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New News is Bad News 新消息就是坏消息
Pub Date : 2023-09-11 DOI: arxiv-2309.05560
Paul Glasserman, Harry Mamaysky, Jimmy Qin
An increase in the novelty of news predicts negative stock market returns andnegative macroeconomic outcomes over the next year. We quantify news novelty -changes in the distribution of news text - through an entropy measure,calculated using a recurrent neural network applied to a large news corpus.Entropy is a better out-of-sample predictor of market returns than a collectionof standard measures. Cross-sectional entropy exposure carries a negative riskpremium, suggesting that assets that positively covary with entropy hedge theaggregate risk associated with shifting news language. Entropy risk cannot beexplained by existing long-short factors.
新闻新颖性的增加预示着明年股市的负回报和负面的宏观经济结果。我们量化新闻新颖性-新闻文本分布的变化-通过熵度量,使用应用于大型新闻语料库的递归神经网络计算。熵比一组标准指标更能预测市场回报。横截面熵暴露具有负风险溢价,表明与熵正协变的资产对冲了与新闻语言变化相关的总风险。熵风险不能用现有的多空因素来解释。
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引用次数: 0
Thiele's PIDE for unit-linked policies in the Heston-Hawkes stochastic volatility model Heston-Hawkes随机波动率模型中单位挂钩政策的Thiele PIDE
Pub Date : 2023-09-07 DOI: arxiv-2309.03541
David R. Baños, Salvador Ortiz-Latorre, Oriol Zamora Font
The main purpose of the paper is to derive Thiele's differential equation forunit-linked policies in the Heston-Hawkes stochastic volatility model presentedin arXiv:2210.15343. This model is an extension of the well-known Heston modelthat incorporates the volatility clustering feature by adding a compound Hawkesprocess in the volatility. Since the model is arbitrage-free, pricingunit-linked policies via the equivalence principle under $mathbb{Q}$ ispossible. Some integrability conditions are checked and a suitable family ofrisk neutral probability measures is found to obtain Thiele's differentialequation. The established and practical method to compute reserves in lifeinsurance is by solving Thiele's equation, which is crucial to guarantee thesolvency of the insurance company.
本文的主要目的是推导出在arXiv:2210.15343中提出的Heston-Hawkes随机波动模型中单位联动策略的Thiele微分方程。该模型是对著名的Heston模型的扩展,该模型通过在波动率中加入复合Hawkesprocess来结合波动率聚类特征。由于模型是无套利的,在$mathbb{Q}$下,通过等价原则对单位挂钩政策定价是可能的。对可积性条件进行了检验,并找到了一类适合的风险中性概率测度,得到了Thiele微分方程。求解Thiele方程是目前公认的实用的寿险准备金计算方法,它对保证保险公司的偿付能力至关重要。
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引用次数: 0
Enhancing accuracy for solving American CEV model with high-order compact scheme and adaptive time stepping 采用高阶紧凑格式和自适应时间步进,提高了求解美国CEV模型的精度
Pub Date : 2023-09-07 DOI: arxiv-2309.03984
Chinonso Nwankwo, Weizhong Dai, Tony Ware
In this research work, we propose a high-order time adapted scheme forpricing a coupled system of fixed-free boundary constant elasticity of variance(CEV) model on both equidistant and locally refined space-grid. The performanceof our method is substantially enhanced to improve irregularities in the modelwhich are both inherent and induced. Furthermore, the system of coupled PDEs isstrongly nonlinear and involves several time-dependent coefficients thatinclude the first-order derivative of the early exercise boundary. Thesecoefficients are approximated from a fourth-order analytical approximationwhich is derived using a regularized square-root function. The semi-discreteequation for the option value and delta sensitivity is obtained from anon-uniform fourth-order compact finite difference scheme. Fifth-order 5(4)Dormand-Prince time integration method is used to solve the coupled system ofdiscrete equations. Enhancing the performance of our proposed method with localmesh refinement and adaptive strategies enables us to obtain highly accuratesolution with very coarse space grids, hence reducing computational runtimesubstantially. We further verify the performance of our methodology as comparedwith some of the well-known and better-performing existing methods.
