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Pricing via Quantization in Stochastic Volatility Models 随机波动率模型的量化定价
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-09-29 DOI: 10.2139/ssrn.2669734
Giorgia Callegaro, Lucio Fiorin, M. Grasselli
{"title":"Pricing via Quantization in Stochastic Volatility Models","authors":"Giorgia Callegaro, Lucio Fiorin, M. Grasselli","doi":"10.2139/ssrn.2669734","DOIUrl":"https://doi.org/10.2139/ssrn.2669734","url":null,"abstract":"In this paper we apply a new methodology based on quantization to price options in stochastic volatility models. This method can be applied to any model for which an Euler scheme is available for the underlying process and it allows for pricing vanillas, as well as exotics, thanks to the knowledge of the transition probabilities for the discretized stock process. We apply the methodology to some celebrated stochastic volatility models, including the Stein and Stein (1991) model and the SABR model introduced in Hagan and Woodward (2002). A numerical exercise shows that the pricing of vanillas turns out to be accurate; in addition, when applied to some exotics like equity-volatility options, the quantization-based method overperforms by far the Monte Carlo simulation.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125190560","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: 4
Mixing SABR Models for Negative Rates 负利率的混合SABR模型
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-08-09 DOI: 10.2139/ssrn.2653682
A. Antonov, M. Konikov, Michael Spector
{"title":"Mixing SABR Models for Negative Rates","authors":"A. Antonov, M. Konikov, Michael Spector","doi":"10.2139/ssrn.2653682","DOIUrl":"https://doi.org/10.2139/ssrn.2653682","url":null,"abstract":"In the current low-interest-rate environment, extending option models to negative rates has become an important issue. In our previous paper, we introduced the Free SABR model, which is a natural and an attractive extension to the classical SABR model. In spite of its advantages over the Shifted SABR, the Free SABR option pricing formula is based on an approximation. Although this approximation is very good, it cannot guarantee the absence of arbitrage.In this article, we build on an exact option pricing formula for the normal SABR with a free boundary and an arbitrary correlation. First, we derive this formula in terms of a 1D integral, which is suitable for fast calibration. Next, we apply the formula as a control variate to the Free SABR to improve the accuracy of its approximation, especially for high correlations. Finally, we come up with a Mixture SABR model, which is a weighted sum of the normal and free zero-correlation models. This model is guaranteed to be arbitrage free and has a closed-form solution for option prices. Added degrees of freedom also allow the Mixture SABR model to be calibrated to a broader set of trades, in particular, to a joint set of swaptions and CMS payment. We demonstrate this capability with a wide set of numerical examples.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133603548","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: 16
The Pricing of Short-Term Market Risk: Evidence from Weekly Options 短期市场风险的定价:来自周期权的证据
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-08-01 DOI: 10.3386/w21491
T. Andersen, Nicola Fusari, V. Todorov
{"title":"The Pricing of Short-Term Market Risk: Evidence from Weekly Options","authors":"T. Andersen, Nicola Fusari, V. Todorov","doi":"10.3386/w21491","DOIUrl":"https://doi.org/10.3386/w21491","url":null,"abstract":"We study short-term market risks implied by weekly S&P 500 index options. The introduction of weekly options has dramatically shifted the maturity profile of traded options over the last five years, with a substantial proportion now having expiry within one week. Economically, this reflects a desire among investors for actively managing their exposure to very short-term risks. Such short-dated options provide an easy and direct way to study market volatility and jump risks. Unlike longer-dated options, they are largely insensitive to the risk of intertemporal shifts in the economic environment, i.e., changes in the investment opportunity set. Adopting a novel general semi-nonparametric approach, we uncover variation in the shape of the negative market jump tail risk which is not spanned by market volatility. Incidents of such tail shape shifts coincide with serious mispricing of standard parametric models for longer-dated options. As such, our approach allows for easy identification of periods of heightened concerns about negative tail events on the market that are not always \"signaled\" by the level of market volatility and elude standard asset pricing models.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130754735","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: 17
