Pub Date : 2019-09-03DOI: 10.1080/1350486X.2020.1725582
Cord Harms, R. Kiesel
ABSTRACT We estimate a structural electricity (multi-commodity) model based on historical spot and futures data (fuels and power prices, respectively) and quantify the inherent parameter risk using an average value at risk approach (‘expected shortfall’). The mathematical proofs use the theory of asymptotic statistics to derive a parameter risk measure. We use far in-the-money options to derive a confidence level and use it as a prudent present value adjustment when pricing a virtual power plant. Finally, we conduct a present value benchmarking to compare the approach of temperature-driven demand (based on load data) to an ‘implied demand approach’ (demand implied from observable power futures prices). We observe that the implied demand approach can easily capture observed electricity price volatility whereas the estimation against observable load data will lead to a gap, because – amongst others – the interplay of demand and supply is not captured in the data (i.e., unexpected mismatches).
{"title":"Structural Electricity Models and Asymptotically Normal Estimators to Quantify Parameter Risk","authors":"Cord Harms, R. Kiesel","doi":"10.1080/1350486X.2020.1725582","DOIUrl":"https://doi.org/10.1080/1350486X.2020.1725582","url":null,"abstract":"ABSTRACT We estimate a structural electricity (multi-commodity) model based on historical spot and futures data (fuels and power prices, respectively) and quantify the inherent parameter risk using an average value at risk approach (‘expected shortfall’). The mathematical proofs use the theory of asymptotic statistics to derive a parameter risk measure. We use far in-the-money options to derive a confidence level and use it as a prudent present value adjustment when pricing a virtual power plant. Finally, we conduct a present value benchmarking to compare the approach of temperature-driven demand (based on load data) to an ‘implied demand approach’ (demand implied from observable power futures prices). We observe that the implied demand approach can easily capture observed electricity price volatility whereas the estimation against observable load data will lead to a gap, because – amongst others – the interplay of demand and supply is not captured in the data (i.e., unexpected mismatches).","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"178 1","pages":"475 - 522"},"PeriodicalIF":0.0,"publicationDate":"2019-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86809866","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 : 2019-08-08DOI: 10.1080/1350486X.2021.1909488
P. Sabino, Nicola Cufaro Petroni
ABSTRACT Most energy and commodity markets exhibit mean-reversion and occasional distinctive price spikes, which result in demand for derivative products which protect the holder against high prices. To this end, in this paper we present a few fast and efficient methodologies for the exact simulation of the spot price dynamics modelled as the exponential of the sum of a Gaussian Ornstein-Uhlenbeck process and an independent pure jump process, where the latter one is driven by a compound Poisson process with (bilateral) exponentially distributed jumps. These methodologies are finally applied to the pricing of Asian options, gas and hydro storages and swing options under different combinations of jump-diffusion market models, and the apparent computational advantages of the proposed procedures are emphasized.
{"title":"Fast Pricing of Energy Derivatives with Mean-Reverting Jump-diffusion Processes","authors":"P. Sabino, Nicola Cufaro Petroni","doi":"10.1080/1350486X.2021.1909488","DOIUrl":"https://doi.org/10.1080/1350486X.2021.1909488","url":null,"abstract":"ABSTRACT Most energy and commodity markets exhibit mean-reversion and occasional distinctive price spikes, which result in demand for derivative products which protect the holder against high prices. To this end, in this paper we present a few fast and efficient methodologies for the exact simulation of the spot price dynamics modelled as the exponential of the sum of a Gaussian Ornstein-Uhlenbeck process and an independent pure jump process, where the latter one is driven by a compound Poisson process with (bilateral) exponentially distributed jumps. These methodologies are finally applied to the pricing of Asian options, gas and hydro storages and swing options under different combinations of jump-diffusion market models, and the apparent computational advantages of the proposed procedures are emphasized.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"76 1","pages":"1 - 22"},"PeriodicalIF":0.0,"publicationDate":"2019-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83131650","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 : 2019-05-04DOI: 10.1080/1350486X.2019.1638276
Géraldine Bouveret
ABSTRACT We consider, within a Markovian complete financial market, the problem of finding the least expensive portfolio process meeting, at each payment date, three different types of risk criterion. Two of them encompass an expected utility-based measure and a quantile hedging constraint imposed at inception on all the future payment dates, while the other one is a quantile hedging constraint set at each payment date over the next one. The quantile risk measures are defined with respect to a stochastic benchmark and the expected utility-based constraint is applied to random payment dates. We explicit the Legendre-Fenchel transform of the pricing function. We also provide, for each quantile hedging problem, a backward dual algorithm allowing to compute their associated value function by backward recursion. The algorithms are illustrated with a numerical example.
