We study the influence of additional intermediate marginal distributions on the value of the martingale optimal transport problem. From a financial point of view, this corresponds to taking into account call option prices not only, as usual, for those call options where the respective future maturities coincide with the maturities of some exotic derivative but also additional maturities and then to study the effect on model-independent price bounds for the exotic derivative. We characterize market settings, i.e., combinations of the payoff of exotic derivatives, call option prices and marginal distributions that guarantee improved price bounds as well as those market settings that exclude any improvement. Eventually, we showcase in numerous examples that the consideration of additional price information on vanilla options may have a considerable impact on the resultant model-independent price bounds.
{"title":"On intermediate Marginals in Martingale Optimal Transportation","authors":"Julian Sester","doi":"arxiv-2307.09710","DOIUrl":"https://doi.org/arxiv-2307.09710","url":null,"abstract":"We study the influence of additional intermediate marginal distributions on\u0000the value of the martingale optimal transport problem. From a financial point\u0000of view, this corresponds to taking into account call option prices not only,\u0000as usual, for those call options where the respective future maturities\u0000coincide with the maturities of some exotic derivative but also additional\u0000maturities and then to study the effect on model-independent price bounds for\u0000the exotic derivative. We characterize market settings, i.e., combinations of\u0000the payoff of exotic derivatives, call option prices and marginal distributions\u0000that guarantee improved price bounds as well as those market settings that\u0000exclude any improvement. Eventually, we showcase in numerous examples that the consideration of\u0000additional price information on vanilla options may have a considerable impact\u0000on the resultant model-independent price bounds.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522572","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 study the impacts of regime changes and related rule implementations on IPOs initial return for China entrepreneurial boards (ChiNext and STAR). We propose that an initial return contains the issuer fair value and an investors overreaction and examine their magnitudes and determinants. Our findings reveal an evolution of IPO pricing in response to the progression of regulation changes along four dimensions: 1) governing regulation regime, 2) listing day trading restrictions, 3) listing rules for issuers, and 4) participation requirements for investors. We find that the most efficient regulation regime in Chinese IPO pricing has four characteristics: 1) registration system, 2) no hard return caps nor trading curbs that restrict the initial return; 3) more specific listing rules for issuers, and 4) more stringent participation requirements for investors. In all contexts, we show that the registration regime governing the STAR IPOs offers the most efficient pricing.
{"title":"The Impacts of Registration Regime Implementation on IPO Pricing Efficiency","authors":"Qi Deng, Linhong Zheng, Jiaqi Peng, Xu Li, Zhong-guo Zhou, Monica Hussein, Dingyi Chen, Mick Swartz","doi":"arxiv-2307.09669","DOIUrl":"https://doi.org/arxiv-2307.09669","url":null,"abstract":"We study the impacts of regime changes and related rule implementations on\u0000IPOs initial return for China entrepreneurial boards (ChiNext and STAR). We\u0000propose that an initial return contains the issuer fair value and an investors\u0000overreaction and examine their magnitudes and determinants. Our findings reveal\u0000an evolution of IPO pricing in response to the progression of regulation\u0000changes along four dimensions: 1) governing regulation regime, 2) listing day\u0000trading restrictions, 3) listing rules for issuers, and 4) participation\u0000requirements for investors. We find that the most efficient regulation regime\u0000in Chinese IPO pricing has four characteristics: 1) registration system, 2) no\u0000hard return caps nor trading curbs that restrict the initial return; 3) more\u0000specific listing rules for issuers, and 4) more stringent participation\u0000requirements for investors. In all contexts, we show that the registration\u0000regime governing the STAR IPOs offers the most efficient pricing.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522636","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}
Path integral method in quantum theory provides a new thinking for time dependent option pricing. For barrier options, the option price changing process is similar to the infinite high barrier scattering problem in quantum mechanics; for double barrier options, the option price changing process is analogous to a particle moving in a infinite square potential well. Using path integral method, the expressions of pricing kernel and option price under Vasicek stochastic interest rate model could be derived. Numerical results of options price as functions of underlying prices are also shown.
