We seek an analytic pricing formula for SOFR futures contracts under an extension of the Hull-White model which incorporates not only the intrinsic convexity adjustments captured by Mercurio [2018], but also the skew and smile observed in options markets as done in Turfus and Romero-Berm'udez [2023].
{"title":"Analytic Pricing of SOFR Futures Contracts with Smile and Skew","authors":"Colin Turfus, Aurelio Romero-Bermúdez","doi":"arxiv-2401.15728","DOIUrl":"https://doi.org/arxiv-2401.15728","url":null,"abstract":"We seek an analytic pricing formula for SOFR futures contracts under an\u0000extension of the Hull-White model which incorporates not only the intrinsic\u0000convexity adjustments captured by Mercurio [2018], but also the skew and smile\u0000observed in options markets as done in Turfus and Romero-Berm'udez [2023].","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139587899","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}
L'evy-driven Ornstein-Uhlenbeck (OU) processes represent an intriguing class of stochastic processes that have garnered interest in the energy sector for their ability to capture typical features of market dynamics. However, in the current state-of-the-art, Monte Carlo simulations of these processes are not straightforward for two main reasons: i) algorithms are available only for some particular processes within this class; ii) they are often computationally expensive. In this paper, we introduce a new simulation technique designed to address both challenges. It relies on the numerical inversion of the characteristic function, offering a general methodology applicable to all L'evy-driven OU processes. Moreover, leveraging FFT, the proposed methodology ensures fast and accurate simulations, providing a solid basis for the widespread adoption of these processes in the energy sector. Lastly, the algorithm allows an optimal control of the numerical error. We apply the technique to the pricing of energy derivatives, comparing the results with existing benchmarks. Our findings indicate that the proposed methodology is at least one order of magnitude faster than existing algorithms, all while maintaining an equivalent level of accuracy.
L'evy-driven Ornstein-Uhlenbeck (OU) 过程是一类引人入胜的随机过程，因其能够捕捉市场动态的典型特征而在能源领域备受关注。然而，在当前最先进的技术中，这些过程的蒙特卡罗模拟并不直接，主要原因有两个：i) 算法仅适用于该类过程中的某些特定过程；ii) 通常计算成本较高。在本文中，我们介绍了一种新的模拟技术，旨在解决这两个难题。它依赖于特征函数的数值反演，提供了一种适用于所有 L'evy-driven OU 过程的通用方法。此外，利用 FFT，所提出的方法确保了快速准确的模拟，为这些过程在能源领域的广泛应用提供了坚实的基础。最后，该算法允许对数值误差进行优化控制。我们将该技术应用于能源衍生品的定价，并将结果与现有基准进行比较。我们的研究结果表明，所提出的方法比现有算法至少快一个数量级，同时还能保持同等的精度水平。
{"title":"Fast and General Simulation of Lévy-driven OU processes for Energy Derivatives","authors":"Roberto Baviera, Pietro Manzoni","doi":"arxiv-2401.15483","DOIUrl":"https://doi.org/arxiv-2401.15483","url":null,"abstract":"L'evy-driven Ornstein-Uhlenbeck (OU) processes represent an intriguing class\u0000of stochastic processes that have garnered interest in the energy sector for\u0000their ability to capture typical features of market dynamics. However, in the\u0000current state-of-the-art, Monte Carlo simulations of these processes are not\u0000straightforward for two main reasons: i) algorithms are available only for some\u0000particular processes within this class; ii) they are often computationally\u0000expensive. In this paper, we introduce a new simulation technique designed to\u0000address both challenges. It relies on the numerical inversion of the\u0000characteristic function, offering a general methodology applicable to all\u0000L'evy-driven OU processes. Moreover, leveraging FFT, the proposed methodology\u0000ensures fast and accurate simulations, providing a solid basis for the\u0000widespread adoption of these processes in the energy sector. Lastly, the\u0000algorithm allows an optimal control of the numerical error. We apply the\u0000technique to the pricing of energy derivatives, comparing the results with\u0000existing benchmarks. Our findings indicate that the proposed methodology is at\u0000least one order of magnitude faster than existing algorithms, all while\u0000maintaining an equivalent level of accuracy.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139587900","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 the local sensitivity of heating degree day (HDD) and cooling degree day (CDD) temperature futures and option prices with respect to perturbations in the deseasonalized temperature or in one of its derivatives up to a certain order determined by the continuous-time autoregressive process modelling the deseasonalized temperature in the HDD and CDD indexes. We also consider an empirical case where a CAR process of autoregressive order 3 is fitted to New York temperatures and we perform a study of the local sensitivity of these financial contracts and a posterior analysis of the results.
