Neural Networks for Estimating Speculative Attacks Models

Currency crises have been analyzed and modeled over the last few decades. These currency crises develop mainly due to a balance of payments crisis, and in many cases, these crises lead to speculative attacks against the price of the currency. Despite the popularity of these models, they are currently shown as models with low estimation precision. In the present study, estimates are made with first- and second-generation speculative attack models using neural network methods. The results conclude that the Quantum-Inspired Neural Network and Deep Neural Decision Trees methodologies are shown to be the most accurate, with results around 90% accuracy. These results exceed the estimates made with Ordinary Least Squares, the usual estimation method for speculative attack models. In addition, the time required for the estimation is less for neural network methods than for Ordinary Least Squares. These results can be of great importance for public and financial institutions when anticipating speculative pressures on currencies that are in price crisis in the markets.     

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In this paper, we establish the option pricing model under sub-fractional Brownian motion, and consider the situation of the continuous dividend payments. Firstly, Wick-It\^{o} integral and partial differential method are used to get the option price of partial differential equation, and then through variable substitution into Cauchy problem, we can get the pricing formula of European call option with dividend-paying in sub-fractional Brownian motion environment. According to the pricing formula of European call option, the European put option pricing formula is obtained. Moreover, we study the parameter estimation in the model, and consider the unbiasedness and the strong convergence of the estimator.     

Fluctuation scaling of quotation activities in the foreign exchange market

We study the scaling behavior of quotation activities for various currency pairs in the foreign exchange market. The components’ centrality is estimated from multiple time series and visualized as a currency pair network. The power-law relationship between a mean of quotation activity and its standard deviation for each currency pair is found. The scaling exponent α and the ratio between common and specific fluctuations η increase with the length of the observation time window . The result means that although for , the market dynamics are governed by specific processes, and at a longer time scale the common information flow becomes more important. We point out that quotation activities are not independently Poissonian for , and temporally or mutually correlated activities of quotations can happen even at this time scale. A stochastic model for the foreign exchange market based on a bipartite graph representation is proposed.     

基于BP—LVQ神经网络的纸币新旧识别算法研究

针对纸币图像的特点,在一个系统同时提取两组表示纸币新旧的图像特征,采用级联的组合方式,设计了一种新的BP—LVQ神经网络组合分类器对纸币进行新旧识别。经过实验对比验证,该方法有效提高15％的系统识别率,可应用于清分系统的纸币新旧识别。     

High-Order Methods for Exotic Options and Greeks Under Regime-Switching Jump-Diffusion Models

This paper aims to develop high-order numerical methods for solving the system partial differential equations (PDEs) and partial integro-differential equations (PIDEs) arising in exotic option pricing under regime-switching models and regime-switching jump-diffusion models, respectively. Using cubic Hermite polynomials, the high-order collocation methods are proposed to solve the system PDEs and PIDEs. This collocation scheme has the second-order convergence rates in time and fourth-order rates in space. The computation of the Greeks for the options is also studied. Numerical examples are carried out to verify the high-order convergence and show the efficiency for computing the Greeks.     

Exponential Rosenbrock integrators for option pricing

In this paper, we are concerned with the time integration of differential equations modeling option pricing. In particular, we consider the Black-Scholes equation for American options. As an alternative to existing methods, we present exponential Rosenbrock integrators. These integrators require the evaluation of the exponential and related functions of the Jacobian matrix. The resulting methods have good stability properties. They are fully explicit and do not require the numerical solution of linear systems, in contrast to standard integrators. We have implemented some numerical experiments in Matlab showing the reliability of the new method.     

Option pricing with regime switching by trinomial tree method

We present a fast and simple tree model to price simple and exotic options in Markov Regime Switching Model (MRSM) with multi-regime. We modify the trinomial tree model of Boyle (1986) [12] by controlling the risk neutral probability measure in different regime states to ensure that the tree model can accommodate the data of all different regimes at the same time preserving its combining tree structure. In MRSM, the market might not be complete, therefore we provide some ideas and discussions on managing the regime switching risk in support of our results.     

Valuing continuous-installment options

Installment options are path-dependent contingent claims in which the premium is paid discretely or continuously in installments, instead of paying a lump sum at the time of purchase. This paper deals with valuing European continuous-installment options written on dividend-paying assets in the standard Black–Scholes–Merton framework. The valuation of installment options can be formulated as a free boundary problem, due to the flexibility of continuing or stopping to pay installments. On the basis of a PDE for the initial premium, we derive an integral representation for the initial premium, being expressed as a difference of the corresponding European vanilla value and the expected present value of installment payments along the optimal stopping boundary. Applying the Laplace transform approach to this PDE, we obtain explicit Laplace transforms of the initial premium as well as its Greeks, which include the transformed stopping boundary in a closed form. Abelian theorems of Laplace transforms enable us to characterize asymptotic behaviors of the stopping boundary close and at infinite time to expiry. We show that numerical inversion of these Laplace transforms works well for computing both the option value and the optimal stopping boundary.     

A simple model of deferred callability in defaultable debt

Banks and other financial institutions issue hybrid capital as part of their risk capital. Hybrid capital has no maturity, but, similarly to most corporate debt, includes an embedded issuer’s call option. To obtain acceptance as risk capital, the first possible exercise date of the embedded call is contractually deferred by several years, generating a protection period. We value the call feature as a European option on perpetual defaultable debt. We do this by first modifying the underlying asset process to incorporate a time-dependent bankruptcy level before the expiration of the embedded option. We identify a call option on debt as a fixed number of put options on a modified asset, which is lognormally distributed, as opposed to the market value of debt. To include the possibility of default before the expiration of the option we apply barrier options results. The formulas are quite general and may be used for valuing both embedded and third-party options. All formulas are developed in the seminal and standard Black–Scholes–Merton model and, thus, standard analytical tools such as ‘the greeks’, are immediately available.     

汇率连动欧式幂型期权鞅定价及避险

研究了汇率连动选择权中执行价是本国货币的外国股票权证的欧式幂型期权的鞅定价问题,推导了其看涨、看跌定价公式,并求出了其相应的避险参数.