Pub Date : 2022-03-19DOI: 10.1142/s0219024922500121
Mesias Alfeus, Xin‐Jiang He, Song‐Ping Zhu
Short sell bans are often imposed during a financial crisis as a desperate measure to stabilize financial markets. Yet, the impact of short sell bans on option pricing and hedging is not well studied, at least quantitatively, until very recently when Guo & Zhu [(2017) Equal risk pricing under convex trading constraints, Journal of Economic Dynamics and Control 76, 136–151] and He & Zhu [(2020) A revised option pricing formula with the underlying being banned from short selling, Quantitative Finance 20 (6), 935–948] formulated a new pricing framework with the underlying being either completely or partially banned from short selling. However, no empirical results were provided to substantiate the usefulness of the formulae, as well as to deepen our understanding on the effects of short sell bans. This paper provides a comprehensive empirical study on the effects of short sell bans to the standard option pricing theory by carrying out both cross-sectional and options time series model calibration of the model devised by He & Zhu (2020) [A revised option pricing formula with the underlying being banned from short selling, Quantitative Finance 20 (6), 935–948]. Overall, our empirical results indicate that the alternative option pricing formula considering short sell restrictions has the ability to capture highly-quoted implied volatility, with an evident improvement of 39% out-of-sample performance compared to the benchmark Black–Scholes model during the period of short sell ban.
{"title":"AN EMPIRICAL ANALYSIS OF OPTION PRICING WITH SHORT SELL BANS","authors":"Mesias Alfeus, Xin‐Jiang He, Song‐Ping Zhu","doi":"10.1142/s0219024922500121","DOIUrl":"https://doi.org/10.1142/s0219024922500121","url":null,"abstract":"Short sell bans are often imposed during a financial crisis as a desperate measure to stabilize financial markets. Yet, the impact of short sell bans on option pricing and hedging is not well studied, at least quantitatively, until very recently when Guo & Zhu [(2017) Equal risk pricing under convex trading constraints, Journal of Economic Dynamics and Control 76, 136–151] and He & Zhu [(2020) A revised option pricing formula with the underlying being banned from short selling, Quantitative Finance 20 (6), 935–948] formulated a new pricing framework with the underlying being either completely or partially banned from short selling. However, no empirical results were provided to substantiate the usefulness of the formulae, as well as to deepen our understanding on the effects of short sell bans. This paper provides a comprehensive empirical study on the effects of short sell bans to the standard option pricing theory by carrying out both cross-sectional and options time series model calibration of the model devised by He & Zhu (2020) [A revised option pricing formula with the underlying being banned from short selling, Quantitative Finance 20 (6), 935–948]. Overall, our empirical results indicate that the alternative option pricing formula considering short sell restrictions has the ability to capture highly-quoted implied volatility, with an evident improvement of 39% out-of-sample performance compared to the benchmark Black–Scholes model during the period of short sell ban.","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46659512","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 : 2022-03-18DOI: 10.1142/s021902492250011x
ORCAN ÖGETBIL, NARAYAN GANESAN, BERNHARD HIENTZSCH
We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates and finally stochastic local volatility with stochastic interest rates. For each model, we include detailed derivations of the corresponding SDE systems and list the required input data and steps for calibration. We give conditions under which a local volatility can exist given European option prices, stochastic interest rate model parameters, and correlations. The models are posed in a foreign exchange setting. The drift term for the exchange rate is given as a difference of two stochastic short rates, domestic and foreign; each modeled by a Gaussian one-factor model with deterministic shift (G1++) process. For stochastic volatility, we model the variance for the exchange rate by a Cox–Ingersoll–Ross (CIR) process. We include tests to show the convergence and the accuracy of the proposed algorithms.
