We provide explicit, simple price formulas for the European options under stochastic volatility and stochastic interest rate. The formulas are as simple as the classical Black-Scholes formula. Moreover, the formulas do not require the normality of the returns. We do not need to know the distribution of the returns/price.
{"title":"Black-Scholes formulas without the normality assumption: Applications to stochastic volatility and stochastic interest rate","authors":"Moawia Alghalith","doi":"10.2139/ssrn.3918488","DOIUrl":"https://doi.org/10.2139/ssrn.3918488","url":null,"abstract":"We provide explicit, simple price formulas for the European options under stochastic volatility and stochastic interest rate. The formulas are as simple as the classical Black-Scholes formula. Moreover, the formulas do not require the normality of the returns. We do not need to know the distribution of the returns/price.","PeriodicalId":209192,"journal":{"name":"ERN: Asset Pricing Models (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121320010","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}
As the USD Libor interest rate benchmark is in the process of being discontinued, there is an increasing occurrence of SOFR-based loans and derivatives. Whereas Libor was most commonly set in-advance, an important difference is that SOFR is commonly set in-arrears when it is used in instruments such as overnight index swaps. Loans and interest-rate cap options used as hedges may both choose to fix the SOFR rate in-advance, which is similar to Libor by allowing the rate to be known in-advance of the interest accrual period. Here we adopt the mild assumption of bivariate normal log-forward rates for adjacent rate periods in the forward market model to derive the convexity adjustment for contracts which reference SOFR in-advance. Due to martingale conditions, when adjacent forward rates are uncorrelated there is no convexity adjustment, but when there is non-zero correlation, there is a convexity adjustment for any derivative payoff including the SOFR in-advance forward rate and the caplet/floorlet payoff which references this rate. These results demonstrate that SOFR in-advance derivatives are correlation-sensitive in their pricing and risk management, which is notably more complex than the situation for Libor.
{"title":"SOFR In-Advance Derivative Pricing: Convexity Adjustment in the Forward Market Model","authors":"Jonathan Rosen","doi":"10.2139/ssrn.3903069","DOIUrl":"https://doi.org/10.2139/ssrn.3903069","url":null,"abstract":"As the USD Libor interest rate benchmark is in the process of being discontinued, there is an increasing occurrence of SOFR-based loans and derivatives. Whereas Libor was most commonly set in-advance, an important difference is that SOFR is commonly set in-arrears when it is used in instruments such as overnight index swaps. Loans and interest-rate cap options used as hedges may both choose to fix the SOFR rate in-advance, which is similar to Libor by allowing the rate to be known in-advance of the interest accrual period. Here we adopt the mild assumption of bivariate normal log-forward rates for adjacent rate periods in the forward market model to derive the convexity adjustment for contracts which reference SOFR in-advance. Due to martingale conditions, when adjacent forward rates are uncorrelated there is no convexity adjustment, but when there is non-zero correlation, there is a convexity adjustment for any derivative payoff including the SOFR in-advance forward rate and the caplet/floorlet payoff which references this rate. These results demonstrate that SOFR in-advance derivatives are correlation-sensitive in their pricing and risk management, which is notably more complex than the situation for Libor.","PeriodicalId":209192,"journal":{"name":"ERN: Asset Pricing Models (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117294266","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}
Options paying the product of put and or call option payouts at different strikes on two underlying assets are observed to synthesize joint densities and replicate differentiable functions of two underlying asset prices. The pricing of such options is undertaken from three perspectives. The first uses a geometric two dimensional Brownian motion model. The second inverts two dimensional characteristic functions. The third uses a bootstrapped physical measure to propose a risk charge minimizing hedge using options on the two underlying assets. The options are priced at the cost of the hedge plus the risk charge.