{"title":"Dual Representation of the Cost of Designing a Portfolio Satisfying Multiple Risk Constraints","authors":"Géraldine Bouveret","doi":"10.1080/1350486X.2019.1638276","DOIUrl":"https://doi.org/10.1080/1350486X.2019.1638276","url":null,"abstract":"ABSTRACT We consider, within a Markovian complete financial market, the problem of finding the least expensive portfolio process meeting, at each payment date, three different types of risk criterion. Two of them encompass an expected utility-based measure and a quantile hedging constraint imposed at inception on all the future payment dates, while the other one is a quantile hedging constraint set at each payment date over the next one. The quantile risk measures are defined with respect to a stochastic benchmark and the expected utility-based constraint is applied to random payment dates. We explicit the Legendre-Fenchel transform of the pricing function. We also provide, for each quantile hedging problem, a backward dual algorithm allowing to compute their associated value function by backward recursion. The algorithms are illustrated with a numerical example.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"109 1","pages":"222 - 256"},"PeriodicalIF":0.0,"publicationDate":"2019-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80089395","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 : 2019-05-04DOI: 10.1080/1350486X.2019.1637268
S. Ninomiya, Yuji Shinozaki
ABSTRACT This study proposes new higher-order discretization methods of forward-backward stochastic differential equations. In the proposed methods, the forward component is discretized using the Kusuoka–Lyons–Ninomiya–Victoir scheme with discrete random variables and the backward component using a higher-order numerical integration method consistent with the discretization method of the forward component, by use of the tree based branching algorithm. The proposed methods are applied to the XVA pricing, in particular to the credit valuation adjustment. The numerical results show that the expected theoretical order and computational efficiency could be achieved.
{"title":"Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing","authors":"S. Ninomiya, Yuji Shinozaki","doi":"10.1080/1350486X.2019.1637268","DOIUrl":"https://doi.org/10.1080/1350486X.2019.1637268","url":null,"abstract":"ABSTRACT This study proposes new higher-order discretization methods of forward-backward stochastic differential equations. In the proposed methods, the forward component is discretized using the Kusuoka–Lyons–Ninomiya–Victoir scheme with discrete random variables and the backward component using a higher-order numerical integration method consistent with the discretization method of the forward component, by use of the tree based branching algorithm. The proposed methods are applied to the XVA pricing, in particular to the credit valuation adjustment. The numerical results show that the expected theoretical order and computational efficiency could be achieved.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"27 1","pages":"257 - 292"},"PeriodicalIF":0.0,"publicationDate":"2019-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85936281","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 : 2019-05-02DOI: 10.1080/1350486X.2021.1891555
Terry Lyons, Sina Nejad, Imanol Perez Arribas
ABSTRACT In the spirit of Arrow–Debreu, we introduce a family of financial derivatives that act as primitive securities in that exotic derivatives can be approximated by their linear combinations. We call these financial derivatives signature payoffs. We show that signature payoffs can be used to non-parametrically price and hedge exotic derivatives in the scenario where one has access to price data for other exotic payoffs. The methodology leads to a computationally tractable and accurate algorithm for pricing and hedging using market prices of a basket of exotic derivatives that has been tested on real and simulated market prices, obtaining good results.
{"title":"Non-parametric Pricing and Hedging of Exotic Derivatives","authors":"Terry Lyons, Sina Nejad, Imanol Perez Arribas","doi":"10.1080/1350486X.2021.1891555","DOIUrl":"https://doi.org/10.1080/1350486X.2021.1891555","url":null,"abstract":"ABSTRACT In the spirit of Arrow–Debreu, we introduce a family of financial derivatives that act as primitive securities in that exotic derivatives can be approximated by their linear combinations. We call these financial derivatives signature payoffs. We show that signature payoffs can be used to non-parametrically price and hedge exotic derivatives in the scenario where one has access to price data for other exotic payoffs. The methodology leads to a computationally tractable and accurate algorithm for pricing and hedging using market prices of a basket of exotic derivatives that has been tested on real and simulated market prices, obtaining good results.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"80 1","pages":"457 - 494"},"PeriodicalIF":0.0,"publicationDate":"2019-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85034656","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 : 2019-04-23DOI: 10.1080/1350486X.2022.2136727
P. Casgrain, Brian Ning, S. Jaimungal
ABSTRACT Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games and are applicable only in small state-action spaces or other simplified settings. Here, we develop a new data-efficient Deep-Q-learning methodology for model-free learning of Nash equilibria for general-sum stochastic games. The algorithm uses a locally linear-quadratic expansion of the stochastic game, which leads to analytically solvable optimal actions. The expansion is parametrized by deep neural networks to give it sufficient flexibility to learn the environment without the need to experience all state-action pairs. We study symmetry properties of the algorithm stemming from label-invariant stochastic games and as a proof of concept, apply our algorithm to learning optimal trading strategies in competitive electronic markets.
