An efficient algorithm for pricing barrier options in arbitrage-free binomial models with calibrated drift terms

The interrelation between the drift coefficient of price processes on arbitrage-free financial markets and the corresponding transition probabilities induced by a martingale measure is analysed in a discrete setup. As a result, we obtain a flexible setting that encompasses most arbitrage-free binomial models. It is argued that knowledge of the link between drift and transition probabilities may be useful for pricing derivatives such as barrier options. The idea is illustrated in a simple example and later extended to a general numerical procedure. The results indicate that the option values in our fitted drift model converge much faster to closed-form solutions of continuous models for a wider range of contract specifications than those of conventional binomial models.     

Smooth convergence in the binomial model

In this article, we consider a general class of binomial models with an additional parameter λ. We show that in the case of a European call option the binomial price converges to the Black–Scholes price at the rate 1/n and, more importantly, give a formula for the coefficient of 1/n in the expansion of the error. This enables us, by making special choices for λ, to prove that convergence is smooth in Tian’s flexible binomial model and also in a new center binomial model which we propose. Ken Palmer was supported by NSC grant 93-2118-M-002-002.     

The smirk in the S&P500 futures options prices: a linearized factor analysis

In the S&P500 futures options, we identify three factors, corresponding to movements in the underlying, parallel movements, and tilting of the cross section of implied volatilities (the “smirk factor”). We relate these factors non-linearly to movements in the option prices. They seem to be diffusive in nature, have significant associated risk premia, and can account for an overwhelming part of the option price movements. We interpret the options smirk, which is the notion that out-of-the-money (OTM) puts seem expensive relative to OTM calls, in terms of the prices of these risk factors. Going short OTM puts and long OTM calls, corresponding to the third factor, makes a profit on average, but this corresponds to its risk premium, and does not represent a market inefficiency. Our smirk factor is useful for hedging option portfolios, but seems unrelated to movements in the underlying, and does not fit into the framework of the jump-diffusion models.      

Static-arbitrage upper bounds for the prices of basket options

In this paper we investigate the possible values of basket options. Instead of postulating a model and pricing the basket option using that model, we consider the set of all models which are consistent with the observed prices of vanilla options, and, within this class, find the model for which the price of the basket option is largest. This price is an upper bound on the prices of the basket option which are consistent with no-arbitrage. In the absence of additional assumptions it is the lowest upper bound on the price of the basket option. Associated with the bound is a simple super-replicating strategy involving trading in the individual calls.     

Binomial basis for linear information dynamics: real options, dividends and the valuation of equity

Analytical research has confirmed that real options give rise to the kind of nonlinearities observed in practice between equity prices and the figures appearing on corporate financial statements. We develop these real option values in terms of a quasi 'supply-side' model of linear information dynamics based on simple discrete time binomial filtration processes. Our analysis shows that the linear models that pervade the empirical (and analytical) work of the area, will almost certainly suffer from an omitted variables problem. Parameter estimation will then be inconsistent and inefficient.     

Contribution rates to funded pension systems in the new member countries

The paper examines implications of real convergence for fully funded pension systems in the new member countries of the European Union. The process of convergence implies that contribution rates would have to be up to 70% higher in the new member countries in order to achieve the same replacement ratio as in a steady-state economy. This effect is partially due to higher growth rates during the process of real convergence and partially due to lower rates of return. The rates of return will be lower due to nominal convergence.     

Non-parametric calibration of the local volatility surface for European options using a second-order Tikhonov regularization

We calibrate the local volatility surface for European options across all strikes and maturities of the same underlying. There is no interpolation or extrapolation of either the option prices or the volatility surface. We do not make any assumption regarding the shape of the volatility surface except to assume that it is smooth. Due to the smoothness assumption, we apply a second-order Tikhonov regularization. We choose the Tikhonov regularization parameter as one of the singular values of the Jacobian matrix of the Dupire model. Finally we perform extensive numerical tests to assess and verify the aforementioned techniques for both volatility models with known analytical solutions of European option prices and real market option data.     

尊重价值规律:人民币汇率形成机制改革未来之出路

“8.11”汇改,人民币汇率市场化改革又迈出重大步伐。进一步深化人民币汇率机制改革,必须尊重“价值决定价格、价格围绕价值上下波动”的价值规律。为此,要让市场在汇率形成中发挥越来越大的作用;要坚持强势人民币理念,不为市场预期所左右;要客服浮动恐惧,逐步调整适应人民币汇率双向波动新常态。同时,中央银行应保持对外汇市场的适度调控,防止汇率短期内过度波动或者长期偏离均衡水平。     

A Generalization of the Formulas for Options on the Maximum or the Minimum of Several Assets

Abstract

This paper generalizes the option on the maximum or the minimum of two assets (several assets) within a stochastic interest rate framework. A Gaussian model is used to describe the interest rates. Closed-form solutions for the market values are presented. The use of the options is illustrated with numerical examples.     