{"title":"Path Integral Method for Barrier Option Pricing Under Vasicek Model","authors":"Qi Chen, Chao Guo","doi":"arxiv-2307.07103","DOIUrl":"https://doi.org/arxiv-2307.07103","url":null,"abstract":"Path integral method in quantum theory provides a new thinking for time\u0000dependent option pricing. For barrier options, the option price changing\u0000process is similar to the infinite high barrier scattering problem in quantum\u0000mechanics; for double barrier options, the option price changing process is\u0000analogous to a particle moving in a infinite square potential well. Using path\u0000integral method, the expressions of pricing kernel and option price under\u0000Vasicek stochastic interest rate model could be derived. Numerical results of\u0000options price as functions of underlying prices are also shown.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522634","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}
Guyon and Lekeufack recently proposed a path-dependent volatility model and documented its excellent performance in fitting market data and capturing stylized facts. The instantaneous volatility is modeled as a linear combination of two processes, one is an integral of weighted past price returns and the other is the square-root of an integral of weighted past squared volatility. Each of the weightings is built using two exponential kernels reflecting long and short memory. Mathematically, the model is a coupled system of four stochastic differential equations. Our main result is the wellposedness of this system: the model has a unique strong (non-explosive) solution for realistic parameter values. We also study the positivity of the resulting volatility process.
{"title":"On the Guyon-Lekeufack Volatility Model","authors":"Marcel Nutz, Andrés Riveros Valdevenito","doi":"arxiv-2307.01319","DOIUrl":"https://doi.org/arxiv-2307.01319","url":null,"abstract":"Guyon and Lekeufack recently proposed a path-dependent volatility model and\u0000documented its excellent performance in fitting market data and capturing\u0000stylized facts. The instantaneous volatility is modeled as a linear combination\u0000of two processes, one is an integral of weighted past price returns and the\u0000other is the square-root of an integral of weighted past squared volatility.\u0000Each of the weightings is built using two exponential kernels reflecting long\u0000and short memory. Mathematically, the model is a coupled system of four\u0000stochastic differential equations. Our main result is the wellposedness of this\u0000system: the model has a unique strong (non-explosive) solution for realistic\u0000parameter values. We also study the positivity of the resulting volatility\u0000process.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522651","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}
Researchers have been using Neural Networks and other related machine-learning techniques to price options since the early 1990s. After three decades of improvements in machine learning techniques, computational processing power, cloud computing, and data availability, this paper is able to provide a comparison of using Google Cloud's AutoML Regressor, TensorFlow Neural Networks, and XGBoost Gradient Boosting Decision Trees for pricing European Options. All three types of models were able to outperform the Black Scholes Model in terms of mean absolute error. These results showcase the potential of using historical data from an option's underlying asset for pricing European options, especially when using machine learning algorithms that learn complex patterns that traditional parametric models do not take into account.
{"title":"Pricing European Options with Google AutoML, TensorFlow, and XGBoost","authors":"Juan Esteban Berger","doi":"arxiv-2307.00476","DOIUrl":"https://doi.org/arxiv-2307.00476","url":null,"abstract":"Researchers have been using Neural Networks and other related\u0000machine-learning techniques to price options since the early 1990s. After three\u0000decades of improvements in machine learning techniques, computational\u0000processing power, cloud computing, and data availability, this paper is able to\u0000provide a comparison of using Google Cloud's AutoML Regressor, TensorFlow\u0000Neural Networks, and XGBoost Gradient Boosting Decision Trees for pricing\u0000European Options. All three types of models were able to outperform the Black\u0000Scholes Model in terms of mean absolute error. These results showcase the\u0000potential of using historical data from an option's underlying asset for\u0000pricing European options, especially when using machine learning algorithms\u0000that learn complex patterns that traditional parametric models do not take into\u0000account.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522643","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}
Equity-linked securities with a guaranteed return become very popular in financial markets ether as investment instruments or life insurance policies. The contract pays off a guaranteed amount plus a payment linked to the performance of a basket of equities averaged over a certain period. This paper presents a new model for valuing equity-linked securities. Our study shows that the security price can be replicated by the sum of the guaranteed amount plus the price of an Asian style option on the basket. Analytical formulas are derived for the security price and corresponding hedge ratios. The model appears to be accurate over a wide range of underlying security parameters according to numerical studies. Finally, we use our model to value a segregated fund with a guarantee at maturity.
