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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
Pub Date : 2015-12-18 DOI: 10.2139/ssrn.2705670
M. Fujii, Akihiko Takahashi
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.
研究了一类带跳跃的二次指数增长BSDEs。Barrieu & El Karoui(2013)引入的二次型结构给出了可能解的普遍边界。利用局部Lipschitz连续性和比较原理的a_gamma条件,证明了一般二次指数结构下唯一解的存在性。我们还证明了强收敛在更一般的(不一定是单调的)驱动序列下发生,然后应用它给出了Malliavin可微性的充分条件。
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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
Pub Date : 2015-11-30 DOI: 10.2139/ssrn.2630430
Sanne de Boer, V. Jeet
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.
我们为定量股票投资组合定制因素归因,以便更好地将因素回报的测量与因素倾斜的方式结合起来。具体而言,我们提供了一个理论论据,包括归因中因素暴露的绝对值,以解释多头约束的影响,以及在存在周转限制的情况下包括滞后因素暴露的直觉。这可能会减少由于不受约束因素倾斜的价格扭曲而导致的任何长期无法解释的表现。此外,我们发现,在不考虑投资约束的情况下,以最准确的因子回报估计为目标可以放大股票特定风险对绩效归因的影响。相反,对因素回报的限制最小二乘估计可以保持良好的准确性,同时让因素归因充分解释短期投资组合的表现,基于最小调整的因素模仿投资组合,跨越考虑的投资组合。我们报告了量化股票策略的回溯测试,证实了我们的直觉,并为考虑采用所提出的归因框架的投资组合经理提出了诊断建议。
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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
Pub Date : 2015-05-01 DOI: 10.2139/ssrn.2508905
Luca Capriotti
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.
我们展示了伴随算法微分如何与所谓的路径导数和似然比方法相结合,以构造衍生投资组合二阶价格敏感性的有效蒙特卡罗估计。我们用一个数值例子证明了该方法是如何直接实现的,从而大大减少了二阶风险的计算时间。
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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?
Pub Date : 2015-04-05 DOI: 10.2139/ssrn.2602744
Marcin Jakubek, Karol Wawrzyniak, Michal Klos, M. Blachnik
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.
通过一个建设性的例子,我们证明了区位边际价格的聚类可能会导致能源市场分区的不满意结果。具体而言,我们发现在某些情况下,由lmp聚类得到的划分可能不会将拥堵线置于区域边界上。这导致在市场耦合机制找到供需平衡后,为了防止区域内拥堵,需要进行代价高昂的调整。
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引用次数: 2
Long Term Risk: A Martingale Approach 长期风险:鞅方法
Pub Date : 2014-11-11 DOI: 10.2139/ssrn.2523110
Likuan Qin, V. Linetsky
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.
本文将Alvarez和Jermann(2005)在离散时间遍历环境中、Hansen和Scheinkman(2009)和Hansen(2012)在马尔可夫环境中引入并研究的随机折现因子的长期分解扩展到一般半鞅环境。临时成分以长期债券的随机收益率折现,并被分解为长期收益率折现和正半鞅,将Hansen和Scheinkman(2009)的主特征函数扩展到半鞅设置。永久分量是一个鞅,它实现了对长期远期测度的概率变化,即T -远期测度的极限。从数据生成到长期远期指标的概率变化吸收了长期风险回报权衡,并将后者解释为长期风险中性指标。
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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
Pub Date : 2014-08-20 DOI: 10.2139/ssrn.2483728
Don Bredin, T. Conlon, Valerio Potì
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.
在市场动荡时期,投资者往往寻求降低与股票和债务等传统投资资产相关的风险。本文从短期和长期角度考察了黄金的套期保值、避险和降低下行风险的特性。利用小波分析,我们发现黄金作为各种国际股票和债券市场的短期对冲。在金融危机期间,黄金的避险属性得到了进一步确立,黄金被证明是各个领域股票和债券投资者的避风港。最后,黄金在短期内降低了投资组合的下行风险,但在经济衰退期间,实际上可能会增加长期的下行风险。
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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
Pub Date : 2014-01-24 DOI: 10.2139/ssrn.2232131
S. Chandra, Diganta Mukherjee, I. Sengupta
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.
本文提出了一种基于Ito-Levy微积分的随机模型,利用Mellin变换建立固定型单障碍期权定价的偏积分微分方程(PIDE)和定价表达式。股票价格是由一类无限活动的Levy过程驱动的,导致市场固有的不完全性,动态套期保值不再是无风险的。我们首先开发了固定类型障碍期权的PIDE,并应用Mellin变换推导出定价表达式。我们的主要贡献是为合同开发一个带有封闭形式定价表达式的PIDE。该程序易于实现所有类型的列维过程的数值。最后,给出了一组Levy过程的数值计算算法。
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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
Pub Date : 2013-12-22 DOI: 10.2139/ssrn.2373347
M. Mousavi, P. Glynn
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.
本文提出了具有非平稳漂移和无限小方差的反射布朗运动(RBM)精确模拟的第一种方法。在任意时刻$t$生成非平稳RBM精确样本的运行时间均匀地以$mathcal{O}(1/bargamma^2)$为界,其中$bargamma$为过程的平均漂移。该方法可用于具有非平稳到达率和/或服务时间的复杂排队系统的规划仿真。
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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
Pub Date : 2013-05-10 DOI: 10.2139/ssrn.2281823
Marc Busse, M. Dacorogna, M. Kratz
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.
通过一个掷骰子的简单例子,我们将展示如何为保险单定价。我们进一步研究了在销售许多类似保单时,价格是如何下降的。多样化收益随着保单数量的增加而增加,同样,风险所需保费的风险负荷也趋于零。只要风险是完全独立的,这是正确的。然而,当引入另外一个由不诚实的庄家掷出的有偏差的骰子时,一个不可分散的风险确实出现了。实际上,我们可以分析地表明,对于偏置骰子,方差中存在一个额外的项,该项不随投资组合中策略的数量而减少,并导致多样化的限制。本文提出并分析研究了三种引入不可分散风险的案例。对于其中的每一种,基于潜在风险过程的风险加载行为进行了检查,并提供了数值说明。然后从风险负荷的角度对结果进行了讨论。这种模型可用于研究不确定性下的特定投资选择。
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引用次数: 9
The Small-Maturity Heston Forward Smile 小成熟的赫斯顿微笑
Pub Date : 2013-03-18 DOI: 10.2139/ssrn.2235196
A. Jacquier, P. Roome
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.
本文研究了Heston模型下远期启动期权和远期隐含波动率smile在期限趋近于零时的渐近性。我们证明了价外期权的前向微笑会爆炸,并计算了一个详细描述爆炸速率的封闭式高阶展开式。此外,结果表明,方差过程的平方根行为引起了一个奇点,使得对于某些参数配置,人们不能获得高阶的非货币正向微笑渐近。在现钞情况下,一个独立于模型的分析表明,对于任何伊藤扩散,小期限极限都是定义良好的。这些证明依赖于急剧大偏差(和改进)理论,顺便我们提供了一个退化大偏差行为的例子。
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引用次数: 23
期刊
Financial Engineering eJournal
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