Modelling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps

It is known that the implied volatility skew of Forex (FX) options demonstrates a stochastic behaviour which is called stochastic skew. In this paper, we create stochastic skew by assuming the spot/instantaneous variance (InV) correlation to be stochastic. Accordingly, we consider a class of Stochastic Local Volatility (SLV) models with stochastic correlation where all drivers – the spot, InV and their correlation – are modelled by processes. We assume all diffusion components to be fully correlated, as well as all jump components. A new fully implicit splitting finite-difference scheme is proposed for solving forward PIDE which is used when calibrating the model to market prices of the FX options with different strikes and maturities. The scheme is unconditionally stable, of second order of approximation in time and space, and achieves a linear complexity in each spatial direction. The results of simulation obtained by using this model demonstrate the capacity of the presented approach in modelling stochastic skew.     

Two asset-barrier option under stochastic volatility

Financial products which depend on hitting times for two underlying assets have become very popular in the last decade. Three common examples are double-digital barrier options, two-asset barrier spread options and double lookback options. Analytical expressions for the joint distribution of the endpoints and the maximum and/or minimum values of two assets are essential in order to obtain quasi-closed form solutions for the price of these derivatives. Earlier authors derived quasi-closed form pricing expressions in the context of constant volatility and correlation. More recently solutions were provided in the presence of a common stochastic volatility factor but with restricted correlations due to the use of a method of images. In this article, we generalize this finding by allowing any value for the correlation. In this context, we derive closed-form expressions for some two-asset barrier options.     

外语类专业开设《大学数学》选修课的实践与探索

作为描述自然科学和社会科学的一个重要工具,数学有着其独特的作用.但长期以来,在外语类专业中数学教学得不到应有的重视,针对此问题,开设了《大学数学》选修课的实践与探索,在形成自己特色的同时,也发现了外语类专业开设数学课面临的一些问题,并提出了应对措施.     

Multifractal analysis of foreign exchange data

In this paper we perform multifractal analyses of five daily Foreign Exchange (FX) rates. These techniques are currently used in turbulence to characterize scaling and intermittency. We show the multifractal nature of FX returns, and estimate the three parameters in the universal multifactal framework, which characterize all small and medium intensity fluctuations, at all scales. For large fluctuations, we address the question of hyperbolic (fat) tails of the distributions which are characterized by a fourth parameter, the tail index. We studied both the prices fluctuations and the returns, finding no systematic difference in the scaling exponents in the two cases. We discuss and compare our results with several recent studies, and show how the additive models are not compatible with data: Brownian, fractional Brownian, Lévy, Truncated Lévy and fractional Lévy models. We analyse in this framework the ARCH(1), GARCH(1,1) and HARCH (7) models, and show that their structure functions scaling exponents are undistinguishable from that of Brownian motion, which means that these models do not adequately describe the scaling properties of the statistics of the data. Our results indicate that there might exist a multiplicative ‘flux of financial information’, which conditions small‐scale statistics to large‐scale values, as an analogy with the energy flux in turbulence. Copyright © 1999 John Wiley & Sons, Ltd.     

对外贸易、经济增长与二氧化碳排放 ——基于分位数回归的实证研究

基于1997-2016年中国30个省级地区的数据,建立面板分位数回归模型考量对外贸易与经济增长对不同分位水平二氧化碳排放的影响.研究发现:在各分位点对外贸易对碳排放的影响为负,但仅在高分位点显著,并且对外贸易的减排效应表现出随碳排放量增加而增加的趋势.经济增长在50%分位点以外的其他分位点对碳排放具有显著的促进作用,但环境库兹涅茨假说只在低排放省份和高排放省份有效;进一步研究显示,对外贸易通过促进经济增长对碳排放产生的正向间接影响大于负向直接影响,对外贸易总体上加剧了环境污染,验证了"污染天堂假说".     

Improved Dividend Estimation from Intraday Quotes

Liquid financial markets, such as the options market of the S&P 500 index, create vast amounts of data every day, i.e., so-called intraday data. However, this highly granular data is often reduced to single-time when used to estimate financial quantities. This under-utilization of the data may reduce the quality of the estimates. In this paper, we study the impacts on estimation quality when using intraday data to estimate dividends. The methodology is based on earlier linear regression (ordinary least squares) estimates, which have been adapted to intraday data. Further, the method is also generalized in two aspects. First, the dividends are expressed as present values of future dividends rather than dividend yields. Second, to account for heteroscedasticity, the estimation methodology was formulated as a weighted least squares, where the weights are determined from the market data. This method is compared with a traditional method on out-of-sample S&P 500 European options market data. The results show that estimations based on intraday data have, with statistical significance, a higher quality than the corresponding single-times estimates. Additionally, the two generalizations of the methodology are shown to improve the estimation quality further.     

Learning Your Options: Option-Based Model of Export Readiness and Optimal Export

In this short note we offer a novel quantitative approach to modeling of early stages of firm’s internalization, namely stages of accumulation of export readiness and their export debut. In particular, we introduce a new model of export readiness and offer an explicit way of how the export readiness can be accounted in the company share price. The model considers export readiness as a non-observable intangible asset that changes a firm’s asset dynamics. This, in the framework of an option-based debt-equity Merton model, affects both the equity and debt of the company. The approach also allows one to define the contribution of export readiness to equity price and to find a self-consistent quantitative solution to the problem of optimal export strategy and the corresponding optimal firm’s capital allocation.     

A Stochastic Programming Model for Currency Option Hedging

In this paper we use a stochastic programming approach to develop currency option hedging models which can address problems with multiple random factors in an imperfect market. The portfolios considered in our model are rebalanced at the end of each time period, and reinvestments are allowed during the hedging process. These sequential decisions (reinvestments) are based on the evolution of random parameters such as exchange rates, interest rates, etc. We also allow the inclusion of a variety of instruments in the hedging portfolio, including short term derivative securities, short term options, and futures. These instruments help generate strategies that provide good liquidity and low trade intensity. One of the important features of the model is that it incorporates constraints on sensitivity measures such as Delta and Gamma. By ensuring that these hedge parameters track a desired trajectory (e.g., the parameters of a target option), the new model provides investment strategies that are robust with respect to the perturbations measured by Delta and Gamma. In order to manage the explosion of scenarios due to multiple random factors, we incorporate sampling within a scenario aggregation algorithm. We illustrate that when compared with other myopic hedging methods in imperfect markets, the new stochastic programming model can provide better performance. Our examples also illustrate stochastic programming as a practical computational tool for realistic hedging problems.     

APPLICATIONS OF HAMILTONIAN AND LAPLACE TRANSFORM IN AN ECONOMIC MODEL

Since 1928, Ramsey introduced variation to analysis the optimal savings in an intertemproal model. Mathematics becomes an important tool for economists, such as Pontryagin'sMaximal Principle, Bellman Principle, Dynamics etc. These mathematical tools give economya new viewpoint, on the other hand, it also gives mathematicians a good application exaxnple.In this paper, we apply Hamilton system and Laplace transform to analysis the long-run effectsand short-run effects of foreign aid on domes…