Pub Date : 2020-04-21DOI: 10.1080/1350486X.2021.2007146
A. Prakash, Nick James, Max Menzies, Gilad Francis
ABSTRACT We develop a new method to find the number of volatility regimes in a nonstationary financial time series by applying unsupervised learning to its volatility structure. We use change point detection to partition a time series into locally stationary segments and then compute a distance matrix between segment distributions. The segments are clustered into a learned number of discrete volatility regimes via an optimization routine. Using this framework, we determine the volatility clustering structure for financial indices, large-cap equities, exchange-traded funds and currency pairs. Our method overcomes the rigid assumptions necessary to implement many parametric regime-switching models while effectively distilling a time series into several characteristic behaviours. Our results provide a significant simplification of these time series and a strong descriptive analysis of prior behaviours of volatility. Finally, we create and validate a dynamic trading strategy that learns the optimal match between the current distribution of a time series and its past regimes, thereby making online risk-avoidance decisions at present.
{"title":"Structural Clustering of Volatility Regimes for Dynamic Trading Strategies","authors":"A. Prakash, Nick James, Max Menzies, Gilad Francis","doi":"10.1080/1350486X.2021.2007146","DOIUrl":"https://doi.org/10.1080/1350486X.2021.2007146","url":null,"abstract":"ABSTRACT We develop a new method to find the number of volatility regimes in a nonstationary financial time series by applying unsupervised learning to its volatility structure. We use change point detection to partition a time series into locally stationary segments and then compute a distance matrix between segment distributions. The segments are clustered into a learned number of discrete volatility regimes via an optimization routine. Using this framework, we determine the volatility clustering structure for financial indices, large-cap equities, exchange-traded funds and currency pairs. Our method overcomes the rigid assumptions necessary to implement many parametric regime-switching models while effectively distilling a time series into several characteristic behaviours. Our results provide a significant simplification of these time series and a strong descriptive analysis of prior behaviours of volatility. Finally, we create and validate a dynamic trading strategy that learns the optimal match between the current distribution of a time series and its past regimes, thereby making online risk-avoidance decisions at present.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"10 1","pages":"236 - 274"},"PeriodicalIF":0.0,"publicationDate":"2020-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83600265","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}
Pub Date : 2020-04-19DOI: 10.1080/1350486X.2020.1859943
Michael Roberts, I. Sengupta
ABSTRACT In this paper, we present a sequential hypothesis test for the detection of the distribution of jump size in Lévy processes. Infinitesimal generators for the corresponding log-likelihood ratios are presented and analysed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. This is shown to be implementable in relation to various classification problems for a crude oil price data set. Machine and deep learning algorithms are implemented to extract a specific deterministic component from the data set, and the deterministic component is implemented to improve the Barndorff-Nielsen & Shephard model, a commonly used stochastic model for derivative and commodity market analysis.
{"title":"Sequential Hypothesis Testing in Machine Learning, and Crude Oil Price Jump Size Detection","authors":"Michael Roberts, I. Sengupta","doi":"10.1080/1350486X.2020.1859943","DOIUrl":"https://doi.org/10.1080/1350486X.2020.1859943","url":null,"abstract":"ABSTRACT In this paper, we present a sequential hypothesis test for the detection of the distribution of jump size in Lévy processes. Infinitesimal generators for the corresponding log-likelihood ratios are presented and analysed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. This is shown to be implementable in relation to various classification problems for a crude oil price data set. Machine and deep learning algorithms are implemented to extract a specific deterministic component from the data set, and the deterministic component is implemented to improve the Barndorff-Nielsen & Shephard model, a commonly used stochastic model for derivative and commodity market analysis.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"55 1","pages":"374 - 395"},"PeriodicalIF":0.0,"publicationDate":"2020-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91153770","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}
Pub Date : 2020-04-14DOI: 10.1080/1350486X.2020.1813040
P. Sabino
ABSTRACT In this study we use a three-step procedure that relates the self-decomposability of the stationary law of a generalized Ornstein-Uhlenbeck process to the transition law of such processes. Based on this procedure and the results of Qu, Dassios, and Zhao (2019), we derive the exact simulation, without numerical inversion, of the skeleton of a Variance Gamma and of a symmetric Variance Gamma driven Ornstein-Uhlenbeck process. Extensive numerical experiments are reported to demonstrate the accuracy and efficiency of our algorithms. These results are instrumental to simulate the spot price dynamics in energy markets and to price Asian options and gas storages by Monte Carlo simulations in a framework similar to the one discussed in Cummins, Kiely and Murphy (2017, 2018).