{"title":"Product Options","authors":"D. Madan, King Wang","doi":"10.2139/ssrn.3883594","DOIUrl":"https://doi.org/10.2139/ssrn.3883594","url":null,"abstract":"Options paying the product of put and or call option payouts at different strikes on two underlying assets are observed to synthesize joint densities and replicate differentiable functions of two underlying asset prices. The pricing of such options is undertaken from three perspectives. The first uses a geometric two dimensional Brownian motion model. The second inverts two dimensional characteristic functions. The third uses a bootstrapped physical measure to propose a risk charge minimizing hedge using options on the two underlying assets. The options are priced at the cost of the hedge plus the risk charge.","PeriodicalId":209192,"journal":{"name":"ERN: Asset Pricing Models (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127465893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper presents art as a special object of investment. The features of works of art and art market are presented in comparison with characteristics of securities and stock exchange market. The author takes into account the following criteria: commodity features, ownership characteristic, markets' classification, liquidity, access to information on prices (market values), kinds of values, incomes, time horizon of investment, market indexes used for art market and stock exchange indexes. The paper takes up the issue of the most important characteristic connected with any type of investment i.e. risk and rates of return. The author proposes the classification of risks related to art investment. Moreover, the multidimensional aspects of rates of return are discussed. Financial rate of return in art, as in case of securities, can be calculated on the basis of monetary fluctuations in value in time. The methods available for estimation of rates of return in art are presented: price indices, repeat sales regression, hedonic regression, hybrid model, 2-step hedonic approach. Apart from financial rates of return the importance of non-financial rates of return in art is strongly emphasized.
{"title":"Investment in Art - Specificity, Risks, and Rates of Return","authors":"Joanna Białynicka-Birula","doi":"10.2139/ssrn.3840724","DOIUrl":"https://doi.org/10.2139/ssrn.3840724","url":null,"abstract":"The paper presents art as a special object of investment. The features of works of art and art market are presented in comparison with characteristics of securities and stock exchange market. The author takes into account the following criteria: commodity features, ownership characteristic, markets' classification, liquidity, access to information on prices (market values), kinds of values, incomes, time horizon of investment, market indexes used for art market and stock exchange indexes. The paper takes up the issue of the most important characteristic connected with any type of investment i.e. risk and rates of return. The author proposes the classification of risks related to art investment. Moreover, the multidimensional aspects of rates of return are discussed. Financial rate of return in art, as in case of securities, can be calculated on the basis of monetary fluctuations in value in time. The methods available for estimation of rates of return in art are presented: price indices, repeat sales regression, hedonic regression, hybrid model, 2-step hedonic approach. Apart from financial rates of return the importance of non-financial rates of return in art is strongly emphasized.","PeriodicalId":209192,"journal":{"name":"ERN: Asset Pricing Models (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129251971","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}
Italian Abstract: In queste note si cerca di evidenziare come l'asset pricing, nel contesto di stati di natura discreti emercati completi, sia un metodo per spostare ricchezza attraverso gli stati di natura, per ottenere un consumo il più possibile omogeneo nei diversi stati di natura. L'obiettivo è costruire il sistema di equazioni da risolvere per le incognite e come meccanizzare il modello in semplici algoritmi risolvibili dal computer. Vengono esposte le due strategie di soluzioni equivalenti: a ritroso (backward) e in avanti (forward, tramite l'equazione di Bellman). I problemi considerati vanno dal caso più semplice di attività finanziarie "pure" ai casi di attività finanziarie "complesse" che danno luogo a rendimenti in più o tutti gli stati di natura.
English Abstract: In these lecture notes I try to emphasize how asset pricing in discrete states of nature and complete markets, is a way to move wealth around states of nature in order to smooth consumption. The aim is to construct the system of equation to be solved for unknowns and how to mechanize the model into simple software algorithms. Two solution strategies are presented: backward and forward, through Bellman equation. The problems to be solved start from the easy case of pure assets to the case of complex assets having yields in many or all states of nature.
