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Pricing Options with the Stochastic Volatility Regime Simulation for GARCH, HAR GARCH-VIX and VIX Models GARCH, HAR, GARCH-VIX和VIX模型的随机波动机制模拟定价期权
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2016-07-05 DOI: 10.2139/ssrn.2805357
Chrilly Donninger
{"title":"Pricing Options with the Stochastic Volatility Regime Simulation for GARCH, HAR GARCH-VIX and VIX Models","authors":"Chrilly Donninger","doi":"10.2139/ssrn.2805357","DOIUrl":"https://doi.org/10.2139/ssrn.2805357","url":null,"abstract":"This working paper uses as a starting point the filtered historical simulation (FHS) approach developed by Barone-Adesi et al. One builds a GJR-GARCH model and generates Monte-Carlo return/price paths with normalized returns. This introduces a severe drift-bias. The Stochastic Volatility Regime Simulation (SVRS) avoids the bias by sampling from the same volatility regime. As an alternative to GJR-GARCH an asymmetric HAR and a GARCH-VIX model is used. Path sampling is done in the same way. As a model free alternative a VIX based approach is additionally investigated. This alternative clearly beats the models during the pre and post-Brexit market turmoil. Barone-Adesi et al. transform the real-world into the risk-neutral measure. The current model stays in the real-measure. One simulates a realistic trading behavior by hedging the options along the Monte-Carlo paths. One can calibrate the model by adding external noise.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116515589","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}
引用次数: 0
Option Pricing in Jump Diffusion Models with Quadratic Spline Collocation 二次样条配置跳跃扩散模型中的期权定价
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2016-04-10 DOI: 10.2139/ssrn.3729049
C. Christara, N. Leung
{"title":"Option Pricing in Jump Diffusion Models with Quadratic Spline Collocation","authors":"C. Christara, N. Leung","doi":"10.2139/ssrn.3729049","DOIUrl":"https://doi.org/10.2139/ssrn.3729049","url":null,"abstract":"In this paper, we develop a robust numerical method in pricing options, when the underlying asset follows a jump diffusion model. We demonstrate that, with the quadratic spline collocation method, the integral approximation in the pricing PIDE is intuitively simple, and comes down to the evaluation of the probabilistic moments of the jump density. When combined with a Picard iteration scheme, the pricing problem can be solved efficiently. We present the method and the numerical results from pricing European and American options with Merton's and Kou's models.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134309346","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}
引用次数: 8
An Overview of Derivative Pricing in Gaussian Affine Asset Pricing Models: An Application to the KNW Model 高斯仿射资产定价模型中的衍生品定价综述:在KNW模型中的应用
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2016-04-05 DOI: 10.2139/ssrn.2759413
Kees E. Bouwman, R. Lord
{"title":"An Overview of Derivative Pricing in Gaussian Affine Asset Pricing Models: An Application to the KNW Model","authors":"Kees E. Bouwman, R. Lord","doi":"10.2139/ssrn.2759413","DOIUrl":"https://doi.org/10.2139/ssrn.2759413","url":null,"abstract":"We present a comprehensive overview of derivative pricing in Gaussian affine asset pricing models. Gaussian affine asset pricing models are widely used in practice for pricing and scenario analysis due to their tractable pricing implications and easy estimation. This tractability is essential to efficiently evaluate portfolios of derivatives within many scenarios and time periods. We present efficient closed-form pricing formulas for the most common derivative instruments used by pension funds and insurance companies, such as interest rate swaps, swaptions, inflation-linked swaps, equity options, based on results from the literature. The pricing formulas are presented in a comprehensive computable form by utilising results based on the matrix exponential. Next, we show how some models commonly used in practice fit in the Gaussian affine framework, so that the pricing formulas can be applied to these cases. In particular, we discuss the KNW model by Koijen, Nijman and Werker (2010), which is widely used in the pension industry. Finally we discuss how our results can be applied to a time-inhomogeneous extension of the model that allows perfect calibration to the observed yield curve.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123251230","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}
引用次数: 1
Credit Default Swaps and Financial Risks in the 21st Century 21世纪的信用违约互换与金融风险
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2016-03-20 DOI: 10.2139/SSRN.2752073
Karin Martín-Bujack, M. T. Corzo
