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.     

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.     

权证对投资者投资偏好影响的实证研究

金融衍生产品的出现提高了证券市场信息传递的速度，知情交易者通过对衍生品的投资提高传递的效率。本文通过对我国权证市场和相应标的股票市场交易高频数据的研究，探讨知情交易者在权证市场出现后是否改变了投资的对象。实证结果表明，尽管有部分知情交易者投资了认购权证，但是并没有证据表明知情交易者偏好认沽权证。造成这一结果的原因可能是权证制度自身的缺陷。     

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     

Entry in the presence of dueling options

This paper investigates the influence of industry uncertainty on the decision by established firms to enter a new industry. Specifically, we examine the tension between the option to defer , which discourages entry in the presence of uncertainty, and the option to grow , which may encourage entry in the presence of uncertainty when there are early mover advantages. Empirical analysis on data from a broad array of industries revealed that the effect of uncertainty on entry is not monotonic. Our findings are the first to find support for the nonmonotonic effect of uncertainty that has only recently emerged in theoretical treatments of real options theory, and amplify the importance of considering both the option to defer and the option to grow when contemplating entry. Furthermore, we found evidence that the relationship between uncertainty and entry is moderated by: (a) irreversibility, which influences the value of the option to defer; (b) the total value of growth opportunities; and (c) early mover advantages, which magnify the value of growth options. Copyright © 2003 John Wiley & Sons, Ltd.     

浅谈煤制甲醇项目的煤气化技术选择

石油是一种不可再生资源,必须要寻求新能源的制造方法,其中,甲醇的大规模生产也受到了各个国家有关部门的高度重视。本文主要从原料、产品与投资方面几个方面对多喷嘴对置式水煤浆气化技术、Shell技术、BGL煤熔渣气化工艺进行分析,得出最优的生产技术。