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Quadratic-Exponential Growth BSDEs with Jumps and Their Malliavin's Differentiability 具有跳跃的二次-指数增长BSDEs及其Malliavin可微性
Financial Engineering eJournal Pub Date : 2015-12-18 DOI: 10.2139/ssrn.2705670
M. Fujii, Akihiko Takahashi
{"title":"Quadratic-Exponential Growth BSDEs with Jumps and Their Malliavin's Differentiability","authors":"M. Fujii, Akihiko Takahashi","doi":"10.2139/ssrn.2705670","DOIUrl":"https://doi.org/10.2139/ssrn.2705670","url":null,"abstract":"We investigate a class of quadratic-exponential growth BSDEs with jumps. The quadratic structure introduced by Barrieu & El Karoui (2013) yields the universal bounds on the possible solutions. With local Lipschitz continuity and the so-called A_gamma-condition for the comparison principle to hold, we prove the existence of a unique solution under the general quadratic-exponential structure. We have also shown that the strong convergence occurs under more general (not necessarily monotone) sequence of drivers, which is then applied to give the sufficient conditions for the Malliavin's differentiability.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122263969","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: 28
Factor Attribution and the Impact of Investment Constraints 要素归因与投资约束的影响
Financial Engineering eJournal Pub Date : 2015-11-30 DOI: 10.2139/ssrn.2630430
Sanne de Boer, V. Jeet
{"title":"Factor Attribution and the Impact of Investment Constraints","authors":"Sanne de Boer, V. Jeet","doi":"10.2139/ssrn.2630430","DOIUrl":"https://doi.org/10.2139/ssrn.2630430","url":null,"abstract":"We customize factor attribution for quantitative equity portfolios to better align the measurement of factor returns with how factor tilts were taken on. Specifically, we provide a theoretical argument for including the absolute value of factor exposures in the attribution to account for the impact of a long-only constraint, as well as intuition for including lagged factor exposures in the presence of turnover limits. This may reduce any long-term unexplained performance resulting from priced distortions of unconstrained factor tilts. In addition, we find that targeting the most accurate estimates of factor returns irrespective of investment constraints can amplify the impact of stock-specific risk on performance attribution. Instead, restricted least squares estimates of the factor returns may retain good accuracy while letting factor attribution explain short-term portfolio performance in full, based on minimally adjusted factor-mimicking portfolios that span the portfolio under consideration. We report back-tests of quantitative equity strategies that confirm our intuition, and suggest diagnostics for portfolio managers who consider adopting the proposed attribution framework.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121925065","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
Likelihood Ratio Method and Algorithmic Differentiation: Fast Second Order Greeks 似然比方法和算法微分:快速二阶希腊文
Financial Engineering eJournal Pub Date : 2015-05-01 DOI: 10.2139/ssrn.2508905
Luca Capriotti
{"title":"Likelihood Ratio Method and Algorithmic Differentiation: Fast Second Order Greeks","authors":"Luca Capriotti","doi":"10.2139/ssrn.2508905","DOIUrl":"https://doi.org/10.2139/ssrn.2508905","url":null,"abstract":"We show how Adjoint Algorithmic Differentiation can be combined with the so-called Pathwise Derivative and Likelihood Ratio Method to construct efficient Monte Carlo estimators of second order price sensitivities of derivative portfolios. We demonstrate with a numerical example how the proposed technique can be straightforwardly implemented to greatly reduce the computation time of second order risk.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133080713","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: 12
Are Locational Marginal Prices a Good Heuristic to Divide Energy Market into Bidding Zones? 区位边际价格是划分能源市场竞价区域的好方法吗?