{"title":"Valuation of Equity Linked Securities with Guaranteed Return","authors":"David Xiao","doi":"arxiv-2306.15026","DOIUrl":"https://doi.org/arxiv-2306.15026","url":null,"abstract":"Equity-linked securities with a guaranteed return become very popular in\u0000financial markets ether as investment instruments or life insurance policies.\u0000The contract pays off a guaranteed amount plus a payment linked to the\u0000performance of a basket of equities averaged over a certain period. This paper\u0000presents a new model for valuing equity-linked securities. Our study shows that\u0000the security price can be replicated by the sum of the guaranteed amount plus\u0000the price of an Asian style option on the basket. Analytical formulas are\u0000derived for the security price and corresponding hedge ratios. The model\u0000appears to be accurate over a wide range of underlying security parameters\u0000according to numerical studies. Finally, we use our model to value a segregated\u0000fund with a guarantee at maturity.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522637","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}
Alain-Philippe Fortin, Patrick Gagliardini, Olivier Scaillet
We develop inferential tools for latent factor analysis in short panels. The pseudo maximum likelihood setting under a large cross-sectional dimension $n$ and a fixed time series dimension $T$ relies on a diagonal $T times T$ covariance matrix of the errors without imposing sphericity or Gaussianity. We outline the asymptotic distributions of the latent factor and error covariance estimates as well as of an asymptotically uniformly most powerful invariant (AUMPI) test based on the likelihood ratio statistic for tests of the number of factors. We derive the AUMPI characterization from inequalities ensuring the monotone likelihood ratio property for positive definite quadratic forms in normal variables. An empirical application to a large panel of monthly U.S. stock returns separates date after date systematic and idiosyncratic risks in short subperiods of bear vs. bull market based on the selected number of factors. We observe an uptrend in idiosyncratic volatility while the systematic risk explains a large part of the cross-sectional total variance in bear markets but is not driven by a single factor. We also find that observed factors, scaled or not, struggle spanning latent factors. Rank tests reveal that observed factors struggle spanning latent factors with a discrepancy between the dimension of the two factor spaces decreasing over time.
{"title":"Latent Factor Analysis in Short Panels","authors":"Alain-Philippe Fortin, Patrick Gagliardini, Olivier Scaillet","doi":"arxiv-2306.14004","DOIUrl":"https://doi.org/arxiv-2306.14004","url":null,"abstract":"We develop inferential tools for latent factor analysis in short panels. The\u0000pseudo maximum likelihood setting under a large cross-sectional dimension $n$\u0000and a fixed time series dimension $T$ relies on a diagonal $T times T$\u0000covariance matrix of the errors without imposing sphericity or Gaussianity. We\u0000outline the asymptotic distributions of the latent factor and error covariance\u0000estimates as well as of an asymptotically uniformly most powerful invariant\u0000(AUMPI) test based on the likelihood ratio statistic for tests of the number of\u0000factors. We derive the AUMPI characterization from inequalities ensuring the\u0000monotone likelihood ratio property for positive definite quadratic forms in\u0000normal variables. An empirical application to a large panel of monthly U.S.\u0000stock returns separates date after date systematic and idiosyncratic risks in\u0000short subperiods of bear vs. bull market based on the selected number of\u0000factors. We observe an uptrend in idiosyncratic volatility while the systematic\u0000risk explains a large part of the cross-sectional total variance in bear\u0000markets but is not driven by a single factor. We also find that observed\u0000factors, scaled or not, struggle spanning latent factors. Rank tests reveal\u0000that observed factors struggle spanning latent factors with a discrepancy\u0000between the dimension of the two factor spaces decreasing over time.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522650","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 article presents a generic framework for modeling the dynamics of forward curves in commodity market as commodity derivatives are typically traded by futures or forwards. We have theoretically demonstrated that commodity prices are driven by multiple components. As such, the model can better capture the forward price and volatility dynamics. Empirical study shows that the model prices are very close to the market prices, indicating prima facie that the model performs quite well.