{"title":"Exact Simulation of Variance Gamma-Related OU Processes: Application to the Pricing of Energy Derivatives","authors":"P. Sabino","doi":"10.1080/1350486X.2020.1813040","DOIUrl":"https://doi.org/10.1080/1350486X.2020.1813040","url":null,"abstract":"ABSTRACT In this study we use a three-step procedure that relates the self-decomposability of the stationary law of a generalized Ornstein-Uhlenbeck process to the transition law of such processes. Based on this procedure and the results of Qu, Dassios, and Zhao (2019), we derive the exact simulation, without numerical inversion, of the skeleton of a Variance Gamma and of a symmetric Variance Gamma driven Ornstein-Uhlenbeck process. Extensive numerical experiments are reported to demonstrate the accuracy and efficiency of our algorithms. These results are instrumental to simulate the spot price dynamics in energy markets and to price Asian options and gas storages by Monte Carlo simulations in a framework similar to the one discussed in Cummins, Kiely and Murphy (2017, 2018).","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"155 1","pages":"207 - 227"},"PeriodicalIF":0.0,"publicationDate":"2020-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73993493","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}
ABSTRACT We empirically investigate the functional link between the variance swap rate and the spot variance. Using S&P500 data over the period 2006–2018, we find overwhelming empirical evidence supporting the affine link implied by exponential affine stochastic volatility models. Tests on yearly subsamples suggest that exponential mean-reverting variance models provide a good fit during periods of extreme volatility, while polynomial modelsare suited for years characterized by more frequent price jumps.
{"title":"Is the Variance Swap Rate Affine in the Spot Variance? Evidence from S&P500 Data","authors":"M. Mancino, Simone Scotti, Giacomo Toscano","doi":"10.2139/ssrn.3571429","DOIUrl":"https://doi.org/10.2139/ssrn.3571429","url":null,"abstract":"ABSTRACT We empirically investigate the functional link between the variance swap rate and the spot variance. Using S&P500 data over the period 2006–2018, we find overwhelming empirical evidence supporting the affine link implied by exponential affine stochastic volatility models. Tests on yearly subsamples suggest that exponential mean-reverting variance models provide a good fit during periods of extreme volatility, while polynomial modelsare suited for years characterized by more frequent price jumps.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"154 1","pages":"288 - 316"},"PeriodicalIF":0.0,"publicationDate":"2020-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77332567","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}
Pub Date : 2020-03-03DOI: 10.1080/1350486X.2020.1726783
Á. Cartea, S. Jaimungal, Yixuan Wang
ABSTRACT We model the trading strategy of an investor who spoofs the limit order book (LOB) to increase the revenue obtained from selling a position in a security. The strategy employs, in addition to sell limit orders (LOs) and sell market orders (MOs), a large number of spoof buy LOs to manipulate the volume imbalance of the LOB. Spoofing is illegal, so the strategy trades off the gains that originate from spoofing against the expected financial losses due to a fine imposed by the financial authorities. As the fine increases, the investor relies less on spoofing, and if the fine is large, the investor does not spoof the LOB. The arrival rate of buy MOs increases because other traders interpret the spoofed buy-heavy LOB as an upward pressure on prices. When the fine is low, spoofing considerably increases the revenues from liquidating a position. Spoofing increases the PnL because (i) the investor employs fewer MOs to draw the inventory to zero and benefits from roundtrip trades, which stem from spoof buy LOs that are ‘inadvertently’ filled and subsequently unwound with sell LOs; and (ii) the midprice trends upward when the book is buy-heavy; therefore the spoofer sells the asset at better prices.
{"title":"Spoofing and Price Manipulation in Order-Driven Markets","authors":"Á. Cartea, S. Jaimungal, Yixuan Wang","doi":"10.1080/1350486X.2020.1726783","DOIUrl":"https://doi.org/10.1080/1350486X.2020.1726783","url":null,"abstract":"ABSTRACT We model the trading strategy of an investor who spoofs the limit order book (LOB) to increase the revenue obtained from selling a position in a security. The strategy employs, in addition to sell limit orders (LOs) and sell market orders (MOs), a large number of spoof buy LOs to manipulate the volume imbalance of the LOB. Spoofing is illegal, so the strategy trades off the gains that originate from spoofing against the expected financial losses due to a fine imposed by the financial authorities. As the fine increases, the investor relies less on spoofing, and if the fine is large, the investor does not spoof the LOB. The arrival rate of buy MOs increases because other traders interpret the spoofed buy-heavy LOB as an upward pressure on prices. When the fine is low, spoofing considerably increases the revenues from liquidating a position. Spoofing increases the PnL because (i) the investor employs fewer MOs to draw the inventory to zero and benefits from roundtrip trades, which stem from spoof buy LOs that are ‘inadvertently’ filled and subsequently unwound with sell LOs; and (ii) the midprice trends upward when the book is buy-heavy; therefore the spoofer sells the asset at better prices.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"42 1","pages":"67 - 98"},"PeriodicalIF":0.0,"publicationDate":"2020-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81641005","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}
Pub Date : 2020-03-03DOI: 10.1080/1350486X.2020.1730202
L. von Sydow, J. Waldén
ABSTRACT We develop and analyse a numerical method for solving the Ross recovery problem for a diffusion problem with unbounded support, with a transition independent pricing kernel. Asset prices are assumed to only be available on a bounded subinterval . Theoretical error bounds on the recovered pricing kernel are derived, relating the convergence rate as a function of to the rate of mean reversion of the diffusion process. Our suggested numerical method for finding the pricing kernel employs finite differences, and we apply Sturm–Liouville theory to make use of inverse iteration on the resulting discretized eigenvalue problem. We numerically verify the derived error bounds on a test bench of three model problems.