{"title":"CALIBRATING LOCAL VOLATILITY MODELS WITH STOCHASTIC DRIFT AND DIFFUSION","authors":"ORCAN ÖGETBIL, NARAYAN GANESAN, BERNHARD HIENTZSCH","doi":"10.1142/s021902492250011x","DOIUrl":"https://doi.org/10.1142/s021902492250011x","url":null,"abstract":"We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates and finally stochastic local volatility with stochastic interest rates. For each model, we include detailed derivations of the corresponding SDE systems and list the required input data and steps for calibration. We give conditions under which a local volatility can exist given European option prices, stochastic interest rate model parameters, and correlations. The models are posed in a foreign exchange setting. The drift term for the exchange rate is given as a difference of two stochastic short rates, domestic and foreign; each modeled by a Gaussian one-factor model with deterministic shift (G1<inline-formula><mml:math display=\"inline\" overflow=\"scroll\"> <mml:mo stretchy=\"false\">+</mml:mo> <mml:mo stretchy=\"false\">+</mml:mo></mml:math></inline-formula>) process. For stochastic volatility, we model the variance for the exchange rate by a Cox–Ingersoll–Ross (CIR) process. We include tests to show the convergence and the accuracy of the proposed algorithms.","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"78 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532157","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 : 2022-03-15DOI: 10.1142/s0219024922500091
T. Pennanen, Luciane Sbaraini Bonatto
In this paper, we develop a stochastic model for future monthly spot prices of the most important crude oils and refined products. The model is easy to calibrate to both historical data and views of a user even in the presence of negative prices which have been observed recently. This makes it particularly useful for risk management and design of optimal hedging strategies in incomplete market situations where perfect hedging may be impossible or prohibitively expensive to implement. We illustrate the model with optimization of hedging strategies for refinery margins in illiquid markets using a portfolio of 12 most liquid derivative contracts with 12 maturities traded on New York Mercantile Exchange (NYMEX) and Intercontinental Exchange (ICE).
{"title":"A STOCHASTIC OIL PRICE MODEL FOR OPTIMAL HEDGING AND RISK MANAGEMENT","authors":"T. Pennanen, Luciane Sbaraini Bonatto","doi":"10.1142/s0219024922500091","DOIUrl":"https://doi.org/10.1142/s0219024922500091","url":null,"abstract":"In this paper, we develop a stochastic model for future monthly spot prices of the most important crude oils and refined products. The model is easy to calibrate to both historical data and views of a user even in the presence of negative prices which have been observed recently. This makes it particularly useful for risk management and design of optimal hedging strategies in incomplete market situations where perfect hedging may be impossible or prohibitively expensive to implement. We illustrate the model with optimization of hedging strategies for refinery margins in illiquid markets using a portfolio of 12 most liquid derivative contracts with 12 maturities traded on New York Mercantile Exchange (NYMEX) and Intercontinental Exchange (ICE).","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41603891","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 : 2022-02-28DOI: 10.1142/s0219024922500078
KRISTOFFER GLOVER, HARDY HULLEY
To investigate the effect of short-selling constraints on investor behavior, we formulate an optimal stopping model in which the decision to cover a short position is affected by two short sale-specific frictions — margin risk and recall risk. Margin risk is introduced by assuming that a short seller is forced to close out their position involuntarily if they cannot fund margin calls (since short sales are collateralized transactions). Recall risk is introduced by permitting the lender to recall borrowed stock at any time, once again triggering an involuntary close-out. Examining the effect of these frictions on the optimal close-out strategy and associated value function, we finding that the optimal behavior can be qualitatively different in their presence. Moreover, these frictions lead to a substantial loss in value, relative to the first-best situation without them (a reduction of approximately 17% for our conservative base-case parameters). This significant effect has important implications for many familiar no-arbitrage identities, which are predicated on the assumption of unfettered short selling.
