Pub Date : 2019-10-07DOI: 10.1002/9781119595663.ch14
John C. Cox
{"title":"Options Markets","authors":"John C. Cox","doi":"10.1002/9781119595663.ch14","DOIUrl":"https://doi.org/10.1002/9781119595663.ch14","url":null,"abstract":"","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"40 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80738601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a Realized-GARCH-Kernel model to predict realized volatilities of 50 ETF in China and S&P500 index in U.S..The Kernel density fitting on disturbance term and semi-parametric method make our model perform well both statistically and economically. First, our model has the lowest in- and out-of-sample prediction errors among five comparable prediction models. The result is robust in eight measures of realized volatility. Second, in both China and U.S. markets, straddle option trading strategies with volatilities predicted with our model generate larger monthly profit and greater Sharpe ratio. Our model is useful in practical investment.
{"title":"Prediction of Realized Volatility Based on Realized-GARCH-Kernel Model: The Comparison of CHINA and US","authors":"Jiazhen Wang, Yuexiang Jiang, Yanjian Zhu, Jing Yu","doi":"10.2139/ssrn.3316068","DOIUrl":"https://doi.org/10.2139/ssrn.3316068","url":null,"abstract":"We propose a Realized-GARCH-Kernel model to predict realized volatilities of 50 ETF in China and S&P500 index in U.S..The Kernel density fitting on disturbance term and semi-parametric method make our model perform well both statistically and economically. First, our model has the lowest in- and out-of-sample prediction errors among five comparable prediction models. The result is robust in eight measures of realized volatility. Second, in both China and U.S. markets, straddle option trading strategies with volatilities predicted with our model generate larger monthly profit and greater Sharpe ratio. Our model is useful in practical investment.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"106 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76235975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.1002/9781119595663.ch25
Dirk Rohmeder
{"title":"Pricing European Options","authors":"Dirk Rohmeder","doi":"10.1002/9781119595663.ch25","DOIUrl":"https://doi.org/10.1002/9781119595663.ch25","url":null,"abstract":"","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"112 2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79459599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-08DOI: 10.1002/9781119507918.ch4
Kaitlyn Hindman
This paper investigates the Black-Scholes model, which is used to obtain an initial fair price for an option in the stock market. The Black-Scholes partial differential equation will be derived using tools from finance, probability theory, stochastic calculus and partial differential equations.
{"title":"Pricing Options","authors":"Kaitlyn Hindman","doi":"10.1002/9781119507918.ch4","DOIUrl":"https://doi.org/10.1002/9781119507918.ch4","url":null,"abstract":"This paper investigates the Black-Scholes model, which is used to obtain an initial fair price for an option in the stock market. The Black-Scholes partial differential equation will be derived using tools from finance, probability theory, stochastic calculus and partial differential equations.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"108 5","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/9781119507918.ch4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72537894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Revisiting the two-factor valuation of financial futures contracts and their derivatives, we propose a new approach in which the covariance process between the underlying asset price and the money market interest rate is set endogenously according to investors' arbitrage operations. The asset-rate covariance turns out to be stochastic, thereby explicitly capturing futures contracts' marking-to-market feature. Our numerical simulations show significant deviations from the traditional cost-of-carry model of futures prices, in line with Cox, Ingersoll and Ross's (1981) theory and a large corpus of past empirical research. Our empirical tests show an impact of several index points magnitude from the recent US Federal Reserve interest rate hikes on the S&P 500 daily spot-futures basis, highlighting the effect of monetary policy at low frequencies on the backwardation vs. contango regime, and shedding new light on Keynes's (1930) theory of normal backwardation.
{"title":"Is Normal Backwardation Normal? Valuing Financial Futures with a Stochastic, Endogenous Index-Rate Covariance","authors":"P. Raimbourg, Paul Zimmermann","doi":"10.2139/ssrn.3189847","DOIUrl":"https://doi.org/10.2139/ssrn.3189847","url":null,"abstract":"Revisiting the two-factor valuation of financial futures contracts and their derivatives, we propose a new approach in which the covariance process between the underlying asset price and the money market interest rate is set endogenously according to investors' arbitrage operations. The asset-rate covariance turns out to be stochastic, thereby explicitly capturing futures contracts' marking-to-market feature. Our numerical simulations show significant deviations from the traditional cost-of-carry model of futures prices, in line with Cox, Ingersoll and Ross's (1981) theory and a large corpus of past empirical research. Our empirical tests show an impact of several index points magnitude from the recent US Federal Reserve interest rate hikes on the S&P 500 daily spot-futures basis, highlighting the effect of monetary policy at low frequencies on the backwardation vs. contango regime, and shedding new light on Keynes's (1930) theory of normal backwardation.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"39 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88442981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we analyze frequently made errors when valuing real options. The best way of doing it is through examples. We start by analyzing Damodaran's proposal to value the option to expand the business of Home Depot. Some of the errors and problems of this and other approaches are: - Assuming that the option is replicable and using Black and Scholes' formula. - The estimation of the option's volatility is arbitrary and has a decisive effect on the option's value. - As there is no riskless arbitrage, the value of the option to expand basically depends on expectations about future cash flows. However, Damodaran assumes that this parameter does not influence the option's value (he does not use it) because he assumes that the option is replicable. - It is not appropriate to discount the expected value of the cash flows at the risk-free rate (as is done implicitly when Black and Scholes' formula is used) because the uncertainty of costs and sales at the exercise date may be greater or less than that estimated today. - Damodaran's valuation assumes that we know exactly the exercise price. - Believing that options' value increases when interest rates increase. - "Playing" with volatility. - Valuing contracts as real options when they are not.
{"title":"Valuing Real Options: Frequently Made Errors","authors":"Pablo Fernández","doi":"10.2139/ssrn.274855","DOIUrl":"https://doi.org/10.2139/ssrn.274855","url":null,"abstract":"In this paper we analyze frequently made errors when valuing real options. The best way of doing it is through examples. We start by analyzing Damodaran's proposal to value the option to expand the business of Home Depot. Some of the errors and problems of this and other approaches are: - Assuming that the option is replicable and using Black and Scholes' formula. - The estimation of the option's volatility is arbitrary and has a decisive effect on the option's value. - As there is no riskless arbitrage, the value of the option to expand basically depends on expectations about future cash flows. However, Damodaran assumes that this parameter does not influence the option's value (he does not use it) because he assumes that the option is replicable. - It is not appropriate to discount the expected value of the cash flows at the risk-free rate (as is done implicitly when Black and Scholes' formula is used) because the uncertainty of costs and sales at the exercise date may be greater or less than that estimated today. - Damodaran's valuation assumes that we know exactly the exercise price. - Believing that options' value increases when interest rates increase. - \"Playing\" with volatility. - Valuing contracts as real options when they are not.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"68 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2015-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75612796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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