我们研究了供暖度日（HDD）和降温度日（CDD）温度期货和期权价格对反季节化温度或其导数之一的扰动的局部敏感性，该扰动的最大阶数由在 HDD 和 CDD 指数中模拟反季节化温度的连续时间自回归过程决定。我们还考虑了一个经验案例，即对纽约气温拟合一个自回归阶次为 3 的 CAR 过程，我们对这些金融合约的局部敏感性进行了研究，并对结果进行了后验分析。
{"title":"Local sensitivity analysis of heating degree day and cooling degree day temperature derivatives prices","authors":"Sara Ana Solanilla Blanco","doi":"arxiv-2403.00006","DOIUrl":"https://doi.org/arxiv-2403.00006","url":null,"abstract":"We study the local sensitivity of heating degree day (HDD) and cooling degree\u0000day (CDD) temperature futures and option prices with respect to perturbations\u0000in the deseasonalized temperature or in one of its derivatives up to a certain\u0000order determined by the continuous-time autoregressive process modelling the\u0000deseasonalized temperature in the HDD and CDD indexes. We also consider an\u0000empirical case where a CAR process of autoregressive order 3 is fitted to New\u0000York temperatures and we perform a study of the local sensitivity of these\u0000financial contracts and a posterior analysis of the results.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"135 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140036561","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 propose an innovative data-driven option pricing methodology that relies exclusively on the dataset of historical underlying asset prices. While the dataset is rooted in the objective world, option prices are commonly expressed as discounted expectations of their terminal payoffs in a risk-neutral world. Bridging this gap motivates us to identify a pricing kernel process, transforming option pricing into evaluating expectations in the objective world. We recover the pricing kernel by solving a utility maximization problem, and evaluate the expectations in terms of a functional optimization problem. Leveraging the deep learning technique, we design data-driven algorithms to solve both optimization problems over the dataset. Numerical experiments are presented to demonstrate the efficiency of our methodology.
{"title":"Data-driven Option Pricing","authors":"Min Dai, Hanqing Jin, Xi Yang","doi":"arxiv-2401.11158","DOIUrl":"https://doi.org/arxiv-2401.11158","url":null,"abstract":"We propose an innovative data-driven option pricing methodology that relies\u0000exclusively on the dataset of historical underlying asset prices. While the\u0000dataset is rooted in the objective world, option prices are commonly expressed\u0000as discounted expectations of their terminal payoffs in a risk-neutral world.\u0000Bridging this gap motivates us to identify a pricing kernel process,\u0000transforming option pricing into evaluating expectations in the objective\u0000world. We recover the pricing kernel by solving a utility maximization problem,\u0000and evaluate the expectations in terms of a functional optimization problem.\u0000Leveraging the deep learning technique, we design data-driven algorithms to\u0000solve both optimization problems over the dataset. Numerical experiments are\u0000presented to demonstrate the efficiency of our methodology.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139558780","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 proposed a two-step Longstaff Schwartz Monte Carlo (LSMC) method with two regression models fitted at each time step to price game options. Although the original LSMC can be used to price game options with an enlarged range of path in regression and a modified cashflow updating rule, we identified a drawback of such approach, which motivated us to propose our approach. We implemented numerical examples with benchmarks using binomial tree and numerical PDE, and it showed that our method produces more reliable results comparing to the original LSMC.