{"title":"Deep Q-Learning for Nash Equilibria: Nash-DQN","authors":"P. Casgrain, Brian Ning, S. Jaimungal","doi":"10.1080/1350486X.2022.2136727","DOIUrl":"https://doi.org/10.1080/1350486X.2022.2136727","url":null,"abstract":"ABSTRACT Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games and are applicable only in small state-action spaces or other simplified settings. Here, we develop a new data-efficient Deep-Q-learning methodology for model-free learning of Nash equilibria for general-sum stochastic games. The algorithm uses a locally linear-quadratic expansion of the stochastic game, which leads to analytically solvable optimal actions. The expansion is parametrized by deep neural networks to give it sufficient flexibility to learn the environment without the need to experience all state-action pairs. We study symmetry properties of the algorithm stemming from label-invariant stochastic games and as a proof of concept, apply our algorithm to learning optimal trading strategies in competitive electronic markets.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"85 1","pages":"62 - 78"},"PeriodicalIF":0.0,"publicationDate":"2019-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85676363","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 : 2019-03-04DOI: 10.1080/1350486X.2019.1590784
Ramin Okhrati
ABSTRACT We investigate hedging the risk of delayed data in certain defaultable securities through the local risk minimization approach. From a financial point of view, this indicates that in addition to the risk of default, investors also face incomplete accounting data. In our analysis, the delay is modelled by a random time change, and different levels of information, including the full market’s, management’s, and investors’ information, are distinguished. We obtain semi-explicit solutions for pseudo locally risk minimizing hedging strategies from the perspective of investors where the results are presented according to the solutions of partial differential equations. In obtaining the main results of this paper, we apply a filtration expansion theorem that determines the canonical decomposition of stopped special semimartingales in an enlarged filtration of investors’ information.
{"title":"Hedging the Risk of Delayed Data in Defaultable Markets","authors":"Ramin Okhrati","doi":"10.1080/1350486X.2019.1590784","DOIUrl":"https://doi.org/10.1080/1350486X.2019.1590784","url":null,"abstract":"ABSTRACT We investigate hedging the risk of delayed data in certain defaultable securities through the local risk minimization approach. From a financial point of view, this indicates that in addition to the risk of default, investors also face incomplete accounting data. In our analysis, the delay is modelled by a random time change, and different levels of information, including the full market’s, management’s, and investors’ information, are distinguished. We obtain semi-explicit solutions for pseudo locally risk minimizing hedging strategies from the perspective of investors where the results are presented according to the solutions of partial differential equations. In obtaining the main results of this paper, we apply a filtration expansion theorem that determines the canonical decomposition of stopped special semimartingales in an enlarged filtration of investors’ information.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"83 12 1","pages":"101 - 130"},"PeriodicalIF":0.0,"publicationDate":"2019-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84359736","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 : 2019-02-02DOI: 10.1080/1350486X.2019.1702068
G. D’Amico, F. Petroni, P. Regnault, S. Scocchera, L. Storchi
ABSTRACT In this paper, we propose a methodology based on piecewise homogeneous Markov chain for credit ratings and a multivariate model of the credit spreads to evaluate the financial risk in the European Union (EU). Two main aspects are considered: how the financial risk is distributed among the European countries and how large is the value of the total risk. The first aspect is evaluated by means of the expected value of a dynamic entropy measure. The second one is solved by computing the evolution of the total credit spread over time. Moreover, the covariance between countries’ total spread allows the understanding of any contagions in the EU. The methodology is applied to real data of 24 European countries for the three major rating agencies: Moody’s, Standard & Poor’s and Fitch. Obtained results suggest that both the financial risk inequality and the value of the total risk increase over time at a different rate depending on the rating agency. Moreover, the results indicate that the dependence structure is characterized by a strong correlation between most of the European countries.
