The accurate valuation of financial derivatives plays a pivotal role in the finance industry. Although closed formulas for pricing are available for certain models and option types, exemplified by the European Call and Put options in the Black-Scholes Model, the use of either more complex models or more sophisticated options precludes the existence of such formulas, thereby requiring alternative approaches. The Monte Carlo simulation, an alternative approach effective in nearly all scenarios, has already been challenged by quantum computing techniques that leverage Amplitude Estimation. Despite its theoretical promise, this approach currently faces limitations due to the constraints of hardware in the Noisy Intermediate-Scale Quantum (NISQ) era. In this study, we introduce and analyze a quantum algorithm for pricing European call options across a broad spectrum of asset models. This method transforms a classical approach, which utilizes the Fast Fourier Transform (FFT), into a quantum algorithm, leveraging the efficiency of the Quantum Fourier Transform (QFT). Furthermore, we compare this novel algorithm with existing quantum algorithms for option pricing.
{"title":"Pricing of European Calls with the Quantum Fourier Transform","authors":"Tom Ewen","doi":"arxiv-2404.14115","DOIUrl":"https://doi.org/arxiv-2404.14115","url":null,"abstract":"The accurate valuation of financial derivatives plays a pivotal role in the\u0000finance industry. Although closed formulas for pricing are available for\u0000certain models and option types, exemplified by the European Call and Put\u0000options in the Black-Scholes Model, the use of either more complex models or\u0000more sophisticated options precludes the existence of such formulas, thereby\u0000requiring alternative approaches. The Monte Carlo simulation, an alternative\u0000approach effective in nearly all scenarios, has already been challenged by\u0000quantum computing techniques that leverage Amplitude Estimation. Despite its\u0000theoretical promise, this approach currently faces limitations due to the\u0000constraints of hardware in the Noisy Intermediate-Scale Quantum (NISQ) era. In this study, we introduce and analyze a quantum algorithm for pricing\u0000European call options across a broad spectrum of asset models. This method\u0000transforms a classical approach, which utilizes the Fast Fourier Transform\u0000(FFT), into a quantum algorithm, leveraging the efficiency of the Quantum\u0000Fourier Transform (QFT). Furthermore, we compare this novel algorithm with\u0000existing quantum algorithms for option pricing.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804241","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}
Providing a measure of market risk is an important issue for investors and financial institutions. However, the existing models for this purpose are per definition symmetric. The current paper introduces an asymmetric capital asset pricing model for measurement of the market risk. It explicitly accounts for the fact that falling prices determine the risk for a long position in the risky asset and the rising prices govern the risk for a short position. Thus, a position dependent market risk measure that is provided accords better with reality. The empirical application reveals that Apple stock is more volatile than the market only for the short seller. Surprisingly, the investor that has a long position in this stock is facing a lower volatility than the market. This property is not captured by the standard asset pricing model, which has important implications for the expected returns and hedging designs.
{"title":"An Asymmetric Capital Asset Pricing Model","authors":"Abdulnasser Hatemi-J","doi":"arxiv-2404.14137","DOIUrl":"https://doi.org/arxiv-2404.14137","url":null,"abstract":"Providing a measure of market risk is an important issue for investors and\u0000financial institutions. However, the existing models for this purpose are per\u0000definition symmetric. The current paper introduces an asymmetric capital asset\u0000pricing model for measurement of the market risk. It explicitly accounts for\u0000the fact that falling prices determine the risk for a long position in the\u0000risky asset and the rising prices govern the risk for a short position. Thus, a\u0000position dependent market risk measure that is provided accords better with\u0000reality. The empirical application reveals that Apple stock is more volatile\u0000than the market only for the short seller. Surprisingly, the investor that has\u0000a long position in this stock is facing a lower volatility than the market.\u0000This property is not captured by the standard asset pricing model, which has\u0000important implications for the expected returns and hedging designs.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804306","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}
Ludovic Goudenège, Andrea Molent, Xiao Wei, Antonino Zanette
This paper extends the valuation and optimal surrender framework for variable annuities with guaranteed minimum benefits in a L'evy equity market environment by incorporating a stochastic interest rate described by the Hull-White model. This approach frames a more dynamic and realistic financial setting compared to previous literature. We exploit a robust valuation mechanism employing a hybrid numerical method that merges tree methods for interest rate modeling with finite difference techniques for the underlying asset price. This method is particularly effective for addressing the complexities of variable annuities, where periodic fees and mortality risks are significant factors. Our findings reveal the influence of stochastic interest rates on the strategic decision-making process concerning the surrender of these financial instruments. Through comprehensive numerical experiments, and by comparing our results with those obtained through the Longstaff-Schwartz Monte Carlo method, we illustrate how our refined model can guide insurers in designing contracts that equitably balance the interests of both parties. This is particularly relevant in discouraging premature surrenders while adapting to the realistic fluctuations of financial markets. Lastly, a comparative statics analysis with varying interest rate parameters underscores the impact of interest rates on the cost of the optimal surrender strategy, emphasizing the importance of accurately modeling stochastic interest rates.
