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Consistent Re-Calibration of the Discrete-Time Multifactor Vasiček Model 离散时间多因素vasi<s:1> ek模型的一致性重新校准
arXiv: Mathematical Finance Pub Date : 2015-12-20 DOI: 10.3390/risks4030018
Philipp Harms, David Stefanovits, J. Teichmann, Mario V. Wuthrich
{"title":"Consistent Re-Calibration of the Discrete-Time Multifactor Vasiček Model","authors":"Philipp Harms, David Stefanovits, J. Teichmann, Mario V. Wuthrich","doi":"10.3390/risks4030018","DOIUrl":"https://doi.org/10.3390/risks4030018","url":null,"abstract":"The discrete-time multifactor Vasicek model is a tractable Gaussian spot rate model. Typically, two- or three-factor versions allow one to capture the dependence structure between yields with different times to maturity in an appropriate way. In practice, re-calibration of the model to the prevailing market conditions leads to model parameters that change over time. Therefore, the model parameters should be understood as being time-dependent or even stochastic. Following the consistent re-calibration (CRC) approach, we construct models as concatenations of yield curve increments of Hull–White extended multifactor Vasicek models with different parameters. The CRC approach provides attractive tractable models that preserve the no-arbitrage premise. As a numerical example, we fit Swiss interest rates using CRC multifactor Vasicek models.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126097196","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 Generalized Intensity-Based Framework for Single-Name Credit Risk 基于强度的单名信用风险广义框架
arXiv: Mathematical Finance Pub Date : 2015-12-12 DOI: 10.1007/978-3-319-33446-2_13
Frank Gehmlich, Thorsten Schmidt
{"title":"A Generalized Intensity-Based Framework for Single-Name Credit Risk","authors":"Frank Gehmlich, Thorsten Schmidt","doi":"10.1007/978-3-319-33446-2_13","DOIUrl":"https://doi.org/10.1007/978-3-319-33446-2_13","url":null,"abstract":"","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132828421","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
Purely pathwise probability-free Ito integral 纯路径无概率伊藤积分
arXiv: Mathematical Finance Pub Date : 2015-12-05 DOI: 10.15330/MS.46.1.96-110
V. Vovk
{"title":"Purely pathwise probability-free Ito integral","authors":"V. Vovk","doi":"10.15330/MS.46.1.96-110","DOIUrl":"https://doi.org/10.15330/MS.46.1.96-110","url":null,"abstract":"This paper gives several simple constructions of the pathwise Ito integral $int_0^tphi domega$ for an integrand $phi$ and a price path $omega$ as integrator, with $phi$ and $omega$ satisfying various topological and analytical conditions. The definitions are purely pathwise in that neither $phi$ nor $omega$ are assumed to be paths of stochastic processes, and the Ito integral exists almost surely in a non-probabilistic financial sense. For example, one of the results shows the existence of $int_0^tphi domega$ for a cadlag integrand $phi$ and a cadlag integrator $omega$ with jumps bounded in a predictable manner.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116328370","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: 15
Incompleteness of the bond market with L'evy noise under the physical measure 不完备的债券市场具有L evy噪声下的物理测度
arXiv: Mathematical Finance Pub Date : 2015-12-01 DOI: 10.4064/BC104-0-3
M. Barski
{"title":"Incompleteness of the bond market with L'evy noise under the physical measure","authors":"M. Barski","doi":"10.4064/BC104-0-3","DOIUrl":"https://doi.org/10.4064/BC104-0-3","url":null,"abstract":"The problem of completeness of the forward rate based bond market model driven by a L'evy process under the physical measure is examined. The incompleteness of market in the case when the L'evy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump measure under a martingale measure is presented and the corresponding integral representation of local martingales is proven.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"156 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":"115002104","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
On the Existence of Martingale Measures in Jump Diffusion Market Models 跳跃扩散市场模型中鞅测度的存在性
arXiv: Mathematical Finance Pub Date : 2015-11-26 DOI: 10.1142/9789814602075_0003
Jacopo Mancin, W. Runggaldier
{"title":"On the Existence of Martingale Measures in Jump Diffusion Market Models","authors":"Jacopo Mancin, W. Runggaldier","doi":"10.1142/9789814602075_0003","DOIUrl":"https://doi.org/10.1142/9789814602075_0003","url":null,"abstract":"In the context of jump-diffusion market models we construct examples that satisfy the weaker no-arbitrage condition of NA1 (NUPBR), but not NFLVR. We show that in these examples the only candidate for the density process of an equivalent local martingale measure is a supermartingale that is not a martingale, not even a local martingale. This candidate is given by the supermartingale deflator resulting from the inverse of the discounted growth optimal portfolio. In particular, we con- sider an example with constraints on the portfolio that go beyond the standard ones for admissibility.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125449218","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
Foundations for Wash Sales 洗涤销售的基础
arXiv: Mathematical Finance Pub Date : 2015-11-11 DOI: 10.4236/JMF.2016.64044
P. Bradford
