A TEST OF A GENERAL EQUILIBRIUM STOCK OPTION PRICING MODEL

An empirical version of the Cox, Ingersoll, and Ross (1985a) call option pricing model is derived, assuming execution price uncertainty in the options market. the pricing restrictions come in the form of moment conditions in the option pricing error. These can be estimated and tested using a version of the method of simulated moments (MSM). Simulation estimates, obtained by discretely approximating the risk-neutral processes of the underlying stock price and the interest rate, are substituted for analytically unknown call prices. the asymptotics and other aspects of the MSM estimator are discussed. the model is tested on transaction prices at 15-minute intervals. It substantially outperforms the Black-Scholes model. the empirical success of the Cox-Ingersoll-Ross model implies that the continuous-time interest rate implicit in synchronous transaction quotes of 90-day Treasury-bill futures contracts is an-albeit noisy-proxy for the instantaneous volatility on common stock. the process of the instantaneous volatility is found to be close to nonstationary. It is well approximated by a heteroskedastic unit-root process. With this approximation, the Cox-Ingersoll-Ross model only slightly overprices long-maturity options.     

Error analysis of finite difference and Markov chain approximations for option pricing

Mijatovi? and Pistorius proposed an efficient Markov chain approximation method for pricing European and barrier options in general one‐dimensional Markovian models. However, sharp convergence rates of this method for realistic financial payoffs, which are nonsmooth, are rarely available. In this paper, we solve this problem for general one‐dimensional diffusion models, which play a fundamental role in financial applications. For such models, the Markov chain approximation method is equivalent to the method of lines using the central difference. Our analysis is based on the spectral representation of the exact solution and the approximate solution. By establishing the convergence rate for the eigenvalues and the eigenfunctions, we obtain sharp convergence rates for the transition density and the price of options with nonsmooth payoffs. In particular, we show that for call‐/put‐type payoffs, convergence is second order, while for digital‐type payoffs, convergence is generally only first order. Furthermore, we provide theoretical justification for two well‐known smoothing techniques that can restore second‐order convergence for digital‐type payoffs and explain oscillations observed in the convergence for options with nonsmooth payoffs. As an extension, we also establish sharp convergence rates for European options for a rich class of Markovian jump models constructed from diffusions via subordination. The theoretical estimates are confirmed using numerical examples.     

Target volatility option pricing in the lognormal fractional SABR model

We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula of Itô's calculus yields an approximation formula for the price of a target volatility option in small time by the technique of freezing the coefficient. A decomposition formula in terms of Malliavin derivatives is also provided. Alternatively, we also derive closed form expressions for a small volatility of volatility expansion of the price of a target volatility option. Numerical experiments show the accuracy of the approximations over a reasonably wide range of parameters.     

快速校正天波雷达电离层相位污染的改进方法

时变的电离层会对天波超视距雷达(OTHR)回波信号相位进行调制,产生相位污染,导致回波谱展宽。最大似然估计(MLE)法具有比相位梯度法更佳的污染校正效果,但计算量非常大。通过引入投影近似子空间跟踪法,提出了一种改进的MLE方法。改进方法采用递归手段估计最大特征值对应的特征向量,避免了特征值分解过程,能够显著降低计算量,污染校正效果与MLE法相当。理论分析与仿真对比表明改进方法普适性强,计算量只有MLE法的万分之一,更适合工程实现。     

An assessment on the quality of China’s preliminary data of quarterly GDP announcements

This article examines the quality of China’s preliminary announcements of the quarterly GDP. We modify the tests for unbiasedness and efficiency by incorporating the Fourier approximation to capture the effect of the state of the economy, and employing the Kiefer, Vogelsang and Bunzel (KVB) approach, developed by KVB in 2000 to reconstruct the tests to improve the finite sample properties. The results show that: (1) there is no enough evidence to support that the preliminary and first revised data are unbiased and efficient; (2) there exist systematic errors related to the state of the economy, and hence information about the state of the economy was not incorporated into the GDP data. Furthermore, we find that there is a possibility that these systematic errors associated with the stages of the business cycle may offset each other, and there is also a possibility that there exist offsetting errors in the underlying components of GDP.     

Lognormal Approximation of Complex Path-Dependent Pension Scheme Payoffs

Abstract

This paper analyzes an explicit return smoothing mechanism which has recently been introduced as part of a new type of pension savings contract that has been offered by Danish life insurers. We establish the payoff function implied by the return smoothing mechanism and show that its probabilistic properties are accurately approximated by a suitably adapted lognormal distribution. The quality of the lognormal approximation is explored via a range of simulation-based numerical experiments, and we point to several other potential practical applications of the paper's theoretical results.     

数理经济方法中跨期因子的推导及应用

本文给出了时间序列的离散和连续两种情形的跨期调整关系和增长率计算公式的推导过程,以及进一步利用等价无穷小关系阐明了离散与连续形式的近似关系,并显示了连续型跨期调整因子在构建理论与计量模型过程中更有优势,相对来说更为常用.     

A supply chain network design considering transportation cost discounts

This study addresses an integrated facility location and inventory allocation problem considering transportation cost discounts. Specifically, this article considers two types of transportation discounts simultaneously: quantity discounts for inbound transportation cost and distance discounts for outbound transportation cost. This study uses an approximation procedure to simplify DC distance calculation details, and develops an algorithm to solve the aforementioned supply chain management (SCM) problems using nonlinear optimization techniques. Numerical studies illustrate the solution procedures and the effects of the model parameters on the SCM decisions and total costs. Results of this study serve as a reference for business managers and administrators.     

Conditional risk measures in a bipartite market structure

In this paper, we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insurance market by a bipartite graph. Using Pareto-tailed losses and multivariate regular variation, we obtain asymptotic results for conditional risk measures based on the Value-at-Risk and the Conditional Tail Expectation. These results allow us to assess the influence of an individual institution on the systemic or market risk and vice versa through a collection of conditional risk measures. For large markets, Poisson approximations of the relevant constants are provided. Differences of the conditional risk measures for an underlying homogeneous and inhomogeneous random graph are illustrated by simulations.