A flexible binomial option pricing model

This article develops a flexible binomial model with a “tilt” parameter that alters the shape and span of the binomial tree. A positive tilt parameter shifts the tree upward while a negative tilt parameter does exactly the opposite. This simple extension of the standard binomial model is shown to converge with any value of the tilt parameter. More importantly, the binomial tree can be recalibrated through the tilt parameter in order to position nodes relative to the strike price or barrier of an option. The rate of convergence is improved as a result. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 817–843, 1999     

On the rate of convergence of binomial Greeks

This study investigates the convergence patterns and the rates of convergence of binomial Greeks for the CRR model and several smooth price convergence models in the literature, including the binomial Black–Scholes (BBS) model of Broadie M and Detemple J ( 1996 ), the flexible binomial model (FB) of Tian YS ( 1999 ), the smoothed payoff (SPF) approach of Heston S and Zhou G ( 2000 ), the GCRR‐XPC models of Chung SL and Shih PT ( 2007 ), the modified FB‐XPC model, and the modified GCRR‐FT model. We prove that the rate of convergence of the CRR model for computing deltas and gammas is of order O(1/n), with a quadratic error term relating to the position of the final nodes around the strike price. Moreover, most smooth price convergence models generate deltas and gammas with monotonic and smooth convergence with order O(1/n). Thus, one can apply an extrapolation formula to enhance their accuracy. The numerical results show that placing the strike price at the center of the tree seems to enhance the accuracy substantially. Among all the binomial models considered in this study, the FB‐XPC and the GCRR‐XPC model with a two‐point extrapolation are the most efficient methods to compute Greeks. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark     

Condorcet's Jury Theorem and the reliability of majority voting

The effect on the Jury Theorem of dependency among votes is discussed. Condorcet's original model and theorem depend crucially on the assumption of independence and the applicability of the binomial distribution. Two simple extensions of the binomial distribution are used to illustrate the effects of dependency on the quality of group decision making. With the correlated binomial model, it is possible to isolate the effect of pairwise dependency. In the presence of fairly strong pairwise dependency, we are not even guaranteed the natural property of monotonicity with respect to voters. A Pólya-Eggenberger model illustrates the effect of contagion on group competence. A special case of the beta-binomial distribution is used to demonstrate that, even in the presence of synergetic group effects, we are not guaranteed infallible decisions from a very large group. Consequences for an epistemic theory of democracy are indicated.     

A Nonstandard Approach to Option Pricing

Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model.     

Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates

Black's (1995) model of interest rates as options assumes that there is a shadow instantaneous interest rate that can become negative, while the nominal instantaneous interest rate is a positive part of the shadow rate due to the option to convert to currency. As a result of this currency option, all term rates are strictly positive. A similar model was independently discussed by Rogers (1995) . When the shadow rate is modeled as a diffusion, we interpret the zero-coupon bond as a Laplace transform of the area functional of the underlying shadow rate diffusion (evaluated at the unit value of the transform parameter). Using the method of eigenfunction expansions, we derive analytical solutions for zero-coupon bonds and bond options under the Vasicek and shifted CIR processes for the shadow rate. This class of models can be used to model low interest rate regimes. As an illustration, we calibrate the model with the Vasicek shadow rate to the Japanese Government Bond data and show that the model provides an excellent fit to the Japanese term structure. The current implied value of the instantaneous shadow rate in Japan is negative.     

Simultaneous option prices and an implied risk-free rate of interest: A test of the Black-Scholes models

Two parameters in the Black-Scholes model, the risk-free rate of interest and standard deviation of stock returns, cannot be directly observed. Nevertheless, it is possible to simultaneously solve for the two parameters by using the prices of two different options written on the same security. If the Black-Scholes model is valid, then the implied interest rate from one repair of options should equal the implied interest rate from another pair of options for a given trading day. The analysis reexamines simultaneous option price data from a previous study using the implied interest rate test, and the results support the validity of the Black-Scholes model if we consider the bid/ask spread of option prices and that options are traded over discrete intervals.     

