PRICING DERIVATIVES ON MULTISCALE DIFFUSIONS: AN EIGENFUNCTION EXPANSION APPROACH

Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a large class of derivative‐assets. The payoff of the derivative‐assets may be path‐dependent. In addition, the process underlying the derivatives may exhibit killing (i.e., jump to default) as well as combined local/nonlocal stochastic volatility. The nonlocal component of volatility may be multiscale, in the sense that it may be driven by one fast‐varying and one slow‐varying factor. The flexibility of our modeling framework is contrasted by the simplicity of our method. We reduce the derivative pricing problem to that of solving a single eigenvalue equation. Once the eigenvalue equation is solved, the approximate price of a derivative can be calculated formulaically. To illustrate our method, we calculate the approximate price of three derivative‐assets: a vanilla option on a defaultable stock, a path‐dependent option on a nondefaultable stock, and a bond in a short‐rate model.     

Pure jump models for pricing and hedging VIX derivatives

Recent non-parametric statistical analysis of high-frequency VIX data (Todorov and Tauchen, 2011) reveals that VIX dynamics is a pure jump semimartingale with infinite jump activity and infinite variation. To our best knowledge, existing models in the literature for pricing and hedging VIX derivatives do not have these features. This paper fills this gap by developing a novel class of parsimonious pure jump models with such features for VIX based on the additive time change technique proposed in Li et al., 2016a, Li et al., 2016b. We time change the 3/2 diffusion by a class of additive subordinators with infinite activity, yielding pure jump Markov semimartingales with infinite activity and infinite variation. These processes have time and state dependent jumps that are mean reverting and are able to capture stylized features of VIX. Our models take the initial term structure of VIX futures as input and are analytically tractable for pricing VIX futures and European options via eigenfunction expansions. Through calibration exercises, we show that our model is able to achieve excellent fit for the VIX implied volatility surface which typically exhibits very steep skews. Comparison to two other models in terms of calibration reveals that our model performs better both in-sample and out-of-sample. We explain the ability of our model to fit the volatility surface by evaluating the matching of moments implied from market VIX option prices. To hedge VIX options, we develop a dynamic strategy which minimizes instantaneous jump risk at each rebalancing time while controlling transaction cost. Its effectiveness is demonstrated through a simulation study on hedging Bermudan style VIX options.     

动液面谱减法滤波

动液面滤波是油井检测动液面的关键技术之一。文章利用谱减法处理油井动液面信号,消除背景噪声的影响,并改进谱减法应用到动液面滤波,取得较好的滤波效果,从而提高对液面反射波位置的辨识能力。     

Forecasting commodity price indexes using macroeconomic and financial predictors

Using a long sample of commodity spot price indexes over the period 1947–2010, we examine the out-of-sample predictability of commodity prices by means of macroeconomic and financial variables. Commodity currencies are found to have some predictive power at short (monthly and quarterly) forecast horizons, while growth in industrial production and the investment–capital ratio have some predictive power at longer (yearly) horizons. Commodity price predictability is strongest when based on multivariate approaches that account for parameter estimation error. Commodity price predictability varies substantially across economic states, being strongest during economic recessions.     

一种基于自适应相似矩阵的谱聚类算法

为了消除在构建谱聚类算法的相似矩阵时,高斯核函数中尺度参数的波动影响,构建了一种自适应相似矩阵,并应用到谱聚类算法中。自适应相似矩阵中数据点间的距离度量采用测地距离算法,相距较近的两点间的距离近似于欧氏距离,相距较远的两点则先根据欧氏距离得到每个数据点的k个近邻点,然后累加近邻点的测地距离,由此得到每对数据点间的最短距离。两点间的局部密度用共享近邻的定义来表示,更好地刻画了数据集的本征结构。在5个人工数据集和国际通用UCI数据库中的5个真实数据集上进行实验。实验结果表明,所提算法的聚类准确率高于对比算法的准确率,对复杂分布数据有很强的自适应能力。研究成果为数据挖掘及机器学习提供了思路和方法。     

