market conditions,\u0000enabling the creation of an adaptive and context-aware composite alpha formula.\u0000Extensive experiments on the Chinese stock markets demonstrate that this\u0000framework significantly outperforms state-of-the-art baselines across multiple\u0000financial metrics. The results underscore the efficacy of combining\u0000LLM-generated alphas with a multi-agent architecture to achieve superior\u0000trading performance and stability. This work highlights the potential of\u0000AI-driven approaches in enhancing quantitative investment strategies and sets a\u0000new benchmark for integrating advanced machine learning techniques in financial\u0000trading can also be applied on diverse markets.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218780","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}
In this paper, we propose a semi-analytical approach to pricing options on SOFR futures where the underlying SOFR follows a time-dependent CEV model. By definition, these options change their type at the beginning of the reference period: before this time, this is an American option written on a SOFR forward price as an underlying, and after this point, this is an arithmetic Asian option with an American style exercise written on the daily SOFR rates. We develop a new version of the GIT method and solve both problems semi-analytically, obtaining the option price, the exercise boundary, and the option Greeks. This work is intended to address the concern that the transfer from LIBOR to SOFR has resulted in a situation in which the options of the key money market (i.e., futures on the reference rate) are options without any pricing model available. Therefore, the trading in options on 3M SOFR futures currently ends before their reference quarter starts, to eliminate the final metamorphosis into exotic options.
{"title":"Semi-analytical pricing of options written on SOFR futures","authors":"Andrey Itkin, Yerkin Kitapbayev","doi":"arxiv-2409.04903","DOIUrl":"https://doi.org/arxiv-2409.04903","url":null,"abstract":"In this paper, we propose a semi-analytical approach to pricing options on\u0000SOFR futures where the underlying SOFR follows a time-dependent CEV model. By\u0000definition, these options change their type at the beginning of the reference\u0000period: before this time, this is an American option written on a SOFR forward\u0000price as an underlying, and after this point, this is an arithmetic Asian\u0000option with an American style exercise written on the daily SOFR rates. We\u0000develop a new version of the GIT method and solve both problems\u0000semi-analytically, obtaining the option price, the exercise boundary, and the\u0000option Greeks. This work is intended to address the concern that the transfer\u0000from LIBOR to SOFR has resulted in a situation in which the options of the key\u0000money market (i.e., futures on the reference rate) are options without any\u0000pricing model available. Therefore, the trading in options on 3M SOFR futures\u0000currently ends before their reference quarter starts, to eliminate the final\u0000metamorphosis into exotic options.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218779","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}
David R. Baños, Salvador Ortiz-Latorre, Oriol Zamora Font
The main purpose of this work is the derivation of a functional partial differential equation (FPDE) for the calculations of equity-linked insurance policies, where the payment stream may depend on the whole past history of the financial asset. To this end, we employ variational techniques from the theory of functional It^o calculus.
{"title":"A functional variational approach to pricing path dependent insurance policies","authors":"David R. Baños, Salvador Ortiz-Latorre, Oriol Zamora Font","doi":"arxiv-2409.00780","DOIUrl":"https://doi.org/arxiv-2409.00780","url":null,"abstract":"The main purpose of this work is the derivation of a functional partial\u0000differential equation (FPDE) for the calculations of equity-linked insurance\u0000policies, where the payment stream may depend on the whole past history of the\u0000financial asset. To this end, we employ variational techniques from the theory\u0000of functional It^o calculus.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218781","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}
This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard models often rely on constant drift and volatility assumptions, which limits their ability to accurately capture the complex and erratic nature of financial markets. By incorporating PDifMPs, our method accounts for sudden market fluctuations, providing a more realistic model of asset price dynamics. We benchmark our approach with the Longstaff-Schwartz algorithm, both in its original form and modified to include PDifMP asset price trajectories. Numerical simulations demonstrate that our PDifMP-based method not only provides a more accurate reflection of market behaviour but also offers practical advantages in terms of computational efficiency. The results suggest that PDifMPs can significantly improve the predictive accuracy of American options pricing by more closely aligning with the stochastic volatility and jumps observed in real financial markets.