{"title":"A Copula-based Markov Reward Approach to the Credit Spread in the European Union","authors":"G. D’Amico, F. Petroni, P. Regnault, S. Scocchera, L. Storchi","doi":"10.1080/1350486X.2019.1702068","DOIUrl":"https://doi.org/10.1080/1350486X.2019.1702068","url":null,"abstract":"ABSTRACT In this paper, we propose a methodology based on piecewise homogeneous Markov chain for credit ratings and a multivariate model of the credit spreads to evaluate the financial risk in the European Union (EU). Two main aspects are considered: how the financial risk is distributed among the European countries and how large is the value of the total risk. The first aspect is evaluated by means of the expected value of a dynamic entropy measure. The second one is solved by computing the evolution of the total credit spread over time. Moreover, the covariance between countries’ total spread allows the understanding of any contagions in the EU. The methodology is applied to real data of 24 European countries for the three major rating agencies: Moody’s, Standard & Poor’s and Fitch. Obtained results suggest that both the financial risk inequality and the value of the total risk increase over time at a different rate depending on the rating agency. Moreover, the results indicate that the dependence structure is characterized by a strong correlation between most of the European countries.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"16 1","pages":"359 - 386"},"PeriodicalIF":0.0,"publicationDate":"2019-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86610278","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 : 2019-01-27DOI: 10.1080/1350486X.2019.1702067
Jorge Guijarro-Ordonez
ABSTRACT The present paper provides a study of high-dimensional statistical arbitrage that combines factor models with the tools from stochastic control, obtaining closed-form optimal strategies which are both interpretable and computationally implementable in a high-dimensional setting. Our setup is based on a general statistically constructed factor model with mean-reverting residuals, in which we show how to construct analytically market-neutral portfolios and we analyse the problem of investing optimally in continuous time and finite horizon under exponential and mean-variance utilities. We also extend our model to incorporate constraints on the investor’s portfolio like dollar-neutrality and market frictions in the form of temporary quadratic transaction costs, provide extensive Monte Carlo simulations of the previous strategies with 100 assets, and describe further possible extensions of our work.
{"title":"High-dimensional Statistical Arbitrage with Factor Models and Stochastic Control","authors":"Jorge Guijarro-Ordonez","doi":"10.1080/1350486X.2019.1702067","DOIUrl":"https://doi.org/10.1080/1350486X.2019.1702067","url":null,"abstract":"ABSTRACT The present paper provides a study of high-dimensional statistical arbitrage that combines factor models with the tools from stochastic control, obtaining closed-form optimal strategies which are both interpretable and computationally implementable in a high-dimensional setting. Our setup is based on a general statistically constructed factor model with mean-reverting residuals, in which we show how to construct analytically market-neutral portfolios and we analyse the problem of investing optimally in continuous time and finite horizon under exponential and mean-variance utilities. We also extend our model to incorporate constraints on the investor’s portfolio like dollar-neutrality and market frictions in the form of temporary quadratic transaction costs, provide extensive Monte Carlo simulations of the previous strategies with 100 assets, and describe further possible extensions of our work.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"42 1","pages":"328 - 358"},"PeriodicalIF":0.0,"publicationDate":"2019-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89898618","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 : 2019-01-02DOI: 10.1080/1350486X.2019.1593866
Yaohao Peng, P. Albuquerque
ABSTRACT This paper analysed the prediction of the spot exchange rate of 10 currency pairs using support vector regression (SVR) based on a fundamentalist model composed of 13 explanatory variables. Different structures of non-linear dependence introduced by nine different Kernel functions were tested and the predictions were compared to the Random Walk benchmark. We checked the explanatory power gain of SVR models over the Random Walk by applying White’s Reality Check Test. The results showed that the majority of SVR models achieved better out-of-sample performance than the Random Walk, but in overall they failed to achieve statistical significance of predictive superiority. Furthermore, we observed that non-mainstream Kernel functions performed better than the ones commonly used in the machine-learning literature, a finding that can provide new insights regarding machine-learning methods applications and the predictability of exchange rates using non-linear interactions between the predictors.
{"title":"Non-Linear Interactions and Exchange Rate Prediction: Empirical Evidence Using Support Vector Regression","authors":"Yaohao Peng, P. Albuquerque","doi":"10.1080/1350486X.2019.1593866","DOIUrl":"https://doi.org/10.1080/1350486X.2019.1593866","url":null,"abstract":"ABSTRACT This paper analysed the prediction of the spot exchange rate of 10 currency pairs using support vector regression (SVR) based on a fundamentalist model composed of 13 explanatory variables. Different structures of non-linear dependence introduced by nine different Kernel functions were tested and the predictions were compared to the Random Walk benchmark. We checked the explanatory power gain of SVR models over the Random Walk by applying White’s Reality Check Test. The results showed that the majority of SVR models achieved better out-of-sample performance than the Random Walk, but in overall they failed to achieve statistical significance of predictive superiority. Furthermore, we observed that non-mainstream Kernel functions performed better than the ones commonly used in the machine-learning literature, a finding that can provide new insights regarding machine-learning methods applications and the predictability of exchange rates using non-linear interactions between the predictors.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"500 1","pages":"100 - 69"},"PeriodicalIF":0.0,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85695643","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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