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.     

高科技企业的合约特征与企业家性质

本文试图说明，从传统企业到高科技企业在契约性质上实现了从劳动合约到知识合约的转变，高科技企业的合约特征是通过知识合约实现企业家的创新精神，是一种创新行为的特定制度安排。     

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.     

On the Distribution of CBOE Option Trade Prices Occurring Between Consecutive Stock Trades

This paper examines the volume distribution of option trade prices that occurs when the underlying stock price remains constant. The width of these option trade price bands provides direct evidence on the law of one price and the redundancy of options assumed in many option models. We find that index option bands are narrower than equity option bands. Furthermore, for both equity and index options, puts have narrower bandwidths than calls. In general, option price bandwidth is narrow and can be explained by the minimum price movement allowed by the Chicago Board Options Exchanges (CBOE). This supports the single price law and the redundancy assumption. The existence of bid/ask quotes on the option does not materially affect the above results although it does alter the frequency of multiple option trade prices for a given underlying stock price. We note that over 53% of option trading volume occurs without bid/ask quotes on the CBOE compared to less than 15% a decade ago. Our results suggest that the effective bid/ask spread on options is probably no larger than the minimum price movements allowed by the CBOE. Furthermore, the need for the liquidity services of market makers may be declining if the decline in quoting activity stems from cross trading (i.e. trades not involving market makers).     

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.     

Do the Forward Sales of Real Estate Stabilize Spot Prices?

We examine the effect of forward sale (pre-sale) activities on the volatility of spot prices in the real estate market. The abundance of pre-sales data and major changes in regulatory control on the pre-sale market during the 90's in Hong Kong allow us to undertake empirical tests using Hong Kong's real estate data. Our results show that the volatility of spot prices increased significantly after forward sales were severely dampened by regulatory control measures introduced in 1994, but decreased again when the measures were partly relaxed in 1998. The results contribute to the long lasting debate on whether the introduction of a futures market reduces the volatility of spot prices. Previous studies were mainly conducted in markets with low transaction costs, notably financial markets. By utilizing the unique regulatory changes in the pre-sale market of Hong Kong, we are able to conduct an experiment on the conditional volatility of spot prices in a high information-cost environment, thereby shedding light on the important role of forward housing contracts in providing price expectation information for spot trading.     

Do executive stock option grants have value implications for firm performance?

Consistent with predictions of agency theory, we find direct evidence that executive stock option grants have value implications for firm performance. This inference is drawn from evaluation of various motivations for the use of such grants in executive compensation: value enhancement, risk taking, tax benefit, signaling and cash conservation. We find consistent evidence for the value enhancement motivation to reduce agency costs. As well, they signal for positive price sensitive information. Our results reject the tax benefit and cash conservation motivations. This finding is robust after controlling for the endogenous character of executive stock option grants and other equity-based grants. JEL Classification G32 • J33 • M52     

基于"综合谈判力"的企业所有权安排

现代企业理论打开了“企业”这一“黑箱”,为理解和创建现代企业制度提供了有力的理论支撑。本文通过对企业各要素所有者谈判力三个方面,即:签约人自身实力、签约人相互关系地位、签约外部环境的具体分析,阐释了各要素所有者对企业剩余的分享,并以此初步构建一个以企业要素所有者“综合谈判力”为基础的企业所有权安排分析框架。