It is a well known fact by academia that traditional valuation methods like DCF and NPV underestimate investments by not including managers’ flexibility and are widely discussed in the financial press. This underestimation and managers’ flexibility is due to investments’ uncertainty and not including irreversibility and investment timing. In this thesis I look at how investments under uncertainty are valued by considering different real option methods. First I consider the numerical approximations methods; the binomial model, Monte Carlo simulation and finite difference method. After this I look at continues time models. Real option theory uses the fundamentals from the financial option theory but also has its differences. This includes the risk neutral pricing that makes it possible to discount at the risk free rate. I exemplifies with different option opportunities including the option to defer and the option to abandon an ongoing investment. This is done by considering the pharmaceutical industry that invests in a patented new drug. Such an investment has uncertainty regarding time and cost to completion, the future cash flow which will not be received before the investment is completed and possibility of a catastrophic event which will drive the value of the project down to zero. This investment problem is solved by the use of Lonfstaff & Schwartz least square Monte Carlo simulation.Lastly I look at why real option theory is not used more in practice and then state some secondary empirical results. Though real option theory has been known and studied by theorists in the last 30 years, it does not seem to have had the big impact in practice yet. As Hartmann & Hassan (2006) mention, academia has a challenge to develop more adequate models to boost acceptance. The question will not be to replace the NPV approach by real option pricing. In contrast, the aim should be a more realistic view of the advantages and disadvantages of both methods as well as using the right methods for the right tasks.
{"title":"Reale Optioner: Hvorledes Projekter og Investeringer Værdisættes Under Usikkerhed (Real Options - How Projects and Investments are Valuated under Uncertainty)","authors":"L. B. Jørgensen","doi":"10.2139/SSRN.1830166","DOIUrl":"https://doi.org/10.2139/SSRN.1830166","url":null,"abstract":"It is a well known fact by academia that traditional valuation methods like DCF and NPV underestimate investments by not including managers’ flexibility and are widely discussed in the financial press. This underestimation and managers’ flexibility is due to investments’ uncertainty and not including irreversibility and investment timing. In this thesis I look at how investments under uncertainty are valued by considering different real option methods. First I consider the numerical approximations methods; the binomial model, Monte Carlo simulation and finite difference method. After this I look at continues time models. Real option theory uses the fundamentals from the financial option theory but also has its differences. This includes the risk neutral pricing that makes it possible to discount at the risk free rate. I exemplifies with different option opportunities including the option to defer and the option to abandon an ongoing investment. This is done by considering the pharmaceutical industry that invests in a patented new drug. Such an investment has uncertainty regarding time and cost to completion, the future cash flow which will not be received before the investment is completed and possibility of a catastrophic event which will drive the value of the project down to zero. This investment problem is solved by the use of Lonfstaff & Schwartz least square Monte Carlo simulation.Lastly I look at why real option theory is not used more in practice and then state some secondary empirical results. Though real option theory has been known and studied by theorists in the last 30 years, it does not seem to have had the big impact in practice yet. As Hartmann & Hassan (2006) mention, academia has a challenge to develop more adequate models to boost acceptance. The question will not be to replace the NPV approach by real option pricing. In contrast, the aim should be a more realistic view of the advantages and disadvantages of both methods as well as using the right methods for the right tasks.","PeriodicalId":447882,"journal":{"name":"ERN: Model Evaluation & Selection (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128722054","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}
. A recent strand of empirical work uses (S; s) models with time-varying stochastic bands to describe infrequent adjustments of prices and other variables. The present paper examines some properties of this model, which encompasses most micro-founded adjustment rules rationalizing infrequent changes. We illustrate that this model is also flexible enough to fit data characterized by infrequent adjustment and variable adjustment size. We show that, to the extent that there is variability in the size of adjustments (e.g. if both small and large price changes are observed), i) a large band parameter is needed to fit the data and ii) the average band of inaction underlying the model may differ strikingly from the typical observed size of adjustment. The paper thus provides a rationalization of a recurrent empirical result: very large estimated values for the parameters measuring the band of inaction.
{"title":"Time-Varying (S, s) Band Models: Empirical Properties and Interpretation","authors":"E. Gautier, Hervé le Bihan","doi":"10.2139/ssrn.1676846","DOIUrl":"https://doi.org/10.2139/ssrn.1676846","url":null,"abstract":". A recent strand of empirical work uses (S; s) models with time-varying stochastic bands to describe infrequent adjustments of prices and other variables. The present paper examines some properties of this model, which encompasses most micro-founded adjustment rules rationalizing infrequent changes. We illustrate that this model is also flexible enough to fit data characterized by infrequent adjustment and variable adjustment size. We show that, to the extent that there is variability in the size of adjustments (e.g. if both small and large price changes are observed), i) a large band parameter is needed to fit the data and ii) the average band of inaction underlying the model may differ strikingly from the typical observed size of adjustment. The paper thus provides a rationalization of a recurrent empirical result: very large estimated values for the parameters measuring the band of inaction.","PeriodicalId":447882,"journal":{"name":"ERN: Model Evaluation & Selection (Topic)","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123419266","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}
Linear and/or quadratic discriminant analysis (based on finite Gaussian mixture) is one of the most useful classification methods, for which the problem of variable selection is poorly understood. To fill this important theoretical gap, a novel BIC-type selection criterion in conjunction with a backward elimination procedure is proposed. We show theoretically that the new method is able to identify the true Gaussian structure consistently, even with a heteroscedastic covariance structure. Numerical studies are presented to demonstrate the new method's usefulness.