{"title":"American option pricing using generalised stochastic hybrid systems","authors":"Evelyn Buckwar, Sascha Desmettre, Agnes Mallinger, Amira Meddah","doi":"arxiv-2409.07477","DOIUrl":"https://doi.org/arxiv-2409.07477","url":null,"abstract":"This paper presents a novel approach to pricing American options using\u0000piecewise diffusion Markov processes (PDifMPs), a type of generalised\u0000stochastic hybrid system that integrates continuous dynamics with discrete jump\u0000processes. Standard models often rely on constant drift and volatility\u0000assumptions, which limits their ability to accurately capture the complex and\u0000erratic nature of financial markets. By incorporating PDifMPs, our method\u0000accounts for sudden market fluctuations, providing a more realistic model of\u0000asset price dynamics. We benchmark our approach with the Longstaff-Schwartz\u0000algorithm, both in its original form and modified to include PDifMP asset price\u0000trajectories. Numerical simulations demonstrate that our PDifMP-based method\u0000not only provides a more accurate reflection of market behaviour but also\u0000offers practical advantages in terms of computational efficiency. The results\u0000suggest that PDifMPs can significantly improve the predictive accuracy of\u0000American options pricing by more closely aligning with the stochastic\u0000volatility and jumps observed in real financial markets.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218782","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}
Rohini Kumar, Frederick "Forrest" Miller, Hussein Nasralah, Stephan Sturm
This paper studies the pricing of contingent claims of American style, using indifference pricing by fully dynamic convex risk measures. We provide a general definition of risk-indifference prices for buyers and sellers in continuous time, in a setting where buyer and seller have potentially different information, and show that these definitions are consistent with no-arbitrage principles. Specifying to stochastic volatility models, we characterize indifference prices via solutions of Backward Stochastic Differential Equations reflected at Backward Stochastic Differential Equations and show that this characterization provides a basis for the implementation of numerical methods using deep learning.
{"title":"Risk-indifference Pricing of American-style Contingent Claims","authors":"Rohini Kumar, Frederick \"Forrest\" Miller, Hussein Nasralah, Stephan Sturm","doi":"arxiv-2409.00095","DOIUrl":"https://doi.org/arxiv-2409.00095","url":null,"abstract":"This paper studies the pricing of contingent claims of American style, using\u0000indifference pricing by fully dynamic convex risk measures. We provide a\u0000general definition of risk-indifference prices for buyers and sellers in\u0000continuous time, in a setting where buyer and seller have potentially different\u0000information, and show that these definitions are consistent with no-arbitrage\u0000principles. Specifying to stochastic volatility models, we characterize\u0000indifference prices via solutions of Backward Stochastic Differential Equations\u0000reflected at Backward Stochastic Differential Equations and show that this\u0000characterization provides a basis for the implementation of numerical methods\u0000using deep learning.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218783","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}
We study optimal stopping for a diffusion process with unknown model primitives within the continuous-time reinforcement learning (RL) framework developed by Wang et al. (2020). By penalizing its variational inequality, we transform the stopping problem into a stochastic optimal control problem with two actions. We then randomize control into Bernoulli distributions and add an entropy regularizer to encourage exploration. We derive a semi-analytical optimal Bernoulli distribution, based on which we devise RL algorithms using the martingale approach established in Jia and Zhou (2022a) and prove a policy improvement theorem. Finally, we demonstrate the effectiveness of the algorithms in examples of pricing finite-horizon American put options and solving Merton's problem with transaction costs, and show that both the offline and online algorithms achieve high accuracy in learning the value functions and characterizing the associated free boundaries.