{"title":"Lezioni di scelta in condizioni di incertezza e asset pricing: Stati di natura discreti e mercati completi. (Choice under Uncertainty and Asset Pricing: Complete Markets)","authors":"Maria-Augusta Miceli","doi":"10.2139/ssrn.3356609","DOIUrl":"https://doi.org/10.2139/ssrn.3356609","url":null,"abstract":"<b>Italian Abstract:</b> In queste note si cerca di evidenziare come l'asset pricing, nel contesto di stati di natura discreti emercati completi, sia un metodo per spostare ricchezza attraverso gli stati di natura, per ottenere un consumo il più possibile omogeneo nei diversi stati di natura. L'obiettivo è costruire il sistema di equazioni da risolvere per le incognite e come meccanizzare il modello in semplici algoritmi risolvibili dal computer. Vengono esposte le due strategie di soluzioni equivalenti: a ritroso (backward) e in avanti (forward, tramite l'equazione di Bellman). I problemi considerati vanno dal caso più semplice di attività finanziarie \"pure\" ai casi di attività finanziarie \"complesse\" che danno luogo a rendimenti in più o tutti gli stati di natura.<br><br><b>English Abstract:</b> In these lecture notes I try to emphasize how asset pricing in discrete states of nature and complete markets, is a way to move wealth around states of nature in order to smooth consumption. The aim is to construct the system of equation to be solved for unknowns and how to mechanize the model into simple software algorithms. Two solution strategies are presented: backward and forward, through Bellman equation. The problems to be solved start from the easy case of pure assets to the case of complex assets having yields in many or all states of nature.","PeriodicalId":209192,"journal":{"name":"ERN: Asset Pricing Models (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115682289","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 devise a new high-frequency covariance matrix estimator based on price durations which is guaranteed to be positive-definite. Both non-parametric and parametric versions are proposed. A comprehensive Monte Carlo simulation shows that this class of estimators are less biased, more efficient, and generate lower RMSE as well as QLIKE errors. Empirically, we apply both estimators to a global minimum variance portfolio allocation problem and find they can generate comparably low portfolio variance, higher Sharpe ratios, but with considerably lower portfolio turnovers. This matrix estimator is also shown empirically to be more well-conditioned.
{"title":"First Passage Time Covariance Matrix Estimators","authors":"Seok Young Hong, O. Linton, Xiaolu Zhao","doi":"10.2139/ssrn.3802618","DOIUrl":"https://doi.org/10.2139/ssrn.3802618","url":null,"abstract":"We devise a new high-frequency covariance matrix estimator based on price durations which is guaranteed to be positive-definite. Both non-parametric and parametric versions are proposed. A comprehensive Monte Carlo simulation shows that this class of estimators are less biased, more efficient, and generate lower RMSE as well as QLIKE errors. Empirically, we apply both estimators to a global minimum variance portfolio allocation problem and find they can generate comparably low portfolio variance, higher Sharpe ratios, but with considerably lower portfolio turnovers. This matrix estimator is also shown empirically to be more well-conditioned.","PeriodicalId":209192,"journal":{"name":"ERN: Asset Pricing Models (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122209857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper examines the efficiency of standard variance reduction techniques across option characteristics when pricing American-style call and put options with the Least-Squares Monte Carlo algorithm of Longstaff & Schwartz (2001). Our numerical experiments evaluate the efficiency of antithetic sampling, control variates, importance sampling, and combinations thereof. Whereas most of the American option pricing literature has focused on either put or call options individually, we employ the symmetry relation of McDonald & Schroder (1998) to compare performance for pairs of call and put options whose solution coincide. Our results first show that variance reduction is generally more efficient for put than call options and that control variates is the most efficient stand-alone method. We also find that marginal gains in efficiency are typically achieved by combining variance reduction techniques, though some techniques may interact conflictingly. Finally, since valuation of American-style call options can be improved by pricing symmetric put options instead (Stentoft 2019), we demonstrate that drastic reductions in the standard deviation of the call is obtained by combining all three variance reduction techniques in a symmetric pricing approach, which reduces the standard deviation by a factor of over 20 for long maturity call options on highly volatile assets.