{"title":"On BIC's Selection Consistency for Discriminant Analysis","authors":"Qiong Zhang, Hansheng Wang","doi":"10.2139/ssrn.1305764","DOIUrl":"https://doi.org/10.2139/ssrn.1305764","url":null,"abstract":"Linear and/or quadratic discriminant analysis (based on finite Gaussian mixture) is one of the most useful classification methods, for which the problem of variable selection is poorly understood. To fill this important theoretical gap, a novel BIC-type selection criterion in conjunction with a backward elimination procedure is proposed. We show theoretically that the new method is able to identify the true Gaussian structure consistently, even with a heteroscedastic covariance structure. Numerical studies are presented to demonstrate the new method's usefulness.","PeriodicalId":447882,"journal":{"name":"ERN: Model Evaluation & Selection (Topic)","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130725365","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 last three decades have witnessed a whole array of option pricing models. We compare the predictive performances of a selection of models by carrying out a horse race on S&P 500 index options along the lines of Jackwerth and Rubinstein (2001). The models we consider include: Black-Scholes, trader rules, Heston's stochastic volatility model, Merton's jump diffusion models with and without stochastic volatility, and more recent Levy type models. Trader rules still dominate mathematically more sophisticated models, and the performance of the trader rules is further improved by incorporating the stable index skew pattern documented in Li and Pearson (2005). Furthermore, after incorporating the stable index skew pattern, the Black-Scholes model beats all mathematically more sophisticated models in almost all cases. Mathematically more sophisticated models vary in their overall performance and their relative accuracy in forecasting future volatility levels and future volatility skew shapes.
{"title":"A 'Horse Race' Among Competing Option Pricing Models Using S&P 500 Index Options","authors":"Minqiang Li, Neil D. Pearson","doi":"10.2139/ssrn.952770","DOIUrl":"https://doi.org/10.2139/ssrn.952770","url":null,"abstract":"The last three decades have witnessed a whole array of option pricing models. We compare the predictive performances of a selection of models by carrying out a horse race on S&P 500 index options along the lines of Jackwerth and Rubinstein (2001). The models we consider include: Black-Scholes, trader rules, Heston's stochastic volatility model, Merton's jump diffusion models with and without stochastic volatility, and more recent Levy type models. Trader rules still dominate mathematically more sophisticated models, and the performance of the trader rules is further improved by incorporating the stable index skew pattern documented in Li and Pearson (2005). Furthermore, after incorporating the stable index skew pattern, the Black-Scholes model beats all mathematically more sophisticated models in almost all cases. Mathematically more sophisticated models vary in their overall performance and their relative accuracy in forecasting future volatility levels and future volatility skew shapes.","PeriodicalId":447882,"journal":{"name":"ERN: Model Evaluation & Selection (Topic)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128837616","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 purpose of this paper is threefold: first, we warn analysts against the use of structural coefficient estimates alone for deducing quantitative inferences concerning many policy experiments. Second, we offer a potential solution to the problem by proposing a mutatis mutandis approach to deducing the ‘full effect’ of a policy change on the endogenous variables of the model. Finally, we show that this approach yields consistent estimates of the reduced form parameters, the true solution to the difficulty. An illustration is provided.
{"title":"On the Interpretation of Policy Effects from Estimates of Simultaneous Systems of Equations","authors":"George S. Ford, J. Jackson","doi":"10.1080/000368498325165","DOIUrl":"https://doi.org/10.1080/000368498325165","url":null,"abstract":"The purpose of this paper is threefold: first, we warn analysts against the use of structural coefficient estimates alone for deducing quantitative inferences concerning many policy experiments. Second, we offer a potential solution to the problem by proposing a mutatis mutandis approach to deducing the ‘full effect’ of a policy change on the endogenous variables of the model. Finally, we show that this approach yields consistent estimates of the reduced form parameters, the true solution to the difficulty. An illustration is provided.","PeriodicalId":447882,"journal":{"name":"ERN: Model Evaluation & Selection (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133673169","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}
A variety of qualitative dependent variable models are surveyed with attention focused on the computational aspects of their analysis. The models covered include single equation dichotomous models; single equation polychotomous models with unordered, ordered, and sequential variables; and simultaneous equation models. Care is taken to illucidate the nature of the suggested "full information" and "limited information" approaches to the simultaneous equation models and the formulation of recursive and causal chain models.
{"title":"Analysis of Qualitative Variables","authors":"G. Maddala, F. Nelson","doi":"10.3386/W0070","DOIUrl":"https://doi.org/10.3386/W0070","url":null,"abstract":"A variety of qualitative dependent variable models are surveyed with attention focused on the computational aspects of their analysis. The models covered include single equation dichotomous models; single equation polychotomous models with unordered, ordered, and sequential variables; and simultaneous equation models. Care is taken to illucidate the nature of the suggested \"full information\" and \"limited information\" approaches to the simultaneous equation models and the formulation of recursive and causal chain models.","PeriodicalId":447882,"journal":{"name":"ERN: Model Evaluation & Selection (Topic)","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1974-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116388335","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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