{"title":"SHORT SELLING WITH MARGIN RISK AND RECALL RISK","authors":"KRISTOFFER GLOVER, HARDY HULLEY","doi":"10.1142/s0219024922500078","DOIUrl":"https://doi.org/10.1142/s0219024922500078","url":null,"abstract":"To investigate the effect of short-selling constraints on investor behavior, we formulate an optimal stopping model in which the decision to cover a short position is affected by two short sale-specific frictions — margin risk and recall risk. Margin risk is introduced by assuming that a short seller is forced to close out their position involuntarily if they cannot fund margin calls (since short sales are collateralized transactions). Recall risk is introduced by permitting the lender to recall borrowed stock at any time, once again triggering an involuntary close-out. Examining the effect of these frictions on the optimal close-out strategy and associated value function, we finding that the optimal behavior can be qualitatively different in their presence. Moreover, these frictions lead to a substantial loss in value, relative to the first-best situation without them (a reduction of approximately 17% for our conservative base-case parameters). This significant effect has important implications for many familiar no-arbitrage identities, which are predicated on the assumption of unfettered short selling.","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"1155 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532131","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 : 2022-02-28DOI: 10.1142/s0219024922500042
ANIS MATOUSSI, MOHAMED MRAD
In this work, we study a class of consistent dynamic utilities in a incomplete financial market including jumps. First, we show that the dynamic utility is solution of a non-linear second-order stochastic partial integro-differential equation (SPIDE). Second, a complete study of the primal and the dual problems, allows us, firstly, to establish a connection between the utility-SPIDE and two SDEs satisfied by the optimal processes. Based on this connection, stochastic flow technics for SDEs and characteristic method, the SPIDE is completely solved and monotony and concavity properties of the solution are proved.
{"title":"DYNAMIC UTILITY AND RELATED NONLINEAR SPDES DRIVEN BY LÉVY NOISE","authors":"ANIS MATOUSSI, MOHAMED MRAD","doi":"10.1142/s0219024922500042","DOIUrl":"https://doi.org/10.1142/s0219024922500042","url":null,"abstract":"In this work, we study a class of consistent dynamic utilities in a incomplete financial market including jumps. First, we show that the dynamic utility is solution of a non-linear second-order stochastic partial integro-differential equation (SPIDE). Second, a complete study of the primal and the dual problems, allows us, firstly, to establish a connection between the utility-SPIDE and two SDEs satisfied by the optimal processes. Based on this connection, stochastic flow technics for SDEs and characteristic method, the SPIDE is completely solved and monotony and concavity properties of the solution are proved.","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"121 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532147","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 : 2022-02-21DOI: 10.1142/s0219024922500030
P. N. Diffouo, P. Devolder
In this paper, we measure the market and the longevity risks borne by an insurer by computing their solvency capital for a given annuity and within an investment strategy. For this purpose, we propose the investment strategy in such a way as to mitigate the solvency capital of the insurer and improve the internal rate of return of a shareholder investing on a given annuity. Numerically, we study the sensitivity of both the solvency capital and the internal rate of return with respect to some significant parameters.
{"title":"SOLVENCY MEASUREMENT OF LIFE ANNUITY PRODUCTS","authors":"P. N. Diffouo, P. Devolder","doi":"10.1142/s0219024922500030","DOIUrl":"https://doi.org/10.1142/s0219024922500030","url":null,"abstract":"In this paper, we measure the market and the longevity risks borne by an insurer by computing their solvency capital for a given annuity and within an investment strategy. For this purpose, we propose the investment strategy in such a way as to mitigate the solvency capital of the insurer and improve the internal rate of return of a shareholder investing on a given annuity. Numerically, we study the sensitivity of both the solvency capital and the internal rate of return with respect to some significant parameters.","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46578160","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 : 2022-02-09DOI: 10.1142/s0219024922500029
R. Korn, Lukas Müller
In this paper, we consider a continuous time portfolio optimization problem that includes the possibility of a crash scenario as well as parameter uncertainty. To do this, we combine the worst-case scenario approach, introduced by Korn & Wilmott (2002) with a model ambiguity approach that is also based on Knightian uncertainty. In our model, the crash scenario occurs at the worst possible time for the investor, which also implies that there can be no crash at all. For the modeling of the parameter uncertainty, we choose a general definition of the sets of possible drift and volatility parameters, conditioned by the solution of an optimization problem. In addition, these sets may be different in the pre-crash and post-crash market. We solve this portfolio problem and then consider two particular examples with box uncertainty and ellipsoidal drift ambiguity.