{"title":"Efficient Variance Reduction with Least-Squares Monte Carlo Pricing","authors":"François-Michel Boire, R. Reesor, Lars Stentoft","doi":"10.2139/ssrn.3795621","DOIUrl":"https://doi.org/10.2139/ssrn.3795621","url":null,"abstract":"This paper examines the efficiency of standard variance reduction techniques across option characteristics when pricing American-style call and put options with the Least-Squares Monte Carlo algorithm of Longstaff & Schwartz (2001). Our numerical experiments evaluate the efficiency of antithetic sampling, control variates, importance sampling, and combinations thereof. Whereas most of the American option pricing literature has focused on either put or call options individually, we employ the symmetry relation of McDonald & Schroder (1998) to compare performance for pairs of call and put options whose solution coincide. Our results first show that variance reduction is generally more efficient for put than call options and that control variates is the most efficient stand-alone method. We also find that marginal gains in efficiency are typically achieved by combining variance reduction techniques, though some techniques may interact conflictingly. Finally, since valuation of American-style call options can be improved by pricing symmetric put options instead (Stentoft 2019), we demonstrate that drastic reductions in the standard deviation of the call is obtained by combining all three variance reduction techniques in a symmetric pricing approach, which reduces the standard deviation by a factor of over 20 for long maturity call options on highly volatile assets.","PeriodicalId":209192,"journal":{"name":"ERN: Asset Pricing Models (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128465521","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}
When investing in derivatives portfolios (such as options), the delta-gamma approximation (DGA) is often used as a risk management strategy to reduce the risk associated with the underlying asset price. However, this approximation is accepted only for small changes of the underlying asset price. When these changes become large, the option prices estimated by the DGA may significantly differ from those of the market, depending mainly on the time-to-maturity, implied volatility, and moneyness. Hence, in practice, before the change of the underlying asset price becomes large, rebalancing operations are demanded to minimize the losses occurred due to the error introduced by the DGA. The frequency of rebalancing may be high when the rate at which the underlying asset price significantly changes. Nonetheless, frequent rebalancing may be unattainable, as there are associated transaction costs. Hence, there is a trade-off between the losses resulting from the inaccuracy inherent to the DGA and the transaction costs incurring from frequent hedging operations. In the present work, with the objective to increase the accuracy of estimating the option prices, we propose a modified version of the DGA that outperforms the original DGA. As another approach to increase the accuracy, we propose the locally weighted regression to regress the option prices. Finally, we compare the performance of these two methods to that of some other existing methods.
{"title":"Approximating Option Prices under Large Changes of Underlying Asset Prices","authors":"Jae-Yun Jun, Y. Rakotondratsimba","doi":"10.2139/ssrn.3790528","DOIUrl":"https://doi.org/10.2139/ssrn.3790528","url":null,"abstract":"When investing in derivatives portfolios (such as options), the delta-gamma approximation (DGA) is often used as a risk management strategy to reduce the risk associated with the underlying asset price. However, this approximation is accepted only for small changes of the underlying asset price. When these changes become large, the option prices estimated by the DGA may significantly differ from those of the market, depending mainly on the time-to-maturity, implied volatility, and moneyness. Hence, in practice, before the change of the underlying asset price becomes large, rebalancing operations are demanded to minimize the losses occurred due to the error introduced by the DGA. The frequency of rebalancing may be high when the rate at which the underlying asset price significantly changes. Nonetheless, frequent rebalancing may be unattainable, as there are associated transaction costs. Hence, there is a trade-off between the losses resulting from the inaccuracy inherent to the DGA and the transaction costs incurring from frequent hedging operations. In the present work, with the objective to increase the accuracy of estimating the option prices, we propose a modified version of the DGA that outperforms the original DGA. As another approach to increase the accuracy, we propose the locally weighted regression to regress the option prices. Finally, we compare the performance of these two methods to that of some other existing methods.","PeriodicalId":209192,"journal":{"name":"ERN: Asset Pricing Models (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132026222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper uses novel environmental, social, and governance (ESG) incident news data to study poor ESG practices. I find that firms’ past ESG incident rates predict more incidents, weaker profits, and lower risk-adjusted stock returns. When examining the cause of these abnormal returns, I find analyst forecast errors as well as lower returns around earnings announcements and subsequent incidents. Moreover, incident rates predict stronger abnormal returns in firms with higher short-term ownership, higher valuation uncertainty, and lower investor attention. Overall, these findings suggest that poor ESG practices negatively impact long-term value, which is not fully reflected in stock prices.