在本研究中,我们提出了一种高阶时间适应方案,用于等距和局部精细空间网格上固定自由边界不变弹性方差(CEV)模型耦合系统的定价。我们的方法大大提高了性能,改善了模型中固有和诱导的不规则性。此外,耦合偏微分方程系统是强非线性的,涉及多个时间相关系数,其中包括早期运动边界的一阶导数。这些系数是从使用正则平方根函数导出的四阶解析近似中近似出来的。在非一致的四阶紧致有限差分格式下,得到了选择值和灵敏度的半离散方程。采用五阶5(4)Dormand-Prince时间积分法求解离散方程耦合系统。通过局部网格细化和自适应策略增强我们提出的方法的性能,使我们能够在非常粗糙的空间网格中获得高度精确的分辨率,从而大大减少了计算运行时间。我们进一步验证了我们的方法的性能,并与一些知名的和性能更好的现有方法进行了比较。
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引用次数: 0
Default Process Modeling and Credit Valuation Adjustment 违约过程建模与信用评估调整
Pub Date : 2023-09-06 DOI: arxiv-2309.03311
David Xiao
This paper presents a convenient framework for modeling default process andpricing derivative securities involving credit risk. The framework provides anintegrated view of credit valuation adjustment by linking distance-to-default,default probability, survival probability, and default correlation together. Weshow that risky valuation is Martingale in our model. The framework reduces thetechnical issues of performing risky valuation to the same issues faced whenperforming the ordinary valuation. The numerical results show that the modelprediction is consistent with the historical observations.
本文提出了一个方便的框架来建模违约过程和定价涉及信用风险的衍生证券。该框架通过将违约距离、违约概率、生存概率和违约相关性联系在一起,提供了信用估值调整的综合视图。在我们的模型中,风险估值是鞅。该框架将执行风险估值的技术问题简化为执行普通估值时面临的相同问题。数值结果表明,模式预测结果与历史观测结果基本一致。
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引用次数: 0
Asymptotics for Short Maturity Asian Options in a Jump-Diffusion model with Local Volatility 具有局部波动率的跳跃-扩散模型下短期限亚洲期权的渐近性
Pub Date : 2023-08-30 DOI: arxiv-2308.15672
Dan Pirjol, Lingjiong Zhu
We present a study of the short maturity asymptotics for Asian options in ajump-diffusion model with a local volatility component, where the jumps aremodeled as a compound Poisson process which are later extended to L'evy jumps,that includes the exponential L'{e}vy model as a special case. Both fixed andfloating strike Asian options are considered. Explicit results are obtained forthe first-order asymptotics of the Asian options prices for a few popularmodels in the literature: the Merton jump-diffusion model, thedouble-exponential jump model, and the Variance Gamma model. We propose ananalytical approximation for Asian option prices which satisfies theconstraints from the short-maturity asymptotics, and test it against MonteCarlo simulations. The asymptotic results are in good agreement with numericalsimulations for sufficiently small maturity.
本文研究了具有局部波动分量的跳跃-扩散模型中亚洲期权的短期限渐近性,其中跳跃被建模为复合泊松过程,后来扩展到L evy跳跃,其中包括指数L evy模型作为特例。固定罢工和浮动罢工都是亚洲的选择。对于文献中比较流行的几种模型:默顿跳跃-扩散模型、双指数跳跃模型和方差伽玛模型,得到了亚洲期权价格一阶渐近的显式结果。我们提出了满足短期限渐近约束的亚洲期权价格的解析逼近,并用MonteCarlo模拟进行了检验。对于足够小的成熟度,其渐近结果与数值模拟结果很好地吻合。
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引用次数: 0
An Empirical Analysis on Financial Market: Insights from the Application of Statistical Physics 金融市场的实证分析:来自统计物理应用的启示
Pub Date : 2023-08-28 DOI: arxiv-2308.14235
Haochen Li, Yi Cao, Maria Polukarov, Carmine Ventre
In this study, we introduce a physical model inspired by statistical physicsfor predicting price volatility and expected returns by leveraging Level 3order book data. By drawing parallels between orders in the limit order bookand particles in a physical system, we establish unique measures for thesystem's kinetic energy and momentum as a way to comprehend and evaluate thestate of limit order book. Our model goes beyond examining merely the toplayers of the order book by introducing the concept of 'active depth', acomputationally-efficient approach for identifying order book levels that haveimpact on price dynamics. We empirically demonstrate that our model outperformsthe benchmarks of traditional approaches and machine learning algorithm. Ourmodel provides a nuanced comprehension of market microstructure and producesmore accurate forecasts on volatility and expected returns. By incorporatingprinciples of statistical physics, this research offers valuable insights onunderstanding the behaviours of market participants and order book dynamics.