{"title":"OPTIMAL PORTFOLIO CHOICE WITH CRASH RISK AND MODEL AMBIGUITY","authors":"R. Korn, Lukas Müller","doi":"10.1142/s0219024922500029","DOIUrl":"https://doi.org/10.1142/s0219024922500029","url":null,"abstract":"In this paper, we consider a continuous time portfolio optimization problem that includes the possibility of a crash scenario as well as parameter uncertainty. To do this, we combine the worst-case scenario approach, introduced by Korn & Wilmott (2002) with a model ambiguity approach that is also based on Knightian uncertainty. In our model, the crash scenario occurs at the worst possible time for the investor, which also implies that there can be no crash at all. For the modeling of the parameter uncertainty, we choose a general definition of the sets of possible drift and volatility parameters, conditioned by the solution of an optimization problem. In addition, these sets may be different in the pre-crash and post-crash market. We solve this portfolio problem and then consider two particular examples with box uncertainty and ellipsoidal drift ambiguity.","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44057484","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 : 2022-01-20DOI: 10.1142/s0219024922500017
A. Roch
We consider a setup in which a large trader has sold a number of American-style derivatives and can have an impact on prices by trading the underlying asset for hedging purposes. The price impacts are assumed to be temporary and decay exponentially with time. Due to the impact of trading on prices, the large trader may also be tempted to minimize the payoff of the derivative by manipulating the underlying asset. Since the option holders have the right to exercise the option at any time before expiry, we consider a robust optimization problem for the large trader, in which the underlying uncertainty is the exercise time. It is shown that the solution of this optimization problem can be described as the solution of a double obstacle variational inequality. The optimal strategy for the large trader and the worst-case exercise time for the option holder are obtained explicitly in terms of the value function. We conclude with a sensitivity analysis in which we compare the timing and size of trades by the large trader as well as the exercise region for the options holders for different levels of liquidity, and identify situations that may lead to potential price manipulation.
{"title":"HEDGING OF AMERICAN OPTIONS IN ILLIQUID MARKETS WITH PRICE IMPACTS","authors":"A. Roch","doi":"10.1142/s0219024922500017","DOIUrl":"https://doi.org/10.1142/s0219024922500017","url":null,"abstract":"We consider a setup in which a large trader has sold a number of American-style derivatives and can have an impact on prices by trading the underlying asset for hedging purposes. The price impacts are assumed to be temporary and decay exponentially with time. Due to the impact of trading on prices, the large trader may also be tempted to minimize the payoff of the derivative by manipulating the underlying asset. Since the option holders have the right to exercise the option at any time before expiry, we consider a robust optimization problem for the large trader, in which the underlying uncertainty is the exercise time. It is shown that the solution of this optimization problem can be described as the solution of a double obstacle variational inequality. The optimal strategy for the large trader and the worst-case exercise time for the option holder are obtained explicitly in terms of the value function. We conclude with a sensitivity analysis in which we compare the timing and size of trades by the large trader as well as the exercise region for the options holders for different levels of liquidity, and identify situations that may lead to potential price manipulation.","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48937403","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 : 2022-01-07DOI: 10.1142/s0219024921500400
SVETLANA BOYARCHENKO, SERGEI LEVENDORSKIĬ, J. LARS KYRKBY, ZHENYU CUI
We clarify the relations among different Fourier-based approaches to option pricing, and improve the B-spline probability density projection method using the sinh-acceleration technique. This allows us to efficiently separate the control of different sources of errors better than the FFT-based realization allows; in many cases, the CPU time decreases as well. We demonstrate the improvement of the B-spline projection method through several numerical experiments in option pricing, including European and barrier options, where the SINH acceleration technique proves to be robust and accurate.
{"title":"SINH-ACCELERATION FOR B-SPLINE PROJECTION WITH OPTION PRICING APPLICATIONS","authors":"SVETLANA BOYARCHENKO, SERGEI LEVENDORSKIĬ, J. LARS KYRKBY, ZHENYU CUI","doi":"10.1142/s0219024921500400","DOIUrl":"https://doi.org/10.1142/s0219024921500400","url":null,"abstract":"We clarify the relations among different Fourier-based approaches to option pricing, and improve the B-spline probability density projection method using the sinh-acceleration technique. This allows us to efficiently separate the control of different sources of errors better than the FFT-based realization allows; in many cases, the CPU time decreases as well. We demonstrate the improvement of the B-spline projection method through several numerical experiments in option pricing, including European and barrier options, where the SINH acceleration technique proves to be robust and accurate.","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"29 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532137","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：