{"title":"Credit Default Swaps and Financial Risks in the 21st Century","authors":"Karin Martín-Bujack, M. T. Corzo","doi":"10.2139/SSRN.2752073","DOIUrl":"https://doi.org/10.2139/SSRN.2752073","url":null,"abstract":"In this paper we pay tribute to one of the most successful financial innovations in recent times: the Credit Default Swap (CDS). Through a literature review on financial risks from 2000-2015 we develop a conceptual map to assess the importance and evolution of the CDS, along with the consequences of its use. CDSs emerge as a powerful and meaningful financial instrument. Given the CDS’s versatility, the 21 st -century literature about the CDS and its usefulness is very extensive, rendering the CDS a valuable guide with which to investigate the financial risks that have worried researchers, regulators and all of the participants in the financial system","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114770297","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}
引用次数: 3
Funding, Repo and Credit Inclusion in Option Pricing via Dividends 股利期权定价中的融资、回购和信用纳入
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2016-02-18 DOI: 10.2139/ssrn.2734459
D. Brigo, Cristin Buescu, M. Rutkowski
{"title":"Funding, Repo and Credit Inclusion in Option Pricing via Dividends","authors":"D. Brigo, Cristin Buescu, M. Rutkowski","doi":"10.2139/ssrn.2734459","DOIUrl":"https://doi.org/10.2139/ssrn.2734459","url":null,"abstract":"This paper specializes a number of earlier contributions to the theory of valuation of financial products in presence of credit risk, repurchase agreements and funding costs. Earlier works, including our own, pointed to the need of tools such as Backward Stochastic Differential Equations (BSDEs) or semi-linear Partial Differential Equations (PDEs), which in practice translate to ad-hoc numerical methods that are time-consuming and which render the full valuation and risk analysis difficult. We specialize here the valuation framework to benchmark derivatives and we show that, under a number of simplifying assumptions, the valuation paradigm can be recast as a Black-Scholes model with dividends. In turn, this allows for a detailed valuation analysis, stress testing and risk analysis via sensitivities. We refer to the full paper for a more complete mathematical treatment.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114506762","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}
引用次数: 0
Local Volatility Models in Commodity Markets and Online Calibration 商品市场局部波动率模型及其在线校准
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2016-02-13 DOI: 10.21314/JCF.2018.345
V. Albani, U. Ascher, J. Zubelli
{"title":"Local Volatility Models in Commodity Markets and Online Calibration","authors":"V. Albani, U. Ascher, J. Zubelli","doi":"10.21314/JCF.2018.345","DOIUrl":"https://doi.org/10.21314/JCF.2018.345","url":null,"abstract":"We introduce a local volatility model for the valuation of options on commodity futures by using European vanilla option prices. The corresponding calibration problem is addressed within an online framework, allowing the use of multiple price surfaces. Since uncertainty in the observation of the underlying future prices translates to uncertainty in data locations, we propose a model-based adjustment of such prices that improves reconstructions and smile adherence. In order to tackle the ill-posedness of the calibration problem we incorporate a priori information through a judiciously designed Tikhonov-type regularization. Extensive empirical tests with market as well as synthetic data are used to demonstrate the effectiveness of the methodology and algorithms.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129089825","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}
引用次数: 7
Option-Based Estimation of the Price of Co-Skewness and Co-Kurtosis Risk 基于期权的共偏度和共峰度风险价格估计
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2016-01-13 DOI: 10.2139/ssrn.2656412
Peter F. Christoffersen, Mathieu Fournier, Kris Jacobs, M. Karoui
{"title":"Option-Based Estimation of the Price of Co-Skewness and Co-Kurtosis Risk","authors":"Peter F. Christoffersen, Mathieu Fournier, Kris Jacobs, M. Karoui","doi":"10.2139/ssrn.2656412","DOIUrl":"https://doi.org/10.2139/ssrn.2656412","url":null,"abstract":"We show that the prices of risk for factors that are nonlinear in the market return are readily obtained using index option prices. We apply this insight to the price of co-skewness and co-kurtosis risk. The price of co-skewness risk corresponds to the spread between the physical and the risk-neutral second moments, and the price of co-kurtosis risk corresponds to the spread between the physical and the risk-neutral third moments. The option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An out-of-sample analysis of factor models with co-skewness and co-kurtosis risk indicates that the new estimates of the price of risk improve the models performance. Models with higher-order market moments also robustly outperform standard competitors such as the CAPM and the Fama-French model.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134462520","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}