{"title":"Numerical Ross Recovery for Diffusion Processes Using a PDE Approach","authors":"L. von Sydow, J. Waldén","doi":"10.1080/1350486X.2020.1730202","DOIUrl":"https://doi.org/10.1080/1350486X.2020.1730202","url":null,"abstract":"ABSTRACT We develop and analyse a numerical method for solving the Ross recovery problem for a diffusion problem with unbounded support, with a transition independent pricing kernel. Asset prices are assumed to only be available on a bounded subinterval . Theoretical error bounds on the recovered pricing kernel are derived, relating the convergence rate as a function of to the rate of mean reversion of the diffusion process. Our suggested numerical method for finding the pricing kernel employs finite differences, and we apply Sturm–Liouville theory to make use of inverse iteration on the resulting discretized eigenvalue problem. We numerically verify the derived error bounds on a test bench of three model problems.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"21 1","pages":"46 - 66"},"PeriodicalIF":0.0,"publicationDate":"2020-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91222861","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}
ABSTRACT The Sato process associated with self decomposable laws at unit time is further generalized to an additive process with arbitrary innovation term structures. A second generalization to additive processes consistent with bilateral gamma marginal distributions is also made. The Sato process is a parametric special case of the two generalizations. This feature is exploited in defining calibration starting values. Calibration results are presented for days of daily data on SPY options. The deterministic innovation variance model makes a median improvement of in root-mean-square error over the Sato process. The comparable value for the general additive process is The Sato process relative to the general additive process overprices negative moves and underprices positive ones. The underpricing of negative moves decreases with maturity. On the positive side, the overpricing decreases with maturity. For negative moves, the overpricing is larger for smaller moves, while for positive moves the underpricing is larger for the larger moves.
{"title":"Additive Processes with Bilateral Gamma Marginals","authors":"D. Madan, King Wang","doi":"10.2139/ssrn.3528510","DOIUrl":"https://doi.org/10.2139/ssrn.3528510","url":null,"abstract":"ABSTRACT The Sato process associated with self decomposable laws at unit time is further generalized to an additive process with arbitrary innovation term structures. A second generalization to additive processes consistent with bilateral gamma marginal distributions is also made. The Sato process is a parametric special case of the two generalizations. This feature is exploited in defining calibration starting values. Calibration results are presented for days of daily data on SPY options. The deterministic innovation variance model makes a median improvement of in root-mean-square error over the Sato process. The comparable value for the general additive process is The Sato process relative to the general additive process overprices negative moves and underprices positive ones. The underpricing of negative moves decreases with maturity. On the positive side, the overpricing decreases with maturity. For negative moves, the overpricing is larger for smaller moves, while for positive moves the underpricing is larger for the larger moves.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"148 1","pages":"171 - 188"},"PeriodicalIF":0.0,"publicationDate":"2020-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79378197","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}
Pub Date : 2019-11-02DOI: 10.1080/1350486X.2020.1727755
Jan-Frederik Mai
ABSTRACT We consider power/logarithmic utility maximization in a multivariate Black–Scholes model that is enhanced by credit risk via the Marshall–Olkin exponential distribution. On the practical side, the model results in an enhancement of the mean variance paradigm, which is easy to interpret and implement. On the theoretical side, the model constitutes a well-justified and intuitive mathematical wrapping to study the effect of extreme and higher-order dependence on optimal portfolios.
{"title":"Portfolio Optimization for Credit-Risky Assets under Marshall–Olkin Dependence","authors":"Jan-Frederik Mai","doi":"10.1080/1350486X.2020.1727755","DOIUrl":"https://doi.org/10.1080/1350486X.2020.1727755","url":null,"abstract":"ABSTRACT We consider power/logarithmic utility maximization in a multivariate Black–Scholes model that is enhanced by credit risk via the Marshall–Olkin exponential distribution. On the practical side, the model results in an enhancement of the mean variance paradigm, which is easy to interpret and implement. On the theoretical side, the model constitutes a well-justified and intuitive mathematical wrapping to study the effect of extreme and higher-order dependence on optimal portfolios.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"9 1","pages":"598 - 618"},"PeriodicalIF":0.0,"publicationDate":"2019-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77988390","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}
Pub Date : 2019-11-02DOI: 10.1080/1350486X.2020.1726784
Terry Lyons, Sina Nejad, Imanol Perez Arribas
ABSTRACT We estimate prices of exotic options in a discrete-time model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved by estimating an unobservable quantity called ‘implied expected signature’ from such market prices, which are used to price other exotic derivatives. The implied expected signature is an object that characterizes the market dynamics.