{"title":"A Two-Step Longstaff Schwartz Monte Carlo Approach to Game Option Pricing","authors":"Ce Wang","doi":"arxiv-2401.08093","DOIUrl":"https://doi.org/arxiv-2401.08093","url":null,"abstract":"We proposed a two-step Longstaff Schwartz Monte Carlo (LSMC) method with two\u0000regression models fitted at each time step to price game options. Although the\u0000original LSMC can be used to price game options with an enlarged range of path\u0000in regression and a modified cashflow updating rule, we identified a drawback\u0000of such approach, which motivated us to propose our approach. We implemented\u0000numerical examples with benchmarks using binomial tree and numerical PDE, and\u0000it showed that our method produces more reliable results comparing to the\u0000original LSMC.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482701","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}
The research delves into the capabilities of a transformer-based neural network for Ethereum cryptocurrency price forecasting. The experiment runs around the hypothesis that cryptocurrency prices are strongly correlated with other cryptocurrencies and the sentiments around the cryptocurrency. The model employs a transformer architecture for several setups from single-feature scenarios to complex configurations incorporating volume, sentiment, and correlated cryptocurrency prices. Despite a smaller dataset and less complex architecture, the transformer model surpasses ANN and MLP counterparts on some parameters. The conclusion presents a hypothesis on the illusion of causality in cryptocurrency price movements driven by sentiments.
该研究深入探讨了基于变压器的神经网络预测以太坊加密货币价格的能力。实验的假设是，加密货币的价格与其他加密货币以及围绕加密货币的情绪密切相关。该模式采用了变压器架构，适用于从单一功能场景到包含交易量、情绪和相关加密货币价格的复杂配置等多种设置。尽管数据集较小，架构也不复杂，但变压器模型在某些参数上超过了 ANN 和 MLP 模型。结论中提出了一个假设，即由情绪驱动的加密货币价格变动中的因果关系假象。
{"title":"Transformer-based approach for Ethereum Price Prediction Using Crosscurrency correlation and Sentiment Analysis","authors":"Shubham Singh, Mayur Bhat","doi":"arxiv-2401.08077","DOIUrl":"https://doi.org/arxiv-2401.08077","url":null,"abstract":"The research delves into the capabilities of a transformer-based neural\u0000network for Ethereum cryptocurrency price forecasting. The experiment runs\u0000around the hypothesis that cryptocurrency prices are strongly correlated with\u0000other cryptocurrencies and the sentiments around the cryptocurrency. The model\u0000employs a transformer architecture for several setups from single-feature\u0000scenarios to complex configurations incorporating volume, sentiment, and\u0000correlated cryptocurrency prices. Despite a smaller dataset and less complex\u0000architecture, the transformer model surpasses ANN and MLP counterparts on some\u0000parameters. The conclusion presents a hypothesis on the illusion of causality\u0000in cryptocurrency price movements driven by sentiments.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482081","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 consider the discrete-time setting, and the market model described by (S,F,T)$. Herein F is the ``public" flow of information which is available to all agents overtime, S is the discounted price process of d-tradable assets, and T is an arbitrary random time whose occurrence might not be observable via F. Thus, we consider the larger flow G which incorporates F and makes T an observable random time. This framework covers the credit risk theory setting, the life insurance setting and the setting of employee stock option valuation. For the stopped model (S^T,G) and for various vulnerable claims, based on this model, we address the super-hedging pricing valuation problem and its intrinsic Immediate-Profit arbitrage (IP hereafter for short). Our first main contribution lies in singling out the impact of change of prior and/or information on conditional essential supremum, which is a vital tool in super-hedging pricing. The second main contribution consists of describing as explicit as possible how the set of super-hedging prices expands under the stochasticity of T and its risks, and we address the IP arbitrage for (S^T,G) as well. The third main contribution resides in elaborating as explicit as possible pricing formulas for vulnerable claims, and singling out the various informational risks in the prices' dynamics.