我们在 Wang 等人（2020）提出的连续时间强化学习（RL）框架内研究了具有未知模型原型的扩散过程的最优停止问题。通过对其变分不等式进行惩罚，我们将停止问题转化为一个具有两个动作的随机最优控制问题。然后，我们将控制随机化为伯努利分布，并添加熵正则来鼓励探索。在此基础上，我们利用贾和周（2022a）建立的马丁格尔方法设计了 RL 算法，并证明了策略改进定理。最后，我们以有限区间美式看跌期权定价和解决有交易成本的默顿问题为例，证明了算法的有效性，并表明离线算法和在线算法在学习价值函数和描述相关自由边界方面都达到了很高的精度。
{"title":"Learning to Optimally Stop a Diffusion Process","authors":"Min Dai, Yu Sun, Zuo Quan Xu, Xun Yu Zhou","doi":"arxiv-2408.09242","DOIUrl":"https://doi.org/arxiv-2408.09242","url":null,"abstract":"We study optimal stopping for a diffusion process with unknown model\u0000primitives within the continuous-time reinforcement learning (RL) framework\u0000developed by Wang et al. (2020). By penalizing its variational inequality, we\u0000transform the stopping problem into a stochastic optimal control problem with\u0000two actions. We then randomize control into Bernoulli distributions and add an\u0000entropy regularizer to encourage exploration. We derive a semi-analytical\u0000optimal Bernoulli distribution, based on which we devise RL algorithms using\u0000the martingale approach established in Jia and Zhou (2022a) and prove a policy\u0000improvement theorem. Finally, we demonstrate the effectiveness of the\u0000algorithms in examples of pricing finite-horizon American put options and\u0000solving Merton's problem with transaction costs, and show that both the offline\u0000and online algorithms achieve high accuracy in learning the value functions and\u0000characterizing the associated free boundaries.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218784","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}
In this article we derive partial differential equations (PDEs) for pricing interest rate derivatives under the generalized Forward Market Model (FMM) recently presented by A. Lyashenko and F. Mercurio in cite{lyashenkoMercurio:Mar2019} to model the dynamics of the Risk Free Rates (RFRs) that are replacing the traditional IBOR rates in the financial industry. Moreover, for the numerical solution of the proposed PDEs formulation, we develop some adaptations of the finite differences methods developed in cite{LopezPerezVazquez:sisc} that are very suitable to treat the presence of spatial mixed derivatives. This work is the first article in the literature where PDE methods are used to value RFR derivatives. Additionally, Monte Carlo-based methods will be designed and the results are compared with those obtained by the numerical solution of PDEs.
{"title":"PDEs for pricing interest rate derivatives under the new generalized Forward Market Model (FMM)","authors":"J. G. López-Salas, S. Pérez-Rodríguez, C. Vázquez","doi":"arxiv-2408.02289","DOIUrl":"https://doi.org/arxiv-2408.02289","url":null,"abstract":"In this article we derive partial differential equations (PDEs) for pricing\u0000interest rate derivatives under the generalized Forward Market Model (FMM)\u0000recently presented by A. Lyashenko and F. Mercurio in\u0000cite{lyashenkoMercurio:Mar2019} to model the dynamics of the Risk Free Rates\u0000(RFRs) that are replacing the traditional IBOR rates in the financial industry.\u0000Moreover, for the numerical solution of the proposed PDEs formulation, we\u0000develop some adaptations of the finite differences methods developed in\u0000cite{LopezPerezVazquez:sisc} that are very suitable to treat the presence of\u0000spatial mixed derivatives. This work is the first article in the literature\u0000where PDE methods are used to value RFR derivatives. Additionally, Monte\u0000Carlo-based methods will be designed and the results are compared with those\u0000obtained by the numerical solution of PDEs.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938678","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}
A. Agarwal, S. De Marco, E. Gobet, J. G. Lopez-Salas, F. Noubiagain, A. Zhou
We introduce a new class of anticipative backward stochastic differential equations with a dependence of McKean type on the law of the solution, that we name MKABSDE. We provide existence and uniqueness results in a general framework with relatively general regularity assumptions on the coefficients. We show how such stochastic equations arise within the modern paradigm of derivative pricing where a central counterparty (CCP) requires the members to deposit variation and initial margins to cover their exposure. In the case when the initial margin is proportional to the Conditional Value-at-Risk (CVaR) of the contract price, we apply our general result to define the price as a solution of a MKABSDE. We provide several linear and non-linear simpler approximations, which we solve using different numerical (deterministic and Monte-Carlo) methods.
{"title":"Numerical approximations of McKean Anticipative Backward Stochastic Differential Equations arising in Initial Margin requirements","authors":"A. Agarwal, S. De Marco, E. Gobet, J. G. Lopez-Salas, F. Noubiagain, A. Zhou","doi":"arxiv-2408.01185","DOIUrl":"https://doi.org/arxiv-2408.01185","url":null,"abstract":"We introduce a new class of anticipative backward stochastic differential\u0000equations with a dependence of McKean type on the law of the solution, that we\u0000name MKABSDE. We provide existence and uniqueness results in a general\u0000framework with relatively general regularity assumptions on the coefficients.\u0000We show how such stochastic equations arise within the modern paradigm of\u0000derivative pricing where a central counterparty (CCP) requires the members to\u0000deposit variation and initial margins to cover their exposure. In the case when\u0000the initial margin is proportional to the Conditional Value-at-Risk (CVaR) of\u0000the contract price, we apply our general result to define the price as a\u0000solution of a MKABSDE. We provide several linear and non-linear simpler\u0000approximations, which we solve using different numerical (deterministic and\u0000Monte-Carlo) methods.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938682","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}
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