在本研究中,我们引入了一个受统计物理学启发的物理模型,通过利用三级订单簿数据来预测价格波动和预期回报。通过将极限订单簿中的订单与物理系统中的粒子进行类比,建立了系统动能和动量的独特度量,作为理解和评估极限订单簿状态的一种方法。我们的模型通过引入“活跃深度”的概念,超越了仅仅检查订单簿的参与者,这是一种有效的计算方法,用于识别影响价格动态的订单簿水平。我们的经验证明,我们的模型优于传统方法和机器学习算法的基准。我们的模型提供了对市场微观结构的细致理解,并对波动性和预期回报做出了更准确的预测。通过结合统计物理原理,本研究为理解市场参与者的行为和订单动态提供了有价值的见解。
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引用次数: 0
Portfolios Generated by Contingent Claim Functions, with Applications to Option Pricing 或有债权函数生成的投资组合及其在期权定价中的应用
Pub Date : 2023-08-26 DOI: arxiv-2308.13717
Ricardo T. Fernholz, Robert Fernholz
In a market of stocks represented by strictly positive continuoussemimartingales, a contingent claim function is a positive C^{2, 1} function ofthe stock prices and time with a given terminal value. If a contingent claimfunction satisfies a certain parabolic differential equation, it will generatea portfolio with value process that replicates the contingent claim function.This parabolic differential equation is a general form of the Black-Scholesequation.
在由严格正连续半鞅表示的股票市场中,或有债权函数是给定终端值的股票价格和时间的正C^{2,1}函数。如果某一或有索求函数满足某一抛物线微分方程,则该或有索求函数将生成具有复制该或有索求函数的价值过程的投资组合。抛物型微分方程是布莱克-斯科尔斯方程的一般形式。
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引用次数: 0
Economic Complexity Limits Accuracy of Price Probability Predictions by Gaussian Distributions 经济复杂性限制了高斯分布预测价格概率的准确性
Pub Date : 2023-08-24 DOI: arxiv-2309.02447
Victor Olkhov
The accuracy of predictions of price and return probabilities substantiallydetermines the reliability of asset pricing and portfolio theories. We developsuccessive approximations that link up predictions of the market-basedprobabilities of price and return for the whole stock market with predictionsof price and return probabilities for stocks of a particular company and showthat economic complexity limits the accuracy of any forecasts. The economicorigin of the restrictions lies in the fact that the predictions of the m-thstatistical moments of price and return require descriptions of the economicvariables composed by sums of the m-th powers of economic or markettransactions during an averaging time interval. The attempts to predict then-th statistical moments of price and return of stocks that are under theaction of a single risk result in estimates of the n-dimensional risk ratingvectors for economic agents. In turn, the risk rating vectors play the role ofcoordinates for the description of the evolution of economic variables. Thelack of a model description of the economic variables composed by sums of the2-d and higher powers of market transactions causes that, in the coming years,the accuracy of the forecasts will be limited at best by the first twostatistical moments of price and return, which determine Gaussiandistributions. One can ignore existing barriers and limits but cannot overcomeor resolve them. That significantly reduces the reliability and veracity ofmodern asset pricing and portfolio theories. Our results could be essential andfruitful for the largest investors and banks, economic and financialauthorities, and market participants.