引用次数: 20
Stochastic Volatility Modeling: Chapter 2 - Local Volatility 随机波动模型:第2章-局部波动
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2016-01-05 DOI: 10.2139/ssrn.2713103
L. Bergomi
{"title":"Stochastic Volatility Modeling: Chapter 2 - Local Volatility","authors":"L. Bergomi","doi":"10.2139/ssrn.2713103","DOIUrl":"https://doi.org/10.2139/ssrn.2713103","url":null,"abstract":"This is Chapter 2 of Stochastic Volatility Modeling, published by CRC/Chapman & Hall.In this chapter the local volatility model is surveyed as a market model for the underlying together with its associated vanilla options.First, relationships of implied to local volatilities are derived, as well as approximations for skew and curvature. Exact and approximate techniques for taking dividends into account are presented.We then turn to the dynamics of the local volatility model. We introduce the Skew Tickiness Ratio (SSR) and derive approximate formulas for the SSR and volatilities of volatilities in the local volatility model.We also examine future skews.We then consider the delta and carry P&L of a hedged option position. We derive the expression of the market-model delta of the local volatility model and discuss the relationship between sticky-strike and market-model deltas. We characterize the gamma/theta break-even levels of a hedged position and show that the local volatility model is indeed a market model.We then derive the expression of the vega-hedge portfolio.Markov-functional models are considered next.Finally, we survey the Uncertain Volatility Model and its usage.A digest summarizes key points.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121291597","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}
引用次数: 1
An Analytical Model for Standard and Volumetric Cap and Floor Pricing in Electricity Markets 电力市场中标准和容量上限和下限定价的分析模型
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-12-01 DOI: 10.2139/ssrn.2694868
J. Maisano, A. Radchik, S. Trück
{"title":"An Analytical Model for Standard and Volumetric Cap and Floor Pricing in Electricity Markets","authors":"J. Maisano, A. Radchik, S. Trück","doi":"10.2139/ssrn.2694868","DOIUrl":"https://doi.org/10.2139/ssrn.2694868","url":null,"abstract":"In this paper we derive the term structure of the implied volatility of an electricity 'cap' contract. We leverage earlier work where we derived analytical representations for stochastic demand and deterministic price.We first demonstrate that we can back-out implied volatility at all points of embedded optionality within the cap using the market cap futures price and the expected price curve (in turn derived from a state demand forecast).We next demonstrate that a cap priced with such a term structure of volatility will return the quoted price, and show the price evolution of the cap based on alternate strike prices (for which futures contracts are not available).Next we turn to a floor contract struck on demand (or output) rather than price. We derive the model for this option, based on the volatility of the underlying demand curve, and price a volumetric floor on state demand. We then describe how such a model could be used as a hedge instrument for an intermittent generator such as a solar or wind farm.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130825119","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}
引用次数: 0
Multi-Curve Modeling Using Trees 多曲线建模使用树
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-11-08 DOI: 10.2139/SSRN.2601457
J. Hull, Alan G. White
{"title":"Multi-Curve Modeling Using Trees","authors":"J. Hull, Alan G. White","doi":"10.2139/SSRN.2601457","DOIUrl":"https://doi.org/10.2139/SSRN.2601457","url":null,"abstract":"Since 2008 the valuation of derivatives has evolved so that OIS discounting rather than LIBOR discounting is used. Payoffs from interest rate derivatives usually depend on LIBOR. This means that the valuation of interest rate derivatives depends on the evolution of two different term structures. The spread between OIS and LIBOR rates is often assumed to be constant or deterministic. This paper explores how this assumption can be relaxed. It shows how well-established methods used to represent one-factor interest rate models in the form of a binomial or trinomial tree can be extended so that the OIS rate and a LIBOR rate are jointly modelled in a three-dimensional tree. The procedures are illustrated with the valuation of spread options and Bermudan swap options. The tree is constructed so that LIBOR swap rates are matched.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132132625","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}
引用次数: 2
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