Pricing Residential Real Estate Derivatives 住宅房地产衍生品定价
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-07-12 DOI: 10.2139/ssrn.2665380
M. Richter
{"title":"Pricing Residential Real Estate Derivatives","authors":"M. Richter","doi":"10.2139/ssrn.2665380","DOIUrl":"https://doi.org/10.2139/ssrn.2665380","url":null,"abstract":"This article, which is primarily didactic in nature, provides basic intuition on asset pricing and risk-neutral valuation with a specific focus on residential real estate. I look into the pricing of physical real estate and two variations of derivative. I derive some specific valuation formulas in a highly simplified context of a one-period economy on a discrete probability space. I generalise the formulas to a limited extent for a multi-period economy. The formulas can be applied to richer structures in a straightforward manner and which I hope to do in future iterations of this text.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"37 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122462497","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
Black Scholes Pricing Concept 布莱克·斯科尔斯定价概念
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-06-25 DOI: 10.2139/ssrn.2623191
I. Gikhman
{"title":"Black Scholes Pricing Concept","authors":"I. Gikhman","doi":"10.2139/ssrn.2623191","DOIUrl":"https://doi.org/10.2139/ssrn.2623191","url":null,"abstract":"In some papers it have been remarked that derivation of the Black Scholes Equation (BSE) contains mathematical ambiguities. In particular there are two problems which can be raise by accepting Black Scholes (BS) pricing concept. One is technical derivation of the BSE and other the pricing definition of the option.In this paper, we show how the ambiguities in derivation of the BSE can be eliminated. We pay attention to option as a hedging instrument and present definition of the option price based on market risk weighting. In such approach, we define random market price for each market scenario. The spot price then is interpreted as a one that reflects balance between profit-loss expectations of the market participants.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122250156","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
Trading the VIX Futures Roll and Volatility Premiums with VIX Options 用波动率指数期权交易波动率指数期货滚动和波动率溢价
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-06-23 DOI: 10.2139/ssrn.2624713
David P. Simon
{"title":"Trading the VIX Futures Roll and Volatility Premiums with VIX Options","authors":"David P. Simon","doi":"10.2139/ssrn.2624713","DOIUrl":"https://doi.org/10.2139/ssrn.2624713","url":null,"abstract":"This study examines the efficiency of VIX option trading strategies that exploit the VIX futures roll and the often substantial VIX futures volatility premiums from January 2007 through March 2014. The study first assesses the related issue of whether VIX options typically are overpriced by examining long VIX option delta-hedged returns and demonstrates that average losses on front contract calls and puts over 5-business day horizons either are not statistically significant or are economically small. In light of the evidence that VIX option buyers on average do not overpay at all or by much for the limited risk associated with VIX options, the study then turns to whether long VIX option positions can be used to exploit the well-documented tendencies of VIX futures to rise and fall when the VIX futures curve is in backwardation and in contango, respectively, as well as the tendency of VIX futures to build in large ex-ante volatility premiums. The results demonstrate that these defined-risk strategies are highly profitable and offer attractive risk-reward tradeoffs. Moreover, the systematic tendencies of VIX futures have far more power for predicting attractive VIX option returns than the ex-ante volatility premiums built into VIX options. The study also shows that long VIX option strategies importantly benefit from a strong tailwind that owes to the tendency of VIX option implied volatilities to rise with increases in the actual volatilities of underlying VIX futures contracts, as VIX futures move toward settlement and their volatilities rise to the typically higher volatility of the VIX.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122089700","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: 4
A Quantum Finance Model 量子金融模型
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-06-20 DOI: 10.2139/ssrn.2621110
Hongbing Su
