Convergence of numerical methods for valuing path-dependent options using interpolation

One method for valuing path-dependent options is the augmented state space approach described in Hull and White (1993) and Barraquand and Pudet (1996), among others. In certain cases, interpolation is required because the number of possible values of the additional state variable grows exponentially. We provide a detailed analysis of the convergence of these algorithms. We show that it is possible for the algorithm to be non-convergent, or to converge to an incorrect answer, if the interpolation scheme is selected in appropriately. We concentrate on Asian options, due to their popularity and because of some errors in the previous literature. This revised version was published online in June 2006 with corrections to the Cover Date.     

从博弈的角度看中小股东解决纠纷的过程--从一个流行模型的残缺谈起

经研究发现 ,张维迎教授在 2 0 0 1年第五版的《博弈论与信息经济学》中所借用的承诺要胁诉讼博弈例子中对诉讼费用的处理有点不妥 ,便作出了适当的调整 ,但却得出了令人沮丧的结论 :承诺要胁诉讼不成立 !继续研究发现只有打破这种败诉风险由当事人承担的机制 ,才能传递出有力量的信号 ,才能做到真正的威胁 ,那就是建立“生死与共”的竞争性的律师定价机制和保费率真正是胜诉率信号的诉讼费用保险机制与最经济的诉讼程序与非诉讼程序、保障其实现的机制和可供的备选机制。本文论证了其合理性     

Pricing U.S. Dollar Index Futures Options: An Empirical Investigation

This paper develops a pricing model and empirically tests the pricing efficiency of options on the U.S. Dollar Index (USDX) futures contract. Empirical tests of the model indicate that the market consistently overprices these options relative to the derived model. This overpricing is more pronounced for out‐of‐the‐money options than for in‐the‐money options and more pronounced for put options than for call options. To validate the above results, delta neutral portfolios are created for one‐ and two‐day holding periods and consistently generate positive arbitrage profits, indicating that on average the market overprices the options on the USDX futures contracts.     

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.     

Observable Consequences of Trading Structure Differences: On the Use of Variance Ratios in Microstructure Studies

This paper examines the variance ratio tests in studies of transitory volatility and concludes that the variance ratio is an appropriate test of trading structure differences only under certain assumptions regarding the evolution of underlying stock prices and the autocorrelation structure of returns. This result raises caution as to the interpretation of results bases upon the 24-hour variance ratio methodologies in studies of transitory volatility and trading structure effects. A numerical example indicates that errors in inferences can be severe.     

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.     

Pricing and hedging power options

In this paper we study the pricing and hedging of options whose payoff is a polynomial function of the underlying price at expiration; so-called ‘power options’. Working in the well-known Black and Scholes (1973) framework we derive closed-form formulas for the prices of general power calls and puts. Parabola options are studied as a special case. Power options can be hedged by statically combining ordinary options in such a way that their payoffs form a piecewise linear function which approximates the power option's payoff. Traditional delta hedging may subsequently be used to reduce any residual risk.     

An outcome-based assessment of international transfer pricing policy

Instead of concentrating on the selection of the optimal transfer pricing method, this paper focuses on the consequences of international transfer pricing for multinational entities. A sample of U.S.-based multinational firms is employed to determine if transfer pricing results in measurable financial outcomes. Results of the study indicate that firms employ international transfer pricing to meet a variety of objectives. The dollar value of international transfers and the foreign sales percentage are both significant explanatory variables for the financial outcomes of these objectives.