本文通过纳入赫尔-怀特模型所描述的随机利率，扩展了在 L'evy 股票市场环境下具有最低收益保证的变额年金的估值和最优退保框架。与之前的文献相比，这种方法构建了一个更加动态和现实的财务设置框架。我们采用了一种混合数值方法，将利率建模的树形方法与基础资产价格的有限差分技术相结合，从而建立了一种稳健的估值机制。这种方法对于解决变额年金的复杂性尤为有效，因为变额年金的定期费用和死亡率风险是重要因素。我们的研究结果揭示了随机利率对这些金融工具退保战略决策过程的影响。通过全面的数字实验，并将我们的结果与 Longstaff-SchwartzMonte Carlo 方法得出的结果进行比较，我们说明了我们改进后的模型如何指导保险公司设计公平平衡双方利益的合同。这对于阻止过早退保，同时适应金融市场的现实波动尤为重要。最后，通过对不同利率参数的比较静态分析，强调了利率对最优退保策略成本的影响，强调了准确模拟随机利率的重要性。
{"title":"Enhancing Valuation of Variable Annuities in Lévy Models with Stochastic Interest Rate","authors":"Ludovic Goudenège, Andrea Molent, Xiao Wei, Antonino Zanette","doi":"arxiv-2404.07658","DOIUrl":"https://doi.org/arxiv-2404.07658","url":null,"abstract":"This paper extends the valuation and optimal surrender framework for variable\u0000annuities with guaranteed minimum benefits in a L'evy equity market\u0000environment by incorporating a stochastic interest rate described by the\u0000Hull-White model. This approach frames a more dynamic and realistic financial\u0000setting compared to previous literature. We exploit a robust valuation\u0000mechanism employing a hybrid numerical method that merges tree methods for\u0000interest rate modeling with finite difference techniques for the underlying\u0000asset price. This method is particularly effective for addressing the\u0000complexities of variable annuities, where periodic fees and mortality risks are\u0000significant factors. Our findings reveal the influence of stochastic interest\u0000rates on the strategic decision-making process concerning the surrender of\u0000these financial instruments. Through comprehensive numerical experiments, and\u0000by comparing our results with those obtained through the Longstaff-Schwartz\u0000Monte Carlo method, we illustrate how our refined model can guide insurers in\u0000designing contracts that equitably balance the interests of both parties. This\u0000is particularly relevant in discouraging premature surrenders while adapting to\u0000the realistic fluctuations of financial markets. Lastly, a comparative statics\u0000analysis with varying interest rate parameters underscores the impact of\u0000interest rates on the cost of the optimal surrender strategy, emphasizing the\u0000importance of accurately modeling stochastic interest rates.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578599","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}
I explore the relationship between investor emotions expressed on social media and asset prices. The field has seen a proliferation of models aimed at extracting firm-level sentiment from social media data, though the behavior of these models often remains uncertain. Against this backdrop, my study employs EmTract, an open-source emotion model, to test whether the emotional responses identified on social media platforms align with expectations derived from controlled laboratory settings. This step is crucial in validating the reliability of digital platforms in reflecting genuine investor sentiment. My findings reveal that firm-specific investor emotions behave similarly to lab experiments and can forecast daily asset price movements. These impacts are larger when liquidity is lower or short interest is higher. My findings on the persistent influence of sadness on subsequent returns, along with the insignificance of the one-dimensional valence metric, underscores the importance of dissecting emotional states. This approach allows for a deeper and more accurate understanding of the intricate ways in which investor sentiments drive market movements.