{"title":"A Quantum Finance Model","authors":"Hongbing Su","doi":"10.2139/ssrn.2621110","DOIUrl":"https://doi.org/10.2139/ssrn.2621110","url":null,"abstract":"Both academic research and practical application of mathematical finance have been extremely fruitful since the seminal work of Black-Scholes-Merton in the early 1970s. In this framework, the prices of financial assets are modeled as stochastic processes in probability spaces inside which the machinery of stochastic calculus is a powerful tool. The fundamental asset pricing theorem states that the absence of arbitrage opportunities in a market is equivalent to the existence of a probability measure, equivalent to the objective probability, under which the discounted prices of the assets become local martingales. This linkage between finance on the one hand and the probability theory on the other is the key to the success of mathematical finance. In this note, we show that it is possible to extend the classical probability model to a quantum probability model. The classical stochastic calculus is replaced by its quantum counterpart on the Boson Fock space. In particular, we show that the fundamental asset pricing theorem remains valid in this non-commutative setting. As an application, prices of quantum European options are obtained.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117198339","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
Feynman Kac for Functional Jump Diffusions with an Application to Credit Value Adjustment 功能跃迁扩散的费曼-卡克（Feynman Kac）与信用值调整的应用
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-06-19 DOI: 10.2139/ssrn.2500782
Eduard Kromer, L. Overbeck, J. Röder
{"title":"Feynman Kac for Functional Jump Diffusions with an Application to Credit Value Adjustment","authors":"Eduard Kromer, L. Overbeck, J. Röder","doi":"10.2139/ssrn.2500782","DOIUrl":"https://doi.org/10.2139/ssrn.2500782","url":null,"abstract":"We provide a proof for the functional Feynman–Kac theorem for jump diffusions with path-dependent coefficients and apply our results to the problem of Credit Value Adjustment (CVA) in a bilateral counterparty risk framework. We derive the corresponding functional CVA-PIDE and extend existing results on CVA to a setting which enables the pricing of path-dependent derivatives.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131367589","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: 14
Numerical Valuation of Derivatives in High-Dimensional Settings Via Partial Differential Equation Expansions 偏微分方程展开式在高维环境下导数的数值计算
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-06-02 DOI: 10.21314/JCF.2015.302
C. Reisinger, R. Wissmann
{"title":"Numerical Valuation of Derivatives in High-Dimensional Settings Via Partial Differential Equation Expansions","authors":"C. Reisinger, R. Wissmann","doi":"10.21314/JCF.2015.302","DOIUrl":"https://doi.org/10.21314/JCF.2015.302","url":null,"abstract":"We propose a new numerical approach to solving high-dimensional partial differential equations (PDEs) that arise in the valuation of exotic derivative securities. The proposed method is extended from the work of Reisinger and Wittum and uses principal component analysis of the underlying process in combination with a Taylor expansion of the value function into solutions to low-dimensional PDEs. The approximation is related to anchored-analysis-of-variance decompositions and is expected to be accurate whenever the covariance matrix has one or few dominating eigenvalues. We give a careful analysis of the numerical accuracy and computational complexity compared with state-of-the-art Monte Carlo methods, using Bermudan swaptions and ratchet floors, which are considered difficult benchmark problems, as examples. We demonstrate that, for problems with medium to high dimensionality and moderate time horizons, the PDE method presented delivers results comparable in accuracy to the Monte Carlo methods considered here in a similar or (often significantly) faster run time.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116016336","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: 4
A Dual Algorithm for Stochastic Control Problems: Applications to Uncertain Volatility Models and CVA 随机控制问题的对偶算法:在不确定波动模型和CVA中的应用
ERN: Other Econometric Modeling: Derivatives (Topic) Pub Date : 2015-04-23 DOI: 10.2139/ssrn.2598529
P. Henry-Labordère, C. Litterer, Zhenjie Ren
{"title":"A Dual Algorithm for Stochastic Control Problems: Applications to Uncertain Volatility Models and CVA","authors":"P. Henry-Labordère, C. Litterer, Zhenjie Ren","doi":"10.2139/ssrn.2598529","DOIUrl":"https://doi.org/10.2139/ssrn.2598529","url":null,"abstract":"We derive an algorithm in the spirit of Rogers [SIAM J. Control Optim., 46 (2007), pp. 1116--1132] and Davis and Burstein [Stochastics Stochastics Rep., 40 (1992), pp. 203--256] that leads to upper bounds for stochastic control problems. Our bounds complement lower biased estimates recently obtained in Guyon and Henry-Labordere [J. Comput. Finance, 14 (2011), pp. 37--71]. We evaluate our estimates in numerical examples motivated by mathematical finance.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127207990","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: 5
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