{"title":"Numerical Method for Model-free Pricing of Exotic Derivatives in Discrete Time Using Rough Path Signatures","authors":"Terry Lyons, Sina Nejad, Imanol Perez Arribas","doi":"10.1080/1350486X.2020.1726784","DOIUrl":"https://doi.org/10.1080/1350486X.2020.1726784","url":null,"abstract":"ABSTRACT We estimate prices of exotic options in a discrete-time model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved by estimating an unobservable quantity called ‘implied expected signature’ from such market prices, which are used to price other exotic derivatives. The implied expected signature is an object that characterizes the market dynamics.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"43 1","pages":"583 - 597"},"PeriodicalIF":0.0,"publicationDate":"2019-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81661166","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}
Pub Date : 2019-09-03DOI: 10.1080/1350486X.2020.1714455
Olivier Gu'eant, Iuliia Manziuk
ABSTRACT In corporate bond markets, which are mainly OTC markets, market makers play a central role by providing bid and ask prices for bonds to asset managers. Determining the optimal bid and ask quotes that a market maker should set for a given universe of bonds is a complex task. The existing models, mostly inspired by the Avellaneda-Stoikov model, describe the complex optimization problem faced by market makers: proposing bid and ask prices for making money out of the difference between them while mitigating the market risk associated with holding inventory. While most of the models only tackle one-asset market making, they can often be generalized to a multi-asset framework. However, the problem of solving the equations characterizing the optimal bid and ask quotes numerically is seldom tackled in the literature, especially in high dimension. In this paper, we propose a numerical method for approximating the optimal bid and ask quotes over a large universe of bonds in a model à la Avellaneda–Stoikov. As classical finite difference methods cannot be used in high dimension, we present a discrete-time method inspired by reinforcement learning techniques, namely, a model-based deep actor-critic algorithm.
在以场外交易市场为主的公司债券市场中，做市商通过向资产管理公司提供债券的买入价和卖出价而发挥着核心作用。确定做市商为特定债券设定的最佳买卖报价是一项复杂的任务。现有的模型大多受到Avellaneda-Stoikov模型的启发，描述了做市商面临的复杂优化问题:提出买入价和卖出价，以便从两者之间的差价中赚钱，同时降低与持有库存相关的市场风险。虽然大多数模型只处理单一资产做市，但它们通常可以推广到多资产框架。然而，文献中对最优买入价和最优卖出价方程的数值求解问题，特别是在高维的情况下，研究较少。在本文中，我们提出了一种数值方法来逼近大范围债券的最优买入价和最优卖出价，该方法适用于a - la Avellaneda-Stoikov模型。由于经典的有限差分方法不能用于高维，我们提出了一种受强化学习技术启发的离散时间方法，即基于模型的深度actor-critic算法。
{"title":"Deep Reinforcement Learning for Market Making in Corporate Bonds: Beating the Curse of Dimensionality","authors":"Olivier Gu'eant, Iuliia Manziuk","doi":"10.1080/1350486X.2020.1714455","DOIUrl":"https://doi.org/10.1080/1350486X.2020.1714455","url":null,"abstract":"ABSTRACT In corporate bond markets, which are mainly OTC markets, market makers play a central role by providing bid and ask prices for bonds to asset managers. Determining the optimal bid and ask quotes that a market maker should set for a given universe of bonds is a complex task. The existing models, mostly inspired by the Avellaneda-Stoikov model, describe the complex optimization problem faced by market makers: proposing bid and ask prices for making money out of the difference between them while mitigating the market risk associated with holding inventory. While most of the models only tackle one-asset market making, they can often be generalized to a multi-asset framework. However, the problem of solving the equations characterizing the optimal bid and ask quotes numerically is seldom tackled in the literature, especially in high dimension. In this paper, we propose a numerical method for approximating the optimal bid and ask quotes over a large universe of bonds in a model à la Avellaneda–Stoikov. As classical finite difference methods cannot be used in high dimension, we present a discrete-time method inspired by reinforcement learning techniques, namely, a model-based deep actor-critic algorithm.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"2 1","pages":"387 - 452"},"PeriodicalIF":0.0,"publicationDate":"2019-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87500219","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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