电感耦合等离子体发射光谱法测定蜂蜜中7种矿物元素的含量

为了快速直接测定蜂蜜中多种矿物元素的含量,采用电感耦合等离子体发射光谱(ICP-AES)法建立了同时测定蜂蜜中钙、钾、镁、钠、锌、铁、铜7种矿物元素含量的方法,考察了方法的标准曲线线性关系、检出限、精密度和准确度,讨论了前处理方法、不同产地以及蜜源植物种类对各元素含量的影响。结果表明:线性相关系数达到0.999 9以上,方法检出限为0.003～0.030 mg/L,相对标准偏差低于2%,回收率为88.66%～105.31%;不同产地的洋槐蜜中,河北洋槐蜜的钙、钾含量明显高于其他地区,广西洋槐蜜的钠、铁含量最高;不同蜜源植物的蜂蜜中,河北枣花蜜的铁含量最高,野生蜜中各种矿物元素都较为丰富。电感耦合等离子体发射光谱法可以快速、同时测定蜂蜜中多种矿物元素含量,方法简便易行,结果准确可靠,可为蜂蜜品质鉴定以及人们对蜂蜜的合理选择提供参考。     

Lookback options and diffusion hitting times: A spectral expansion approach

Lookback options have payoffs dependent on the maximum and/or minimum of the underlying price attained during the options lifetime. Based on the relationship between diffusion maximum and minimum and hitting times and the spectral decomposition of diffusion hitting times, this paper gives an analytical characterization of lookback option prices in terms of spectral expansions. In particular, analytical solutions for lookback options under the constant elasticity of variance (CEV) diffusion are obtained.Received: 1 October 2003, Mathematics Subject Classification: 60J35, 60J60, 60G70JEL Classification: G13The author thanks Phelim Boyle for bringing the problem of pricing lookback options under the CEV process to his attention and for useful discussions and Viatcheslav Gorovoi for computational assistance. This research was supported by the U.S. National Science Foundation under grants DMI-0200429 and DMS-0223354.     

Evaluation of American option prices in a path integral framework using Fourier–Hermite series expansions

In this paper we review the path integral technique which has wide applications in statistical physics and relate it to the backward recursion technique which is widely used for the evaluation of derivative securities. We formulate the pricing of equity options, both European and American, using the path integral framework. Discretising in the time variable and using expansions in Fourier–Hermite series for the continuous representation of the underlying asset price, we show how these options can be evaluated in the path integral framework. For American options, the solution technique facilitates the accurate determination of the early exercise boundary as part of the solution. Additionally, the continuous representation of the state variable allows the relatively accurate and efficient evaluation of the option prices and the delta hedge ratio.     

Modelling inflation shifts and persistence in Tunisia: perspectives from an evolutionary spectral approach

This article examines the dynamic characteristics of the inflation rate in Tunisia over the last two decades, and particularly following the onset of the Arab Spring in 2010 which causes distortions in this country’s monetary policy. We focus on the two specific dimensions of the Tunisian inflation rate: inflation regimes and persistence. We tackle this issue by adopting an evolutionary spectral approach, initially proposed by Priestley and Tong (1973). Our main findings indicate a stable inflation regime in the last 10 years, with an average inflation rate of around 5.5%. It is also found that the Tunisian inflation experienced a high degree of inertia which reflects its gradual responses to shocks. We also discuss the policy implications of these results, which typically require policy-makers to implement sound institutional reforms to reduce inflation.     

部分相干高斯—谢尔模光束在负色散介质中的光谱特性

文章利用由部分相干光理论及张量方法推导出的部分相干高斯—谢尔模(GSM)光束在介质中的传输公式,计算分析了部分相干GSM光束在负色散介质中的演化特性.研究结果表明,部分相干GSM光束在负色散介质中传输时会出现光谱分裂和频移现象.