{"title":"Social Media Emotions and Market Behavior","authors":"Domonkos F. Vamossy","doi":"arxiv-2404.03792","DOIUrl":"https://doi.org/arxiv-2404.03792","url":null,"abstract":"I explore the relationship between investor emotions expressed on social\u0000media and asset prices. The field has seen a proliferation of models aimed at\u0000extracting firm-level sentiment from social media data, though the behavior of\u0000these models often remains uncertain. Against this backdrop, my study employs\u0000EmTract, an open-source emotion model, to test whether the emotional responses\u0000identified on social media platforms align with expectations derived from\u0000controlled laboratory settings. This step is crucial in validating the\u0000reliability of digital platforms in reflecting genuine investor sentiment. My\u0000findings reveal that firm-specific investor emotions behave similarly to lab\u0000experiments and can forecast daily asset price movements. These impacts are\u0000larger when liquidity is lower or short interest is higher. My findings on the\u0000persistent influence of sadness on subsequent returns, along with the\u0000insignificance of the one-dimensional valence metric, underscores the\u0000importance of dissecting emotional states. This approach allows for a deeper\u0000and more accurate understanding of the intricate ways in which investor\u0000sentiments drive market movements.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140579240","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 consider the computation of model-free bounds for multi-asset options in a setting that combines dependence uncertainty with additional information on the dependence structure. More specifically, we consider the setting where the marginal distributions are known and partial information, in the form of known prices for multi-asset options, is also available in the market. We provide a fundamental theorem of asset pricing in this setting, as well as a superhedging duality that allows to transform the maximization problem over probability measures in a more tractable minimization problem over trading strategies. The latter is solved using a penalization approach combined with a deep learning approximation using artificial neural networks. The numerical method is fast and the computational time scales linearly with respect to the number of traded assets. We finally examine the significance of various pieces of additional information. Empirical evidence suggests that "relevant" information, i.e. prices of derivatives with the same payoff structure as the target payoff, are more useful that other information, and should be prioritized in view of the trade-off between accuracy and computational efficiency.
{"title":"Improved model-free bounds for multi-asset options using option-implied information and deep learning","authors":"Evangelia Dragazi, Shuaiqiang Liu, Antonis Papapantoleon","doi":"arxiv-2404.02343","DOIUrl":"https://doi.org/arxiv-2404.02343","url":null,"abstract":"We consider the computation of model-free bounds for multi-asset options in a\u0000setting that combines dependence uncertainty with additional information on the\u0000dependence structure. More specifically, we consider the setting where the\u0000marginal distributions are known and partial information, in the form of known\u0000prices for multi-asset options, is also available in the market. We provide a\u0000fundamental theorem of asset pricing in this setting, as well as a superhedging\u0000duality that allows to transform the maximization problem over probability\u0000measures in a more tractable minimization problem over trading strategies. The\u0000latter is solved using a penalization approach combined with a deep learning\u0000approximation using artificial neural networks. The numerical method is fast\u0000and the computational time scales linearly with respect to the number of traded\u0000assets. We finally examine the significance of various pieces of additional\u0000information. Empirical evidence suggests that \"relevant\" information, i.e.\u0000prices of derivatives with the same payoff structure as the target payoff, are\u0000more useful that other information, and should be prioritized in view of the\u0000trade-off between accuracy and computational efficiency.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578598","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 two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The second approach does use a riskless asset. However, by ensuring equality between real-world and risk-neutral price-change probabilities, the second approach enables the computation of risk-neutral option prices utilizing expectations under the natural world probability P. This produces the same option prices as the classical approach in which prices are computed under the risk neutral measure Q. The second approach and the two specific examples of the first approach require the introduction of new, marketable asset types, specifically perpetual derivatives of a stock, and a stock whose cumulative return (rather than price) is deflated.