对城市商业银行实施新资本管理办法的调查思考

《商业银行资本管理办法（试行）》（以下简称《资本办法》）正式实施一年多来,深刻影响了我国银行业的经营发展。而实施新资本管理办法是一项复杂的系统工程,相比较大型银行而言,城市商业银行实施基础相对薄弱,面临的挑战更多、困难更大,需要主动转变传统粗放的经营理念和模式,搭建全面风险管理框架,真正实现经营转型。     

适度提高通胀容忍度有利于引导和管理通胀预期

中央银行应当致力于提高货币政策透明度,设置合适的通胀目标,以此引导和管理通胀预期。现阶段经济主体对通货膨胀的容忍度有所提高,适度提高通胀目标能减少频繁的目标偏离,增强中央银行的公信力,提高货币政策的有效性。实证研究表明,4.5%左右和[2%,6%]可以作为现阶段通胀目标值和目标区间的参考值。     

Predictability of structural co-movement in commodity prices: the role of technical indicators

This paper investigates the financialization and structural co-movement of several commodity futures using factor variance decomposition and predictability of technical indicators and macro variables. We find that financialization is still a dominant player in the commodity market and that recent commodity price fluctuations can be significantly and robustly forecasted by technical analyses of commodity index investments. Moreover, the co-movement of commodities is demonstrated by variance decomposition and explained as commodity index investment, which provides evidence of financialization. The overall empirical analysis reveals that technical indicators and macro variables can statistically and economically forecast the indexed investment and off-index trading, respectively, which indicates that they are suitable predictors of the commodity markets.     

金融开放条件下利率改革和汇率改革的协同效应分析

在金融开放条件下,汇率、利率与套利资本流动存在着内在联系,我国在进行汇率制度改革、货币政策改革与金融市场改革时,应注意三者协调发展和整体平衡,寻求利率政策与汇率政策之间的最佳政策组合,发挥利率改革和汇率改革的协同效应。为发挥金融改革协同效应,必须注重货币政策工具改革之间协调与配合,增强利率汇率的联动机制,积极推进与利率市场化相协调的汇率市场化形成机制,从而推动货币内外均衡进程。     

Errors and weaknesses detected by the European Court of Auditors in the reports on the European Structural Funds 2000–2004

The present paper shows the weaknesses and the errors detected by the European Court of Auditors (ECA) in the reports regarding the Structural Funds (the European Social Fund (ESF); the European Agricultural Guidance and Guarantee Fund, ‘Guidance’ section (EAGGF-Guidance), the European Regional Development Fund (ERDF) and the Financial Instrument for Fisheries Guidance (FIFG)), presented by 15 countries of the European Union from the year 2000 to 2004. We have classified the said countries in four groups, regarding the date of their EU incorporation. The main aim of our work is to highlight the errors made by the Member States on the management and control of the structural funds received from the EU, analysing the likely causes and consequences of such errors.     

沪深300指数期货价格随机利率效应研究

经典持有成本模型在非随机利率假设无法满足的条件下仅仅是远期合约而非期货的定价模型。本文采用拟合SHIBOR曲线的方法生成无风险纯折现债券模拟价格序列,对沪深300指数期货价格的随机利率效应进行了实证检验。研究结果表明,由于利率管制、股指期货市场和货币市场发展不成熟等因素的共同作用,沪深300指数期货价格中不含随机利率效应,指数远期和期货理论价格相等;如果持有成本模型其他假设条件也得到满足,则该模型可以用于沪深300指数期货定价。     

发展中国家的货币错配与汇率制度选择困境

货币错配是诱发发展中国家货币金融危机的一个重要因素,也加大了危机的解决成本。货币错配问题的形成是内外因素双重作用的结果,长期实行的“软”钉住汇率制度是其中的一个重要原因。发展中国家普遍遇到了货币错配与汇率制度选择的两难困境,僵硬的汇率制度为货币错配风险的累积提供了正向激励,加深了货币错配,货币错配程度的加深强化了汇率制度的“浮动恐惧”,必须采取有效措施走出这个困境。     

Two-Sided Bounds for Tails of Compound Negative Binomial Distributions in the Exponential and Heavy-Tailed Cases

This paper derives two-sided bounds for tails of compound negative binomial distributions, both in the exponential and heavy-tailed cases. Two approaches are employed to derive the two-sided bounds in the case of exponential tails. One is the convolution technique, as in Willmot & Lin (1997). The other is based on an identity of compound negative binomial distributions; they can be represented as a compound Poisson distribution with a compound logarithmic distribution as the underlying claims distribution. This connection between the compound negative binomial, Poisson and logarithmic distributions results in two-sided bounds for the tails of the compound negative binomial distribution, which also generalize and improve a result of Willmot & Lin (1997). For the heavy-tailed case, we use the method developed by Cai & Garrido (1999b). In addition, we give two-sided bounds for stop-loss premiums of compound negative binomial distributions. Furthermore, we derive bounds for the stop-loss premiums of general compound distributions among the classes of HNBUE and HNWUE.     

A data driven binning strategy for the construction of insurance tariff classes

We present a fully data driven strategy to incorporate continuous risk factors and geographical information in an insurance tariff. A framework is developed that aligns flexibility with the practical requirements of an insurance company, the policyholder and the regulator. Our strategy is illustrated with an example from property and casualty (P&C) insurance, namely a motor insurance case study. We start by fitting generalized additive models (GAMs) to the number of reported claims and their corresponding severity. These models allow for flexible statistical modeling in the presence of different types of risk factors: categorical, continuous, and spatial risk factors. The goal is to bin the continuous and spatial risk factors such that categorical risk factors result which captures the effect of the covariate on the response in an accurate way, while being easy to use in a generalized linear model (GLM). This is in line with the requirement of an insurance company to construct a practical and interpretable tariff that can be explained easily to stakeholders. We propose to bin the spatial risk factor using Fisher’s natural breaks algorithm and the continuous risk factors using evolutionary trees. GLMs are fitted to the claims data with the resulting categorical risk factors. We find that the resulting GLMs approximate the original GAMs closely, and lead to a very similar premium structure.