Financial Engineering eJournal Pub Date : 2015-04-05 DOI: 10.2139/ssrn.2602744
Marcin Jakubek, Karol Wawrzyniak, Michal Klos, M. Blachnik
{"title":"Are Locational Marginal Prices a Good Heuristic to Divide Energy Market into Bidding Zones?","authors":"Marcin Jakubek, Karol Wawrzyniak, Michal Klos, M. Blachnik","doi":"10.2139/ssrn.2602744","DOIUrl":"https://doi.org/10.2139/ssrn.2602744","url":null,"abstract":"By means of a constructive example we show that clustering of Locational Marginal Prices (LMPs) might give unsatisfactory results of zonal division of energy market. Specifically, we find that the division obtained from clustering of LMPs in some cases may not place the congested lines on the zones’ borders. This results in a need for costly readjustments after the Market Coupling mechanism has found the supply/demand equilibrium in order to prevent intra-zonal congestion.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126594901","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
Long Term Risk: A Martingale Approach 长期风险:鞅方法
Financial Engineering eJournal Pub Date : 2014-11-11 DOI: 10.2139/ssrn.2523110
Likuan Qin, V. Linetsky
{"title":"Long Term Risk: A Martingale Approach","authors":"Likuan Qin, V. Linetsky","doi":"10.2139/ssrn.2523110","DOIUrl":"https://doi.org/10.2139/ssrn.2523110","url":null,"abstract":"This paper extends the long‐term factorization of the stochastic discount factor introduced and studied by Alvarez and Jermann (2005) in discrete‐time ergodic environments and by Hansen and Scheinkman (2009) and Hansen (2012) in Markovian environments to general semimartingale environments. The transitory component discounts at the stochastic rate of return on the long bond and is factorized into discounting at the long‐term yield and a positive semimartingale that extends the principal eigenfunction of Hansen and Scheinkman (2009) to the semimartingale setting. The permanent component is a martingale that accomplishes a change of probabilities to the long forward measure, the limit of T‐forward measures. The change of probabilities from the data‐generating to the long forward measure absorbs the long‐term risk‐return trade‐off and interprets the latter as the long‐term risk‐neutral measure.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114065656","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: 57
Does Gold Glitter in the Long-Run? Gold as a Hedge and Safe Haven Across Time and Investment Horizon 黄金会长期发光吗?黄金作为对冲和避险的时间和投资范围
Financial Engineering eJournal Pub Date : 2014-08-20 DOI: 10.2139/ssrn.2483728
Don Bredin, T. Conlon, Valerio Potì
{"title":"Does Gold Glitter in the Long-Run? Gold as a Hedge and Safe Haven Across Time and Investment Horizon","authors":"Don Bredin, T. Conlon, Valerio Potì","doi":"10.2139/ssrn.2483728","DOIUrl":"https://doi.org/10.2139/ssrn.2483728","url":null,"abstract":"During times of market turmoil, investors often seek to mitigate the risk associated with traditional investment assets such as equities and debt. The hedging, safe-haven and downside risk reduction properties of gold are examined in this paper for investors with short- and long-run horizons. Utilizing wavelet analysis, we find that gold acts as a short-run hedge for a variety of international equity and debt markets. The safe haven properties of gold during financial crises are further established, with gold shown to act as a safe haven for equity and debt investors across all horizons. Finally, gold is shown to reduce portfolio downside risk in the short-term but may actually contribute to increased long horizon downside risk during recessionary periods.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132171200","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: 220
Barrier Option Under Lévy Model: A PIDE and Mellin Transform Approach lsamvy模型下的障碍期权:PIDE和Mellin变换方法
Financial Engineering eJournal Pub Date : 2014-01-24 DOI: 10.2139/ssrn.2232131
S. Chandra, Diganta Mukherjee, I. Sengupta
{"title":"Barrier Option Under Lévy Model: A PIDE and Mellin Transform Approach","authors":"S. Chandra, Diganta Mukherjee, I. Sengupta","doi":"10.2139/ssrn.2232131","DOIUrl":"https://doi.org/10.2139/ssrn.2232131","url":null,"abstract":"We propose a stochastic model to develop a partial integro-differential equation (PIDE) for pricing and pricing expression for fixed type single Barrier options based on the Ito-Levy calculus with the help of Mellin transform. The stock price is driven by a class of infinite activity Levy processes leading to the market inherently incomplete, and dynamic hedging is no longer risk free. We first develop a PIDE for fixed type Barrier options, and apply the Mellin transform to derive a pricing expression. Our main contribution is to develop a PIDE with its closed form pricing expression for the contract. The procedure is easy to implement for all class of Levy processes numerically. Finally, the algorithm for computing numerically is presented with results for a set of Levy processes.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126735864","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