{"title":"Foundations for Wash Sales","authors":"P. Bradford","doi":"10.4236/JMF.2016.64044","DOIUrl":"https://doi.org/10.4236/JMF.2016.64044","url":null,"abstract":"Consider an ephemeral sale-and-repurchase of a security resulting in the same position before the sale and after the repurchase. A sale-and-repurchase is a wash sale if these transactions result in a loss within $pm 30$ calendar days. Since a portfolio is essentially the same after a wash sale, any tax advantage from such a loss is not allowed. That is, after a wash sale a portfolio is unchanged so any loss captured by the wash sale is deemed to be solely for tax advantage and not investment purposes. \u0000This paper starts by exploring variations of the birthday problem to model wash sales. The birthday problem is: Determine the number of independent and identically distributed random variables required so there is a probability of at least 1/2 that two or more of these random variables share the same outcome. This paper gives necessary conditions for wash sales based on variations on the birthday problem. This allows us to answer questions such as: What is the likelihood of a wash sale in an unmanaged portfolio where purchases and sales are independent, uniform, and random? This paper ends by exploring the Littlewood-Offord problem as it relates capital gains and losses with wash sales.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123568536","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 elementary approach to the option pricing problem 期权定价问题的一种基本方法
arXiv: Mathematical Finance Pub Date : 2015-10-20 DOI: 10.9734/arjom/2016/26251
N. Halidias
{"title":"An elementary approach to the option pricing problem","authors":"N. Halidias","doi":"10.9734/arjom/2016/26251","DOIUrl":"https://doi.org/10.9734/arjom/2016/26251","url":null,"abstract":"Our goal here is to discuss the pricing problem of European and American options in discrete time using elementary calculus so as to be an easy reference for first year undergraduate students. Using the binomial model we compute the fair price of European and American options. We explain the notion of Arbitrage and the notion of the fair price of an option using common sense. We give a criterion that the holder can use to decide when it is appropriate to exercise the option. We prove the put-call parity formulas for both European and American options and we discuss the relation between American and European options. We give also the bounds for European and American options. We also discuss the portfolio's optimization problem and the fair value in the case where the holder can not produce the opposite portfolio.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125510394","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
The pricing of contingent claims and optimal positions in asymptotically complete markets 渐近完全市场中或有债权的定价和最优头寸
arXiv: Mathematical Finance Pub Date : 2015-09-21 DOI: 10.1214/16-AAP1246
Michail Anthropelos, Scott Robertson, K. Spiliopoulos
{"title":"The pricing of contingent claims and optimal positions in asymptotically complete markets","authors":"Michail Anthropelos, Scott Robertson, K. Spiliopoulos","doi":"10.1214/16-AAP1246","DOIUrl":"https://doi.org/10.1214/16-AAP1246","url":null,"abstract":"We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken positions become large in absolute value at a specific rate. We draw motivation from and make connections to Large Deviations theory, and in particular, the celebrated G\"{a}rtner-Ellis theorem. We analyze a series of well studied examples where this limiting behavior occurs, such as fixed markets with vanishing risk aversion, the basis risk model with high correlation, models of large markets with vanishing trading restrictions and the Black-Scholes-Merton model with either vanishing default probabilities or vanishing transaction costs. Lastly, we show that the large claim regime could naturally arise in partial equilibrium models.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131680512","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
Utility Maximisation for Exponential Levy Models with option and information processes 具有选项和信息过程的指数Levy模型的效用最大化
arXiv: Mathematical Finance Pub Date : 2015-09-09 DOI: 10.4213/TVP5042
L. Vostrikova
{"title":"Utility Maximisation for Exponential Levy Models with option and information processes","authors":"L. Vostrikova","doi":"10.4213/TVP5042","DOIUrl":"https://doi.org/10.4213/TVP5042","url":null,"abstract":"We consider expected utility maximisation problem for exponential Levy models and HARA utilities in presence of illiquid asset in portfolio. This illiquid asset is modelled by an option of European type on another risky asset which is correlated with the first one. Under some hypothesis on Levy processes, we give the expressions of information processes figured in maximum utility formula. As applications, we consider Black-Scholes models with correlated Brownian Motions, and also Black-Scholes models with jump part represented by Poisson process.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121107091","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
REVISITING A THEOREM OF L.A. SHEPP ON OPTIMAL STOPPING 重新考察L.A. - shepp关于最优停车的定理
arXiv: Mathematical Finance Pub Date : 2015-09-01 DOI: 10.31390/COSA.9.3.08
Philip A. Ernst, L. Shepp
{"title":"REVISITING A THEOREM OF L.A. SHEPP ON OPTIMAL STOPPING","authors":"Philip A. Ernst, L. Shepp","doi":"10.31390/COSA.9.3.08","DOIUrl":"https://doi.org/10.31390/COSA.9.3.08","url":null,"abstract":"Using a bondholder who seeks to determine when to sell his bond as our motivating example, we revisit one of Larry Shepp's classical theorems on optimal stopping. We offer a novel proof of Theorem 1 from from cite{Shepp}. Our approach is that of guessing the optimal control function and proving its optimality with martingales. Without martingale theory one could hardly prove our guess to be correct.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126669072","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: 11
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