我们开发了两种无套利、市场完全期权定价的替代方法。第一种方法不需要无风险资产。我们建立了这种方法的一般框架，并用两个具体例子加以说明。第二种方法确实使用了无风险资产。然而，通过确保现实世界与风险中性价格变化概率之间的不平等，第二种方法可以利用自然世界概率 P 下的预期来计算风险中性期权价格，从而产生与经典方法相同的期权价格，后者的价格是在风险中性度量 Q 下计算的。
{"title":"Alternatives to classical option pricing","authors":"W. Brent Lindquist, Svetlozar T. Rachev","doi":"arxiv-2403.17187","DOIUrl":"https://doi.org/arxiv-2403.17187","url":null,"abstract":"We develop two alternate approaches to arbitrage-free, market-complete,\u0000option pricing. The first approach requires no riskless asset. We develop the\u0000general framework for this approach and illustrate it with two specific\u0000examples. The second approach does use a riskless asset. However, by ensuring\u0000equality between real-world and risk-neutral price-change probabilities, the\u0000second approach enables the computation of risk-neutral option prices utilizing\u0000expectations under the natural world probability P. This produces the same\u0000option prices as the classical approach in which prices are computed under the\u0000risk neutral measure Q. The second approach and the two specific examples of\u0000the first approach require the introduction of new, marketable asset types,\u0000specifically perpetual derivatives of a stock, and a stock whose cumulative\u0000return (rather than price) is deflated.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314257","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}
Recent empirical evidence has highlighted the crucial role of jumps in both price and volatility within the cryptocurrency market. In this paper, we introduce an analytical model framework featuring fractional stochastic volatility, accommodating price--volatility co-jumps and volatility short-term dependency concurrently. We particularly focus on inverse options, including the emerging Quanto inverse options and their power-type generalizations, aimed at mitigating cryptocurrency exchange rate risk and adjusting inherent risk exposure. Characteristic function-based pricing--hedging formulas are derived for these inverse options. The general model framework is then applied to asymmetric Laplace jump-diffusions and Gaussian-mixed tempered stable-type processes, employing three types of fractional kernels, for an extensive empirical analysis involving model calibration on two independent Bitcoin options data sets, during and after the COVID-19 pandemic. Key insights from our theoretical analysis and empirical findings include: (1) the superior performance of fractional stochastic-volatility models compared to various benchmark models, including those incorporating jumps and stochastic volatility, (2) the practical necessity of jumps in both price and volatility, along with their co-jumps and rough volatility, in the cryptocurrency market, (3) stability of calibrated parameter values in line with stylized facts, and (4) the suggestion that a piecewise kernel offers much higher computational efficiency relative to the commonly used Riemann--Liouville kernel in constructing fractional models, yet maintaining the same accuracy level, thanks to its potential for obtaining explicit model characteristic functions.
{"title":"Crypto Inverse-Power Options and Fractional Stochastic Volatility","authors":"Boyi Li, Weixuan Xia","doi":"arxiv-2403.16006","DOIUrl":"https://doi.org/arxiv-2403.16006","url":null,"abstract":"Recent empirical evidence has highlighted the crucial role of jumps in both\u0000price and volatility within the cryptocurrency market. In this paper, we\u0000introduce an analytical model framework featuring fractional stochastic\u0000volatility, accommodating price--volatility co-jumps and volatility short-term\u0000dependency concurrently. We particularly focus on inverse options, including\u0000the emerging Quanto inverse options and their power-type generalizations, aimed\u0000at mitigating cryptocurrency exchange rate risk and adjusting inherent risk\u0000exposure. Characteristic function-based pricing--hedging formulas are derived\u0000for these inverse options. The general model framework is then applied to\u0000asymmetric Laplace jump-diffusions and Gaussian-mixed tempered stable-type\u0000processes, employing three types of fractional kernels, for an extensive\u0000empirical analysis involving model calibration on two independent Bitcoin\u0000options data sets, during and after the COVID-19 pandemic. Key insights from\u0000our theoretical analysis and empirical findings include: (1) the superior\u0000performance of fractional stochastic-volatility models compared to various\u0000benchmark models, including those incorporating jumps and stochastic\u0000volatility, (2) the practical necessity of jumps in both price and volatility,\u0000along with their co-jumps and rough volatility, in the cryptocurrency market,\u0000(3) stability of calibrated parameter values in line with stylized facts, and\u0000(4) the suggestion that a piecewise kernel offers much higher computational\u0000efficiency relative to the commonly used Riemann--Liouville kernel in\u0000constructing fractional models, yet maintaining the same accuracy level, thanks\u0000to its potential for obtaining explicit model characteristic functions.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301772","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 a unifying framework for the pricing of debt securities under general time-inhomogeneous short-rate diffusion processes. The pricing of bonds, bond options, callable/putable bonds, and convertible bonds (CBs) are covered. Using continuous-time Markov chain (CTMC) approximation, we obtain closed-form matrix expressions to approximate the price of bonds and bond options under general one-dimensional short-rate processes. A simple and efficient algorithm is also developed to price callable/putable debts. The availability of a closed-form expression for the price of zero-coupon bonds allows for the perfect fit of the approximated model to the current market term structure of interest rates, regardless of the complexity of the underlying diffusion process selected. We further consider the pricing of CBs under general bi-dimensional time-inhomogeneous diffusion processes to model equity and short-rate dynamics. Credit risk is also incorporated into the model using the approach of Tsiveriotis and Fernandes (1998). Based on a two-layer CTMC method, an efficient algorithm is developed to approximate the price of convertible bonds. When conversion is only allowed at maturity, a closed-form matrix expression is obtained. Numerical experiments show the accuracy and efficiency of the method across a wide range of model parameters and short-rate models.