Exact Simulation of Non-Stationary Reflected Brownian Motion 非平稳反射布朗运动的精确模拟
Financial Engineering eJournal Pub Date : 2013-12-22 DOI: 10.2139/ssrn.2373347
M. Mousavi, P. Glynn
{"title":"Exact Simulation of Non-Stationary Reflected Brownian Motion","authors":"M. Mousavi, P. Glynn","doi":"10.2139/ssrn.2373347","DOIUrl":"https://doi.org/10.2139/ssrn.2373347","url":null,"abstract":"This paper develops the first method for the exact simulation of reflected Brownian motion (RBM) with non-stationary drift and infinitesimal variance. The running time of generating exact samples of non-stationary RBM at any time $t$ is uniformly bounded by $mathcal{O}(1/bargamma^2)$ where $bargamma$ is the average drift of the process. The method can be used as a guide for planning simulations of complex queueing systems with non-stationary arrival rates and/or service time.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130758904","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
Does Risk Diversification Always Work? The Answer Through Simple Modelling 风险分散是否总是有效?通过简单的建模得到答案
Financial Engineering eJournal Pub Date : 2013-05-10 DOI: 10.2139/ssrn.2281823
Marc Busse, M. Dacorogna, M. Kratz
{"title":"Does Risk Diversification Always Work? The Answer Through Simple Modelling","authors":"Marc Busse, M. Dacorogna, M. Kratz","doi":"10.2139/ssrn.2281823","DOIUrl":"https://doi.org/10.2139/ssrn.2281823","url":null,"abstract":"With a simple example of throwing a die, we show how to price an insurance policy. We further study how this price decreases when many similar policies are sold. The diversification benefits increase with the number of policies and similarly the risk loading of the premium required for the risk decreases tending to zero. This is true as long as the risks are completely independent. However, when introducing in addition a biased die played by a crooked croupier, a non-diversifiable risk does appear. Indeed, we can show analytically that, with the biased die, there exists an additional term in the variance, which does not decrease with the number of policies in the portfolio and leads to a limit to diversification. We propose and study analytically three cases of introducing the non-diversifiable risk. For each of them, the behavior of the risk loading based on the underlying risk process is examined and a numerical illustration is provided. Then the results are discussed in view of the risk loading. Such a modelling could be used to study particular investment choices under uncertainty.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133226360","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: 9
The Small-Maturity Heston Forward Smile 小成熟的赫斯顿微笑
Financial Engineering eJournal Pub Date : 2013-03-18 DOI: 10.2139/ssrn.2235196
A. Jacquier, P. Roome
{"title":"The Small-Maturity Heston Forward Smile","authors":"A. Jacquier, P. Roome","doi":"10.2139/ssrn.2235196","DOIUrl":"https://doi.org/10.2139/ssrn.2235196","url":null,"abstract":"In this paper we investigate the asymptotics of forward-start options and the forward implied volatility smile in the Heston model as the maturity approaches zero. We prove that the forward smile for out-of-the-money options explodes and compute a closed-form high-order expansion detailing the rate of the explosion. Furthermore the result shows that the square-root behaviour of the variance process induces a singularity such that for certain parameter configurations one cannot obtain high-order out-of-the-money forward smile asymptotics. In the at-the-money case a separate model-independent analysis shows that the small-maturity limit is well defined for any Ito diffusion. The proofs rely on the theory of sharp large deviations (and refinements) and incidentally we provide an example of degenerate large deviations behaviour.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125927355","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: 23
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