在本文中，我们考虑离散时间设置，以及由 (S,F,T)$ 描述的市场模型。其中，F 是 "公开 "的信息流，所有代理人都能在超时获得；S 是可交易资产的贴现价格过程；T 是任意随机时间，其发生可能无法通过 F 观察到。这一框架涵盖了信用风险理论环境、人寿保险环境和员工股票期权估值环境。对于停止模型（S^T,G）和基于该模型的各种脆弱索赔，我们解决了超级套期保值定价估值问题及其内在的立即获利套利（以下简称 IP）问题。我们的第一个主要贡献在于挑出了先验和/或信息变化对条件基本上量的影响，这是超级套期保值定价的重要工具。我们的第二个主要贡献在于尽可能明确地描述了超级套期保值价格集合是如何在 T 及其风险的随机性条件下扩展的，同时我们还解决了 (S^T,G) 的 IP 套利问题。第三个主要贡献在于尽可能明确地阐述了脆弱债权的定价公式，并将价格动态中的各种信息风险单独列出。
{"title":"Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon","authors":"Tahir Choulli, Emmanuel Lepinette","doi":"arxiv-2401.05713","DOIUrl":"https://doi.org/arxiv-2401.05713","url":null,"abstract":"In this paper, we consider the discrete-time setting, and the market model\u0000described by (S,F,T)$. Herein F is the ``public\" flow of information which is\u0000available to all agents overtime, S is the discounted price process of\u0000d-tradable assets, and T is an arbitrary random time whose occurrence might not\u0000be observable via F. Thus, we consider the larger flow G which incorporates F\u0000and makes T an observable random time. This framework covers the credit risk\u0000theory setting, the life insurance setting and the setting of employee stock\u0000option valuation. For the stopped model (S^T,G) and for various vulnerable\u0000claims, based on this model, we address the super-hedging pricing valuation\u0000problem and its intrinsic Immediate-Profit arbitrage (IP hereafter for short).\u0000Our first main contribution lies in singling out the impact of change of prior\u0000and/or information on conditional essential supremum, which is a vital tool in\u0000super-hedging pricing. The second main contribution consists of describing as\u0000explicit as possible how the set of super-hedging prices expands under the\u0000stochasticity of T and its risks, and we address the IP arbitrage for (S^T,G)\u0000as well. The third main contribution resides in elaborating as explicit as\u0000possible pricing formulas for vulnerable claims, and singling out the various\u0000informational risks in the prices' dynamics.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139459693","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 develop a novel time-change approach to study the shape of implied volatility smiles. The method is applicable to common semimartingale models, including jump-diffusion, rough volatility and infinite activity models. We approximate the at-the-money skew and curvature with an improved moment-based formula. The moments are further explicitly computed under a time change framework. The limiting skew and curvature for several models are considered. We also test the accuracy of the short-term approximation results on models via numerical methods and on empirical data. Finally, we apply the method to the calibration problem.
{"title":"Decomposing Smiles: A Time Change Approach","authors":"Liexin Cheng, Xue Cheng","doi":"arxiv-2401.03776","DOIUrl":"https://doi.org/arxiv-2401.03776","url":null,"abstract":"We develop a novel time-change approach to study the shape of implied\u0000volatility smiles. The method is applicable to common semimartingale models,\u0000including jump-diffusion, rough volatility and infinite activity models. We\u0000approximate the at-the-money skew and curvature with an improved moment-based\u0000formula. The moments are further explicitly computed under a time change\u0000framework. The limiting skew and curvature for several models are considered.\u0000We also test the accuracy of the short-term approximation results on models via\u0000numerical methods and on empirical data. Finally, we apply the method to the\u0000calibration problem.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139408558","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}
An extensive empirical study of the class of Volterra Bergomi models using SPX options data between 2011 and 2022 reveals the following fact-check on two fundamental claims echoed in the rough volatility literature: Do rough volatility models with Hurst index $H in (0,1/2)$ really capture well SPX implied volatility surface with very few parameters? No, rough volatility models are inconsistent with the global shape of SPX smiles. They suffer from severe structural limitations imposed by the roughness component, with the Hurst parameter $H in (0,1/2)$ controlling the smile in a poor way. In particular, the SPX at-the-money skew is incompatible with the power-law shape generated by rough volatility models. The skew of rough volatility models increases too fast on the short end, and decays too slow on the longer end where "negative" $H$ is sometimes needed. Do rough volatility models really outperform consistently their classical Markovian counterparts? No, for short maturities they underperform their one-factor Markovian counterpart with the same number of parameters. For longer maturities, they do not systematically outperform the one-factor model and significantly underperform when compared to an under-parametrized two-factor Markovian model with only one additional calibratable parameter. On the positive side: our study identifies a (non-rough) path-dependent Bergomi model and an under-parametrized two-factor Markovian Bergomi model that consistently outperform their rough counterpart in capturing SPX smiles between one week and three years with only 3 to 4 calibratable parameters. end{abstract}