{"title":"Generic Forward Curve Dynamics for Commodity Derivatives","authors":"David Xiao","doi":"arxiv-2306.12921","DOIUrl":"https://doi.org/arxiv-2306.12921","url":null,"abstract":"This article presents a generic framework for modeling the dynamics of\u0000forward curves in commodity market as commodity derivatives are typically\u0000traded by futures or forwards. We have theoretically demonstrated that\u0000commodity prices are driven by multiple components. As such, the model can\u0000better capture the forward price and volatility dynamics. Empirical study shows\u0000that the model prices are very close to the market prices, indicating prima\u0000facie that the model performs quite well.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"273 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I examine potential mechanisms behind two stylized facts of initial public offerings (IPOs) returns. By analyzing investor sentiment expressed on StockTwits and Twitter, I find that emotions conveyed through these social media platforms can help explain the mispricing of IPO stocks. The abundance of information and opinions shared on social media can generate hype around certain stocks, leading to investors' irrational buying and selling decisions. This can result in an overvaluation of the stock in the short term but often leads to a correction in the long term as the stock's performance fails to meet the inflated expectations. In particular, I find that IPOs with high levels of pre-IPO investor enthusiasm tend to have a significantly higher first-day return of 29.54%, compared to IPOs with lower levels of pre-IPO investor enthusiasm, which have an average first-day return of 16.91%. However, this initial enthusiasm may be misplaced, as IPOs with high pre-IPO investor enthusiasm demonstrate a much lower average long-run industry-adjusted return of -8.53%, compared to IPOs with lower pre-IPO investor enthusiasm, which have an average long-run industry-adjusted return of -1.1%.
{"title":"Social Media Emotions and IPO Returns","authors":"Domonkos F. Vamossy","doi":"arxiv-2306.12602","DOIUrl":"https://doi.org/arxiv-2306.12602","url":null,"abstract":"I examine potential mechanisms behind two stylized facts of initial public\u0000offerings (IPOs) returns. By analyzing investor sentiment expressed on\u0000StockTwits and Twitter, I find that emotions conveyed through these social\u0000media platforms can help explain the mispricing of IPO stocks. The abundance of\u0000information and opinions shared on social media can generate hype around\u0000certain stocks, leading to investors' irrational buying and selling decisions.\u0000This can result in an overvaluation of the stock in the short term but often\u0000leads to a correction in the long term as the stock's performance fails to meet\u0000the inflated expectations. In particular, I find that IPOs with high levels of\u0000pre-IPO investor enthusiasm tend to have a significantly higher first-day\u0000return of 29.54%, compared to IPOs with lower levels of pre-IPO investor\u0000enthusiasm, which have an average first-day return of 16.91%. However, this\u0000initial enthusiasm may be misplaced, as IPOs with high pre-IPO investor\u0000enthusiasm demonstrate a much lower average long-run industry-adjusted return\u0000of -8.53%, compared to IPOs with lower pre-IPO investor enthusiasm, which have\u0000an average long-run industry-adjusted return of -1.1%.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522635","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 investigate the most common type of blockchain-based decentralized exchange, which are known as constant function market makers (CFMMs). We examine the the market microstructure around CFMMs and present a model for valuing the liquidity provider (LP) mechanism and estimating the value of the associated derivatives. We develop a model with two types of traders that have different information and contribute methods for simulating the behavior of each trader and accounting for trade PnL. We also develop ideas around the equilibrium distribution of fair price conditional on the arrival of traders. Finally, we show how these findings might be used to think about parameters for alternative CFMMs.
{"title":"The Pricing And Hedging Of Constant Function Market Makers","authors":"Richard Dewey, Craig Newbold","doi":"arxiv-2306.11580","DOIUrl":"https://doi.org/arxiv-2306.11580","url":null,"abstract":"We investigate the most common type of blockchain-based decentralized\u0000exchange, which are known as constant function market makers (CFMMs). We\u0000examine the the market microstructure around CFMMs and present a model for\u0000valuing the liquidity provider (LP) mechanism and estimating the value of the\u0000associated derivatives. We develop a model with two types of traders that have\u0000different information and contribute methods for simulating the behavior of\u0000each trader and accounting for trade PnL. We also develop ideas around the\u0000equilibrium distribution of fair price conditional on the arrival of traders.\u0000Finally, we show how these findings might be used to think about parameters for\u0000alternative CFMMs.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138522642","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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