Option pricing with the control variate technique beyond Monte Carlo simulation

Although mostly used alongside Monte Carlo simulation, the control-variate (CV) technique can be applied to other numerical algorithms in option pricing. This paper studies the conditions under which a numerical method (simulation-based or not) can benefit from the CV technique and what approximators can serve as CVs. We demonstrate the ideas with Carr and Madan’s Fourier transform-based algorithm, convolution-based pricing algorithms, and classic binomial trees. Numerical results are provided to show that the CV-enhanced versions are more efficient than the original algorithms.     

国企收购上市公司股权定价的研究

资本市场是资源合理配置的有效场所。国有企业通过并购重组收购上市公司股权提升资产证券化率,实现国有资产保值增值的目标。国有企业收购上市公司股权过程中,定价是最核心的问题,然而,不确定性资产定价又是非常复杂的事情。对目标企业的定价除考虑定价理论和估值方法外,还考虑控制权、流动性、协同效应、支付方式等因素。虽然交易方式更加丰富多样,但从本质上讲,所有方式的背后都会通过定价反映出来。     

On pricing lookback options under the CEV process

Abstract We consider the problem of pricing European lookback options when the underlying asset price is driven by a constant elasticity of variance (CEV) process. The evaluation model is based on the binomial approximation developed by Nelson and Ramaswamy (1990) and we show how to apply it in the case of such options. We develop simple pricing algorithms that compute accurate estimates of the option prices.     

The dynamics of cost-plus pricing

Researchers report a sizable number of companies that use cost-plus pricing. While such a policy is normatively suspect, it is simple, conventional, and occasionally mandated by regulation. This paper investigates cost-plus pricing as a dynamic adjustment process. As a dynamic policy, cost-plus pricing is more flexible than has commonly been realized. When firms have constant or decreasing average costs, dynamic cost-plus pricing typically exhibits rapid convergence to the attracting member of a pair of fixed points. If the average cost function is sufficiently U-shaped, complicated and chaotic dynamics can emerge.     

Convergence rates of recombining trees for pricing options on stocks under GBM and regime-switching models with known cash dividends

In the literature there appear various kinds of binomial trees for pricing options on stocks under geometric Brownian motions (GBMs) with known cash dividends. The aim of this paper is to compare the performance of the existing binomial trees in aspect of the convergence rates, which are usually used to measure precisely how fast the approximate values converge to the exact one, and to give a theoretical proof of the convergence rates for the interpolation binomial trees which are based on a model that excludes the arbitrage possibilities. Also the paper extends the studies to the regime-switching models with known cash dividend payment.     

基于增长期权的并购目标企业价值评估

实物期权评价方法的引入弥补了传统现金流量法在并购目标企业价值评估中的不足,并充分考虑了管理灵活性所具有的价值。首先,回顾了国内运用实物期权评价法对并购目标企业价值评估的研究;然后,建立包含增长期权的并购目标企业价值评估模型,在对其中增长期权的定价中加入市场竞争及企业竞争力的影响;最后,运用案例演示具体计算过程。     

Forecasting recovery rates on non-performing loans with machine learning

We compare the performance of a wide set of regression techniques and machine-learning algorithms for predicting recovery rates on non-performing loans, using a private database from a European debt collection agency. We find that rule-based algorithms such as Cubist, boosted trees, and random forests perform significantly better than other approaches. In addition to loan contract specificities, predictors that refer to the bank recovery process — prior to the portfolio’s sale to a debt collector — are also shown to enhance forecasting performance. These variables, derived from the time series of contacts to defaulted clients and client reimbursements to the bank, help all algorithms better identify debtors with different repayment ability and/or commitment, and in general those with different recovery potential.     

Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem

This paper investigates whether a regime switching model of stochastic lumber prices is better for the analysis of optimal harvesting problems in forestry than a more traditional single regime model. Prices of lumber derivatives are used to calibrate a regime switching model, with each of two regimes characterized by a different mean reverting process. A single regime, mean reverting process is also calibrated. The value of a representative stand of trees and optimal harvesting prices are determined by specifying a Hamilton-Jacobi-Bellman Variational Inequality, which is solved for both pricing models using a implicit finite difference approach. The regime switching model is found to more closely match the behavior of futures prices than the single regime model. In addition, analysis of a tree harvesting problem indicates significant differences in terms of land value and optimal harvest thresholds between the regime switching and single regime models.     

试论招标控制价对投标报价的影响

随着我国社会主义市场经济的飞速发展,我国的地铁工程也在发展之中,越来越多的工程改变了传统的定额计价方式,采用了更为科学的工程量清单计价方式。在工程量清单计价方式下,建设单位在招投标的过程中越来越重视招标控制价的编制,这直接导致招标评审要求的变化,进一步对招标控制价的编制内容、范围和质量提出了更高的要求。当前,我国虽然已经有了相应的法律规范招投标,但仍存在一些问题,尤其是有些工程项目的招标控制价的编制质量不高,会导致施工过程中的计价纠纷,严重的还会影响到工程项目的安全和质量。     

Exit problems in regime-switching models

This paper provides a general framework for pricing of perpetual American and real options in regime-switching Lévy models. In each state of the Markov chain, which determines switches from one Lévy process to another, the payoff stream is a monotone function of the Lévy process labeled by the state. This allows for additional switching within each state of the Markov chain (payoffs can be different in different regions of the real line). The pricing procedure is efficient even if the number of states is large provided the transition rates are not very large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modeled as finite-state Markov chains. As an application, we solve exit problems for a price-taking firm, and study the dependence of the exit threshold on the interest rate uncertainty.     