{"title":"A Unifying Approach for the Pricing of Debt Securities","authors":"Marie-Claude Vachon, Anne Mackay","doi":"arxiv-2403.06303","DOIUrl":"https://doi.org/arxiv-2403.06303","url":null,"abstract":"We propose a unifying framework for the pricing of debt securities under\u0000general time-inhomogeneous short-rate diffusion processes. The pricing of\u0000bonds, bond options, callable/putable bonds, and convertible bonds (CBs) are\u0000covered. Using continuous-time Markov chain (CTMC) approximation, we obtain\u0000closed-form matrix expressions to approximate the price of bonds and bond\u0000options under general one-dimensional short-rate processes. A simple and\u0000efficient algorithm is also developed to price callable/putable debts. The\u0000availability of a closed-form expression for the price of zero-coupon bonds\u0000allows for the perfect fit of the approximated model to the current market term\u0000structure of interest rates, regardless of the complexity of the underlying\u0000diffusion process selected. We further consider the pricing of CBs under\u0000general bi-dimensional time-inhomogeneous diffusion processes to model equity\u0000and short-rate dynamics. Credit risk is also incorporated into the model using\u0000the approach of Tsiveriotis and Fernandes (1998). Based on a two-layer CTMC\u0000method, an efficient algorithm is developed to approximate the price of\u0000convertible bonds. When conversion is only allowed at maturity, a closed-form\u0000matrix expression is obtained. Numerical experiments show the accuracy and\u0000efficiency of the method across a wide range of model parameters and short-rate\u0000models.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140106430","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 recent years, the dynamic factor model has emerged as a dominant tool in economics and finance, particularly for investment strategies. This model offers improved handling of complex, nonlinear, and noisy market conditions compared to traditional static factor models. The advancement of machine learning, especially in dealing with nonlinear data, has further enhanced asset pricing methodologies. This paper introduces a groundbreaking dynamic factor model named RVRAE. This model is a probabilistic approach that addresses the temporal dependencies and noise in market data. RVRAE ingeniously combines the principles of dynamic factor modeling with the variational recurrent autoencoder (VRAE) from deep learning. A key feature of RVRAE is its use of a prior-posterior learning method. This method fine-tunes the model's learning process by seeking an optimal posterior factor model informed by future data. Notably, RVRAE is adept at risk modeling in volatile stock markets, estimating variances from latent space distributions while also predicting returns. Our empirical tests with real stock market data underscore RVRAE's superior performance compared to various established baseline methods.
{"title":"RVRAE: A Dynamic Factor Model Based on Variational Recurrent Autoencoder for Stock Returns Prediction","authors":"Yilun Wang, Shengjie Guo","doi":"arxiv-2403.02500","DOIUrl":"https://doi.org/arxiv-2403.02500","url":null,"abstract":"In recent years, the dynamic factor model has emerged as a dominant tool in\u0000economics and finance, particularly for investment strategies. This model\u0000offers improved handling of complex, nonlinear, and noisy market conditions\u0000compared to traditional static factor models. The advancement of machine\u0000learning, especially in dealing with nonlinear data, has further enhanced asset\u0000pricing methodologies. This paper introduces a groundbreaking dynamic factor\u0000model named RVRAE. This model is a probabilistic approach that addresses the\u0000temporal dependencies and noise in market data. RVRAE ingeniously combines the\u0000principles of dynamic factor modeling with the variational recurrent\u0000autoencoder (VRAE) from deep learning. A key feature of RVRAE is its use of a\u0000prior-posterior learning method. This method fine-tunes the model's learning\u0000process by seeking an optimal posterior factor model informed by future data.\u0000Notably, RVRAE is adept at risk modeling in volatile stock markets, estimating\u0000variances from latent space distributions while also predicting returns. Our\u0000empirical tests with real stock market data underscore RVRAE's superior\u0000performance compared to various established baseline methods.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140044548","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 present closed analytical approximations for the pricing of Asian options with discrete averaging under the Black-Scholes model with time-dependent parameters. The formulae are obtained by using a stochastic Taylor expansion around a log-normal proxy model and are found to be highly accurate in practice.
{"title":"Stochastic expansion for the pricing of Asian options","authors":"Fabien Le Floc'h","doi":"arxiv-2402.17684","DOIUrl":"https://doi.org/arxiv-2402.17684","url":null,"abstract":"We present closed analytical approximations for the pricing of Asian options\u0000with discrete averaging under the Black-Scholes model with time-dependent\u0000parameters. The formulae are obtained by using a stochastic Taylor expansion\u0000around a log-normal proxy model and are found to be highly accurate in\u0000practice.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987963","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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