Interest Rate Dynamics and Consistent Forward Rate Curves

We consider as given an arbitrage‐free interest rate model M, and a parametrized family of forward rate curves G. We study the question as to when the given family G is consistent with the dynamics of the interest rate model M, in the sense that M actually will produce forward rate curves belonging to G. We allow the interest rate model to be driven by a multidimensional Wiener process, as well as by a marked point process, and we give necessary and sufficient conditions for consistency. As test cases, we study some popular models, obtaining both positive and negative results about consistency. We also introduce a natural exponential‐polynomial family of forward rate curves, and for this family we give necessary and sufficient conditions for the existence of consistent interest rate models with deterministic volatility functions.     

"利率通道"调控模式对我国利率市场化改革的启示

金融自由化理论的发展对各国金融改革提供了理论支持,我国正在进行的利率市场化改革,迫切需要构建适合实际和发展需要的利率调控模式,所以必须了解“利率通道”调控模式的运行机制,运用实证数据对“利率通道”调控模式进行模拟分析,从而建立以“利率通道”调控为主、公开市场操作调控为辅的利率调控模式作为我国利率市场化改革的选择。     

The rise of dollar credit in emerging market economies and US monetary policy

This paper examines the hypothesis that the boom in dollar credit in emerging market economies (EMEs) is associated with an excessively low interest rate in the US. For this purpose, we use a multivariate correlated unobserved component model that allows for correlation between shocks to dollar credit, cross‐border interest rate gaps—measured as the difference between emerging market interest rate and the US interest rate, and dollar index both in the short run and in the long run. In addition, it also provides us a quantitative estimate of the permanent and transitory movements in dollar credit in EMEs, interest rate gaps and dollar index. The results from this model do suggest that a temporary increase in interest rate gaps and decline in the dollar index are associated with a temporary increase in the dollar credit in EMEs with a very high degree of correlation. The estimate of the cyclical component of the dollar credit in EMEs from our model captures the recent boom and bust in this market and compares favourably to alternative trend–cycle decomposition methods.     

Interest Rate,Currency and Equity Derivatives Valuation Using the Potential Approach

Based on the potential approach to interest rate modelling, we introduce a simple tractable model for the unified valuation of interest rate, currency and equity derivatives. Our model is able to accommodate the initial term structure of zero‐coupon bond prices, generate positive and bounded interest rates, and handle cross products such as differential swaps, quanto options and equity swaps. As our model is specified under the actual probability measure, it can be directly used for portfolio risk management and the computation of value at risk. Furthermore, our model yields simple analytical formulas that are easy to calibrate and implement.     

Option pricing for the transformed‐binomial class

This article generalizes the seminal Cox‐Ross‐Rubinstein (1979) binomial option pricing model to all members of the class of transformed‐binomial pricing processes. The investigation addresses issues related with asset pricing modeling, hedging strategies, and option pricing. Formulas are derived for (a) replicating or hedging portfolios, (b) risk‐neutral transformed‐binomial probabilities, (c) limiting transformed‐normal distributions, and (d) the value of contingent claims, including limiting analytical option pricing equations. The properties of the transformed‐binomial class of asset pricing processes are also studied. The results of the article are illustrated with several examples. © 2006 Wiley Periodicals, Inc. Jrl. Fut Mark 26:759–787, 2006     

人民币利率对汇率影响的实证研究：1981—2003

定量分析人民币利率对汇率长期走势与短期波动的影响,对于中国利率市场化与汇率制度选择等问题意义重大.对时间序列变量进行单位根检验、协整检验,以及建立误差修正模型等实证研究表明:无论在长期还是短期,人民币利率对汇率都是反向影响.长期内,利率对人民币汇率存在较强的影响;短期内,利率对人民币汇率影响较弱.我国利率主要还是通过商品市场间接地对汇率产生作用.     

Asymptotics of the price oscillations of a European call option in a tree model

It is well known that the price of a European vanilla option computed in a binomial tree model converges toward the Black-Scholes price when the time step tends to zero. Moreover, it has been observed that this convergence is of order 1/ n in usual models and that it is oscillatory. In this paper, we compute this oscillatory behavior using asymptotics of Laplace integrals, giving explicitly the first terms of the asymptotics. This allows us to show that there is no asymptotic expansion in the usual sense, but that the rate of convergence is indeed of order 1/ n in the case of usual binomial models since the second term (in     ) vanishes. The next term is of type   C ₂( n )/ n   , with   C ₂( n )  some explicit bounded function of n that has no limit when n tends to infinity.     