{"title":"Repeat Offenders: ESG Incident Recidivism and Investor Underreaction","authors":"Simon Glossner","doi":"10.2139/ssrn.3004689","DOIUrl":"https://doi.org/10.2139/ssrn.3004689","url":null,"abstract":"This paper uses novel environmental, social, and governance (ESG) incident news data to study poor ESG practices. I find that firms’ past ESG incident rates predict more incidents, weaker profits, and lower risk-adjusted stock returns. When examining the cause of these abnormal returns, I find analyst forecast errors as well as lower returns around earnings announcements and subsequent incidents. Moreover, incident rates predict stronger abnormal returns in firms with higher short-term ownership, higher valuation uncertainty, and lower investor attention. Overall, these findings suggest that poor ESG practices negatively impact long-term value, which is not fully reflected in stock prices.","PeriodicalId":209192,"journal":{"name":"ERN: Asset Pricing Models (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134393463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper develops and presents the prior adaptive group lasso for generalized linear models. The prior adaptive group lasso is an extension of the prior lasso developed by Jiang, He, and Zhang (2016), which allows for the use of existing information from previous or similar studies in the estimation of the lasso. We demonstrate that the estimator exhibits consistent variable selection and estimation similarly to those derived in Wang and Tian (2019) under at set of similar conditions. The performance of the prior adaptive group lasso estimator is illustrated in a Monte Carlo study. Finally, the estimator is applied in selecting the set of relevant risk factors in asset pricing models conditioning on the fact that the chosen factors must be able to price the test assets as well as the remaining factors. The empirical study shows that the prior adaptive group lasso yields a set of factors that explain the time variation in the returns while delivering 𝛼 estimates close to zero. We also show how this set of factors has evolved over time. We find that the canonical factor models of Fama and French (1993), (Carhart, 1997), (Fama and French, 2015), and (Hou, Xue, and Zhang, 2015) are insufficient to price the cross section of the test assets together with the remaining traded factors, and we find that the required number of pricing factors to include at any given time is closer to 20.
提出了广义线性模型的先验自适应群套索。先验自适应组套索是Jiang、He和Zhang(2016)开发的先验套索的扩展，它允许在套索的估计中使用以前或类似研究的现有信息。我们证明，在一组相似的条件下，估计量与Wang和Tian(2019)的推导结果相似，具有一致的变量选择和估计。通过蒙特卡罗研究说明了先验自适应群套索估计的性能。最后，在选择的风险因素必须能够对测试资产以及其他因素进行定价的前提下，将估计器应用于选择资产定价模型中相关风险因素的集合。实证研究表明，先前的自适应组套索产生了一组因素，这些因素解释了收益的时间变化，同时提供了接近于零的时延估计。我们还展示了这些因素是如何随着时间的推移而演变的。我们发现Fama和French (1993)， (Carhart, 1997)， (Fama和French, 2015)和(Hou, Xue, and Zhang, 2015)的典型因子模型不足以将测试资产的横截面与剩余的交易因子一起定价，并且我们发现在任何给定时间需要包含的定价因子的数量接近20。
{"title":"The Prior Adaptive Group Lasso with an Application to Risk Factor Selection","authors":"Kristoffer Pons Bertelsen","doi":"10.2139/ssrn.3785286","DOIUrl":"https://doi.org/10.2139/ssrn.3785286","url":null,"abstract":"This paper develops and presents the prior adaptive group lasso for generalized linear models. The prior adaptive group lasso is an extension of the prior lasso developed by Jiang, He, and Zhang (2016), which allows for the use of existing information from previous or similar studies in the estimation of the lasso. We demonstrate that the estimator exhibits consistent variable selection and estimation similarly to those derived in Wang and Tian (2019) under at set of similar conditions. The performance of the prior adaptive group lasso estimator is illustrated in a Monte Carlo study. Finally, the estimator is applied in selecting the set of relevant risk factors in asset pricing models conditioning on the fact that the chosen factors must be able to price the test assets as well as the remaining factors. The empirical study shows that the prior adaptive group lasso yields a set of factors that explain the time variation in the returns while delivering 𝛼 estimates close to zero. We also show how this set of factors has evolved over time. We find that the canonical factor models of Fama and French (1993), (Carhart, 1997), (Fama and French, 2015), and (Hou, Xue, and Zhang, 2015) are insufficient to price the cross section of the test assets together with the remaining traded factors, and we find that the required number of pricing factors to include at any given time is closer to 20.","PeriodicalId":209192,"journal":{"name":"ERN: Asset Pricing Models (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126783409","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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