带Poisson跳的Black-Scholes模型的期权定价

主要讨论欧式期权的定价公式。首先给出一个B-S期权定价公式的简化方法,使具有一般微积分知识的读者就能理解;并假定股票价格过程遵循带Poisson跳的扩散过程,在股票预期收益率、波动率和无风险利率均为时间函数的情况下,得到欧式期权定价公式和买权与卖权之间的平价关系。     

Weak convergence of tree methods,to price options on defaultable assets

Abstract We discuss a practical method to price and hedge European contingent claims on assets with price processes which follow a jump-diffusion. The method consists of a sequence of trinomial models for the asset price and option price processes which are shown to converge weakly to the corresponding continuous time jump-diffusion processes. The main difference with many existing methods is that our approach ensures that the intermediate discrete time approximations generate models which are themselves complete, just as in the Black-Scholes binomial approximations. This is only possible by dropping the assumption that the approximations of increments of the Wiener and Poisson processes on our trinomial tree are independent, but we show that the dependence between these processes disappears in the weak limit. The approximations thus define an easy and flexible method for pricing and hedging in jump-diffusion models using explicit trees for hedging and pricing. Mathematics Subject Classification (2000): 60B10, 60H35 Journal of Economic Literature Classification: G13     

风险投资与IPO抑价——基于创业板上市公司的实证分析

自创业板设立以来,创业板市场定价效率未能充分体现,创业板上市企业IPO抑价率较高,风险资本支持的企业IPO抑价率高于非风险资本支持的企业,风险资本的持股比例、介入时间及持股机构数量都和IPO抑价有一定的关系。     

A pricing‐error rule on share distribution in equity joint ventures: The Bayesian approach

Equity joint ventures (EJVs) are a popular governance mode of inter‐firm cooperation that has attracted substantial research attention. The literature, however, still lacks a precise rule for the parents to follow in splitting the equity shares of an EJV, although share distribution is critical to almost all aspects of the co‐ownership relationship. In this study, we fill this literature gap by taking the Bayesian approach to draw a pricing‐error rule on share distribution in EJVs. More specifically, we contend that equity participation by two firms in an EJV allows profit sharing to correct for the errors that they might commit in pricing their inputs to the EJV. For profit sharing to fully nullify such pricing errors, the shares of an EJV must be split between the parent firms in a percentage combination that matches the relative sizes of their pricing errors. Because pricing errors are observable only afterward, share distribution in EJVs resembles a Bayesian process, in which the partners keep updating their estimates on pricing errors to adjust share distribution to a percentage combination that could best nullify their pricing errors. Thus, the eventual outcome of share adjustment is EJV buyout, in that the partner whose pricing errors remain substantial buys out the shares of the other whose pricing errors have become tolerable.     

供应链目标成本的战略选择

着重分析供应链成本管理方法中的供应链目标成本法。在介绍供应链目标成本法的基础上,分析了供应链目标成本战略及战略选择问题,并进一步提出了基于成本定价的目标成本法,以适应战略选择的要求。     

计算机在股票定价方法方面的应用——以中国石化(600028)为例

股票买卖的定价问题,是关系到股票投资者投资效益的最直接、最关键、最根本性的问题。本文的目的就是提供一种能指导股票投资者如何在最好的时机买卖股票的好方法。本文的研究课题是运用计算机的快速计算功能为股票二级市场上的任何股票作出合理买卖定价的方法问题,从中国石化股票2012、2013年的大量历史资料入手,采用数据挖掘技术运用计算机中的电子表格进行大量股票价格数据的运算,找出股票价格的变化规律性,制定出股票买卖定价模型,并通过后期实际验证,得出这种定价方法的合理性和可行性的结论。     

基于分数布朗运动和跳过程的股本权证定价模型

考虑到金融市场中资产价格具有的记忆性和长期相关性,模型假设股本权证标的资产价格服从分数布朗运动过程;并考虑到市场存在不确定因素而引起的价格巨大的波动,在模型中又引入了一个跳过程。首先得出权证定价的一般公式,最后在考虑股本权证行权后产生的稀释效应,得出稀释调整后的股本权证定价公式,并将其延伸到支付红利情况下。     

The Revenue Gains from Multi‐Tier Ticket Pricing: Evidence from Pop Music Concerts

We provide empirical estimates of the revenue benefits of multi‐tier pricing at a major US pop music venue. Our unique sample includes data on the number of tickets sold at every price. Mean revenue gain from multi‐tier pricing is estimated to be about $20,000 per show, a 4.2% increase over uniform pricing, although the gains were as high as 21.2% for one performer. We also provide evidence that customer segmentation by income is a likely motive of multi‐tier pricing and, for the first time, that the standard assumption of zero marginal cost of additional venue attendees is valid. Copyright © 2012 John Wiley & Sons, Ltd.     

基于双指数跳扩散过程的亚式期权的解析定价

研究了双指数跳-扩散模型下亚式期权的定价,得到了这些期权定价得解析公式。在风险中性下,亚式期权的值在恰当的边际条件和终值条件下满足广义Black-Scholes方程;我们提出一种在跳扩散模型下亚式期权定价的新方法。该方法在于为亚式期权所满足的偏积分——微分方程指定恰当的边际条件和终值条件;然后,利用拉普拉斯变换求解该方程,得到了亚式期权的解析定价公式。     

从价值创造的角度看我国合理的MBO定价

我国管理层收购中的焦点问题之一是定价的不合理,本文从并购中价值创造的角度出发,综合考虑管理层收购这种收购形式的特殊性,借鉴国外定价的成功经验,指出我国合理的管理层收购定价不应当以每股净资产作为唯一的定价标准,应以投资资本净现金流为衡量价值的标准,综合考虑控制权溢价和流动性折价,并且引入市场竞争机制,真正实现以市场为舞台的双赢。