Nonconvergence in the Variation of the Hedging Strategy of a European Call Option

In this paper we consider the variation of the hedging strategy of a European call option when the underlying asset follows a binomial tree. In a binomial tree model the hedging strategy of a European call option converges to a continuous process when the number of time points increases so that the price process of the underlying asset converges to a Brownian motion, the Bachelier model. However, the variation of the hedging strategy need not converge to the variation of the limit process. In fact, it is shown that the asymptotic variation of the hedging strategy may be of any order.     

INTEREST RATE,DEBT, DISTRIBUTION AND CAPITAL ACCUMULATION IN A POST‐KALECKIAN MODEL

In the present paper we extend Lavoie's (Metroeconomica, 1995, vol. 46, pp. 146–177) ‘Minsky–Steindl’ model, building our analysis on a Kaleckian distribution and growth model which has already taken into account distribution effects of interest rate variations on the short‐run equilibrium. Into this model the effects of debt and debt services are explicitly introduced and the effects of interest rate variations on the short‐ and the long‐run equilibrium are derived. It is shown that the effects of interest rate variations on the endogenously determined equilibrium values of the model not only depend on the parameter values in the saving and investment functions but also on the interest elasticity of distribution and on initial conditions with respect to the interest rate and the debt–capital ratio.     

Short Rate Dynamics and Regime Shifts*

We characterize the dynamics of the US short‐term interest rate using a Markov regime‐switching model. Using a test developed by Garcia, we show that there are two regimes in the data: In one regime, the short rate behaves like a random walk with low volatility; in another regime, it exhibits strong mean reversion and high volatility. In our model, the sensitivity of interest rate volatility to the level of interest rate is much lower than what is commonly found in the literature. We also show that the findings of nonlinear drift in Aït‐Sahalia and Stanton, using nonparametric methods, are consistent with our regime‐switching model.     

调整个人储蓄利息所得税率对我国稳态人均消费的影响——基于拉姆齐模型的实证研究

本文将利息税引入拉姆齐模型,求出稳态人均消费路径.利用经验数据动态模拟与实证分析,发现调整利息税率对我国人均消费的影响有两种效应:"从短期来看,降低利息税率将使人均消费减少;从长期来看,降低利息税率将提高我国稳态人均消费水平".因此,在当前急需拉动内需之时,我国不应降低而应提高利息税率.     

A study of the effect of OHSAS 18001 on the occupational injury rate in Iran

The occupational health and safety management system (OHSMS) has been a widely used approach for managing occupational health and safety more effectively worldwide. Despite the interest of organizations in implementing OHSMS in recent decades, few studies have examined the effectiveness of these interventions. This study presents an empirical investigation of the effect of occupational health and safety assessment series (OHSAS) 18001 as a worldwide-accepted OHSMS on the occupational injury rate (OIR) in Iran. This study was carried out in six companies: three OHSAS 18001-certified, and three non-certified, including 998 occupational injuries for 15,842 person-months. A before–after analysis showed a positive safety performance change in one out of the three certified companies. For all 66 study years in the six companies, a negative binomial regression did not indicate a lower occupational injury during the certified years and a repeated measures analysis of variance (ANOVA) did not confirm the effect of certification. The results of this study indicated that the implementation of OHSAS 18001 is not a guarantee of improved safety.     

货币政策的利率期限结构效应的理论解释及其经验证据

文章首先运用一个利率期限结构的预期理论模型,证明了“在预期假说框架内货币政策只能引起收益率曲线平行移动而不会改变它的坡度”这一论断是错误的;接下来运用一个局部均衡模型在利率期限结构的预期理论框架下,证明了货币政策行动模式（参数）会影响货币政策对市场利率的影响效果、利率期限结构（收益率曲线）的斜率及其动态特征;之后用一个基于中关两国比较的经验证据说明上述理论解释的可靠性。     

Does the world real interest rate affect the real exchange rate? The South East Asian experience

Abstract

We analyze the consequences of US real interest rate rises on the real exchange rate (RER) in a two-good overlapping generations model of a semi-small open economy. The equilibrium RER depreciates (appreciates) when the world interest rate increases in a debtor (creditor) country. We then study empirically the reaction of the RER in a set of South East Asian (SEA) countries to shocks in US real interest rates. The results support the conclusions of the theory model at least for Singapore, Thailand and South Korea during the period 1980 – 2001. This points towards world interest rate shocks as possible trigger factors for exchange rate crises during the adjustment process towards the new equilibrium.