价格和回报概率预测的准确性在很大程度上决定了资产定价和投资组合理论的可靠性。我们开发了连续的近似,将整个股票市场的基于市场的价格和回报概率的预测与特定公司股票的价格和回报概率的预测联系起来,并表明经济复杂性限制了任何预测的准确性。这些限制的经济学根源在于,对价格和收益的第m个统计时刻的预测需要对经济变量的描述,这些变量由平均时间间隔内经济或市场交易的第m次幂的总和组成。试图预测在单一风险作用下股票价格和收益的统计时刻,结果是对经济主体的n维风险评级向量的估计。而风险评级向量则扮演了描述经济变量演化的坐标角色。由于缺乏对经济变量的模型描述,这些经济变量是由二维和更高的市场交易力量的总和构成的,因此,在未来几年,预测的准确性最多将受到价格和回报的前两个统计时刻的限制,而这两个统计时刻决定了高斯分布。人们可以忽略现有的障碍和限制,但无法克服或解决它们。这大大降低了现代资产定价和投资组合理论的可靠性和准确性。我们的研究结果对最大的投资者和银行、经济和金融当局以及市场参与者来说可能是必不可少和富有成效的。
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引用次数: 0
Pragmatic Comparison Analysis of Alternative Option Pricing Models 备选期权定价模型的实用比较分析
Pub Date : 2023-08-23 DOI: arxiv-2309.09890
Natasha Latif, Shafqat Ali Shad, Muhammad Usman, Chandan Kumar, Bahman B Motii, MD Mahfuzer Rahman, Khuram Shafi, Zahra Idrees
In this paper, we price European Call three different option pricing models,where the volatility is dynamically changing i.e. non constant. In stochasticvolatility (SV) models for option pricing a closed form approximation techniqueis used, indicating that these models are computationally efficient and havethe same level of performance as existing ones. We show that the calibration ofSV models, such as Heston model and the High Order Moment based StochasticVolatility (MSV) is often faster and easier. On 15 different datasets of indexoptions, we show that models which incorporates stochastic volatility achievesaccuracy comparable with the existing models. Further, we compare the In Sampleand Out Sample pricing errors of each model on each date. Lastly, the pricingof models is compared among three different market to check model performancein different markets. Keywords: Option Pricing Model, Simulations, IndexOptions, Stochastic Volatility Models, Loss Functionhttp://www.sci-int.com/pdf/638279543859822650.pdf
本文对欧洲看涨期权的三种不同的期权定价模型进行了定价,其中波动率是动态变化的,即是非恒定的。在期权定价的随机波动率(SV)模型中使用了封闭形式的近似技术,表明这些模型具有计算效率,并且与现有模型具有相同的性能水平。我们证明了sv模型(如Heston模型和基于高阶矩的随机波动率(MSV))的校准通常更快,更容易。在15个不同的指数期权数据集上,我们证明了纳入随机波动率的模型达到了与现有模型相当的准确性。此外,我们比较了每个模型在每个日期的In Sample和Out Sample定价误差。最后,对三种不同市场的模型定价进行比较,检验模型在不同市场的表现。关键词:期权定价模型,模拟,IndexOptions,随机波动率模型,损失函数http://:/www.sci-int.com/pdf/638279543859822650.pdf
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引用次数: 0
Analytical valuation of vulnerable derivative contracts with bilateral cash flows under credit, funding and wrong-way risks 信贷、融资和错误路径风险下双边现金流的脆弱衍生品合约分析估值
Pub Date : 2023-08-21 DOI: arxiv-2308.10568
Juan Jose Francisco Miguelez, Cristin Buescu
We study the problem of valuing a vulnerable derivative with bilateral cashflows between two counterparties in the presence of funding, credit andwrong-way risks, and derive a closed-form valuation formula for an at-the-money(ATM) forward contract as well as a second order approximation for the generalcase. We posit a model with heterogeneous interest rates and default occurrenceand infer a Cauchy problem for the pre-default valuation function of thecontract, which includes ab initio any counterparty risk - as opposed tocalculating valuation adjustments collectively known as XVA. Under a specificfunding policy which linearises the Cauchy problem, we obtain a genericprobabilistic representation for the pre-default valuation (Theorem 1). Weapply this general framework to the valuation of an equity forward andestablish the contract can be expressed as a continuous portfolio of Europeanoptions with suitably chosen strikes and expiries under a particularprobability measure (Theorem 2). Our valuation formula admits a closed-formexpression when the forward contract is ATM (Corollary 2) and we derive asecond order approximation in moneyness when the contract is close to ATM(Theorem 3). Numerical results of our model show that the forward is moresensitive to funding factors than credit ones, while higher stock funding costsincrease sensitivity to credit spreads and wrong-way risk.
我们研究了在存在资金、信用和错误风险的情况下,交易双方之间存在双边现金流的脆弱衍生品的估值问题,并推导了现价(ATM)远期合约的封闭形式估值公式以及一般情况下的二阶近似。我们假设了一个具有异质利率和违约发生的模型,并推断了合约违约前估值函数的柯西问题,其中包括从头开始计算任何交易对手风险-而不是计算估值调整统称为XVA。在将柯西问题线性化的特定资助政策下,我们获得了违约前估值的一般概率表示(定理1)。我们将这个一般框架应用于股权远期的估值,并建立了合约可以表示为在特定概率度量下适当选择罢工和到期日的欧式期权的连续投资组合(定理2)。当远期合约为ATM时,我们的估值公式允许一个封闭的形式表达式(推论2),并且我们推导了二阶近似模型的数值结果表明,远期合约对融资因素比信用因素更敏感,而较高的股票融资成本增加了对信用利差和错误风险的敏感性。
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引用次数: 0
期刊
arXiv - QuantFin - Pricing of Securities
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