Sub-Replication and Replenishing Premium: Efficient Pricing of Multi-State Lookbacks

The direct valuation procedure of performing discounted expectation to obtain the prices of multi-state lookback options may lead to insurmountable complexity and numerical difficulties. The computation may require numerical differentiation of the joint distribution function of the extremum values, then followed by numerical integration over a semi-infinite domain. In this paper, we illustrate the use of an alternative approach that significantly simplifies the calculations of multi-state lookback option prices. The financial intuition behind the new approach involves the choice of a sub-replicating portfolio and the adoption of the corresponding replenishing strategy to achieve the subsequent full replication of the derivative. The replenishing premium is obtained by performing the integration of an appropriate distribution function over the range of asset price within which under replication occurs. The sub-replication and replenishment procedures may be utilized as hedging strategies for the lookback options. The pricing and hedging properties of multi-state lookback options are also discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Impact of Divergent Consumer Confidence on Option Prices

This paper investigates the impact of divergent consumer confidence on option prices. To model this, we assume that consumers disagree on the expected growth rate of aggregate consumption. With other conditions unchanged in the discrete-time Black–Scholes option-pricing model, we show that the representative consumer will have declining relative risk aversion instead of the assumed constant relative risk aversion. In this case all options will be underpriced by the Black–Scholes model under the assumption of bivariate lognormality. This revised version was published online in June 2006 with corrections to the Cover Date.     

Option pricing in the presence of natural boundaries and a quadratic diffusion term

This paper uses a probabilistic change-of-numeraire technique to compute closed-form prices of European options to exchange one asset against another when the relative price of the underlying assets follows a diffusion process with natural boundaries and a quadratic diffusion coefficient. The paper shows in particular how to interpret the option price formula in terms of exercise probabilities which are calculated under the martingale measures associated with two specific numeraire portfolios. An application to the pricing of bond options and certain interest rate derivatives illustrates the main results.     

Binomial Option Pricing with Skewed Asset Returns

This research presents a method for estimating the parameters of the binomial option pricing model necessary to appropriately price calls on assets with asymmetric end-of-period return distributions. Parameters of the binomial model are shown to be a function of the mean, variance, and skewness of the underlying return distribution. It is also shown that failure to incorporate skewness results in the mispricing of the call.     

股票增值权激励有效吗

股票增值权是上市公司对管理层实施激励的重要做法，在我国大型国有控股境外上市公司中普遍采用。本文以中国石化为研究对象，对实施股票增值权计划后的公司财务绩效、治理机制与管理层代理成本、股票市场反应等作了实证检验。本文认为，股票增值权计划对公司财务绩效提升、治理机制改善具有一定的积极正面效应；股票增值权在等待期结束后的开始行权年度激励效果最大；股票市场对股票增值权的行权存在着过度反应。最后本文提出了改进股票增值权激励的政策建议。     

American Parisian options

In this article, we describe the various sorts of American Parisian options and propose valuation formulae. Although there is no closed-form valuation for these products in the non-perpetual case, we have been able to reformulate their price as a function of the exercise frontier. In the perpetual case, closed-form solutions or approximations are obtained by relying on excursion theory. We derive the Laplace transform of the first instant Brownian motion reaches a positive level or, without interruption, spends a given amount of time below zero. We perform a detailed comparison of perpetual standard, barrier and Parisian options.     

Valuation of vulnerable American options with correlated credit risk

This article evaluates vulnerable American options based on the two-point Geske and Johnson method. In accordance with the Martingale approach, we provide analytical pricing formulas for European and multi-exercisable options under risk-neutral measures. Employing Richardson’s extrapolation gets the values of vulnerable American options. To demonstrate the accuracy of our proposed method, we use numerical examples to compare the values of vulnerable American options from our proposed method with the benchmark values from the least-square Monte Carlo simulation method. We also perform sensitivity analyses for vulnerable American options and show how the prices of vulnerable American options vary with the correlation between the underlying assets and the option writer’s assets.      

A semi-analytic method for valuing high-dimensional options on the maximum and minimum of multiple assets

Valuing high-dimensional options has many important applications in finance but when the true distributions are unknown or complex, numerical approximations must be used. Approximation methods based on Monte-Carlo simulation show a steep trade-off between estimation accuracy and computational efficiency. This article presents an alternative semi-analytic approximation method for pricing options on the maximum or minimum of multiple assets with unknown distributions. Computational efficiency is shown to improve significantly without sacrificing estimation accuracy. The method is illustrated with applications to options on underlying assets with mean-reverting prices, time-dependent correlations, and stochastic volatility The authors would like to thank the two anonymous referees, the associate editor, and Dr. Jess H. Chua at the University of Calgary for valuable comments and insights on this research. This research was partly supported by NUS grant R-146-000-059-112     

Assessing the Least Squares Monte-Carlo Approach to American Option Valuation

A detailed analysis of the Least Squares Monte-Carlo (LSM) approach to American option valuation suggested in Longstaff and Schwartz (2001) is performed. We compare the specification of the cross-sectional regressions with Laguerre polynomials used in Longstaff and Schwartz (2001) with alternative specifications and show that some of these have numerically better properties. Furthermore, each of these specifications leads to a trade-off between the time used to calculate a price and the precision of that price. Comparing the method-specific trade-offs reveals that a modified specification using ordinary monomials is preferred over the specification based on Laguerre polynomials. Next, we generalize the pricing problem by considering options on multiple assets and we show that the LSM method can be implemented easily for dimensions as high as ten or more. Furthermore, we show that the LSM method is computationally more efficient than existing numerical methods. In particular, when the number of assets is high, say five, Finite Difference methods are infeasible, and we show that our modified LSM method is superior to the Binomial Model.