{"title":"Volatility models in practice: Rough, Path-dependent or Markovian?","authors":"Eduardo Abi JaberXiaoyuan, ShaunXiaoyuan, Li","doi":"arxiv-2401.03345","DOIUrl":"https://doi.org/arxiv-2401.03345","url":null,"abstract":"An extensive empirical study of the class of Volterra Bergomi models using\u0000SPX options data between 2011 and 2022 reveals the following fact-check on two\u0000fundamental claims echoed in the rough volatility literature: Do rough volatility models with Hurst index $H in (0,1/2)$ really capture\u0000well SPX implied volatility surface with very few parameters? No, rough\u0000volatility models are inconsistent with the global shape of SPX smiles. They\u0000suffer from severe structural limitations imposed by the roughness component,\u0000with the Hurst parameter $H in (0,1/2)$ controlling the smile in a poor way.\u0000In particular, the SPX at-the-money skew is incompatible with the power-law\u0000shape generated by rough volatility models. The skew of rough volatility models\u0000increases too fast on the short end, and decays too slow on the longer end\u0000where \"negative\" $H$ is sometimes needed. Do rough volatility models really outperform consistently their classical\u0000Markovian counterparts? No, for short maturities they underperform their\u0000one-factor Markovian counterpart with the same number of parameters. For longer\u0000maturities, they do not systematically outperform the one-factor model and\u0000significantly underperform when compared to an under-parametrized two-factor\u0000Markovian model with only one additional calibratable parameter. On the positive side: our study identifies a (non-rough) path-dependent\u0000Bergomi model and an under-parametrized two-factor Markovian Bergomi model that\u0000consistently outperform their rough counterpart in capturing SPX smiles between\u0000one week and three years with only 3 to 4 calibratable parameters.\u0000end{abstract}","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139408815","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 sets out a framework for the valuation of insurance liabilities that is intended to be economically realistic, elementary, reasonably practically applicable, and as a special case to provide a basis for the valuation in regulatory solvency systems such as Solvency II and the SST. The valuation framework is based on the cost of producing the liabilities to an insurance company that is subject to solvency regulation (regulatory solvency capital requirements) and insolvency laws (consequences of failure) in finite discrete time. Starting from the replication approach of classical no-arbitrage theory, the framework additionally considers the nature and cost of capital (expressed by a ``financiability condition"), that the liabilities may be required to be fulfilled only ``in sufficiently many cases" (expressed by a ``fulfillment condition"), production using ``fully illiquid" assets in addition to tradables, and the asymmetry between assets and liabilities. We identify necessary and sufficient conditions on the capital investment under which the framework recovers the market prices of tradables, investigate extending production to take account of insolvency, implications of using illiquid assets in the production, and show how Solvency II and SST valuation can be derived with specific assumptions.
{"title":"A framework for the valuation of insurance liabilities by production cost","authors":"Christoph Moehr","doi":"arxiv-2401.00263","DOIUrl":"https://doi.org/arxiv-2401.00263","url":null,"abstract":"This paper sets out a framework for the valuation of insurance liabilities\u0000that is intended to be economically realistic, elementary, reasonably\u0000practically applicable, and as a special case to provide a basis for the\u0000valuation in regulatory solvency systems such as Solvency II and the SST. The\u0000valuation framework is based on the cost of producing the liabilities to an\u0000insurance company that is subject to solvency regulation (regulatory solvency\u0000capital requirements) and insolvency laws (consequences of failure) in finite\u0000discrete time. Starting from the replication approach of classical no-arbitrage\u0000theory, the framework additionally considers the nature and cost of capital\u0000(expressed by a ``financiability condition\"), that the liabilities may be\u0000required to be fulfilled only ``in sufficiently many cases\" (expressed by a\u0000``fulfillment condition\"), production using ``fully illiquid\" assets in\u0000addition to tradables, and the asymmetry between assets and liabilities. We\u0000identify necessary and sufficient conditions on the capital investment under\u0000which the framework recovers the market prices of tradables, investigate\u0000extending production to take account of insolvency, implications of using\u0000illiquid assets in the production, and show how Solvency II and SST valuation\u0000can be derived with specific assumptions.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139077878","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：