A new closed-form solution as an extension of the Black–Scholes formula allowing smile curve plotting

In this paper, as a generalization of the Black–Scholes (BS) model, we elaborate a new closed-form solution for a uni-dimensional European option pricing model called the J-model. This closed-form solution is based on a new stochastic process, called the J-process, which is an extension of the Wiener process satisfying the martingale property. The J-process is based on a new statistical law called the J-law, which is an extension of the normal law. The J-law relies on four parameters in its general form. It has interesting asymmetry and tail properties, allowing it to fit the reality of financial markets with good accuracy, which is not the case for the normal law. Despite the use of one state variable, we find results similar to those of Heston dealing with the bi-dimensional stochastic volatility problem for pricing European calls. Inverting the BS formula, we plot the smile curve related to this closed-form solution. The J-model can also serve to determine the implied volatility by inverting the J-formula and can be used to price other kinds of options such as American options.     

美式期权的Monte Carlo模拟法定价理论及应用

近年来随着计算机技术的飞速发展,美式期权的Monte Carlo模拟法定价取得了实质性的突破。本文分析介绍了美式期权的Monte Carlo模拟法定价理论及在此基础上推导出的线性回归MonteCarlo模拟法定价公式及其在实际的应用。     

On the use of options by mutual funds: Do they know what they are doing?

Given recent regulatory inquiries into the derivative-trading practices of mutual funds, we examine their detailed option holdings to assess how mutual funds employ options, what funds use options, and how that affects performance and risk. Mutual funds’ use of options appears consistent with income generation and hedging motives, is systematically related to experience, education, and gender characteristics of portfolio managers, and does not lead to performance benefits, on average. Instead, certain uses of options lead to underperformance. We document no permanent or temporary aggressive risk taking by options users, finding instead that some funds use options to effectively lower risk.     

Investment decisions in finite-lived monopolies

This paper studies the value and optimal timing for investment in finite-lived monopolies, extending the literature on real option games by considering the cases of random and certain-lived monopolies. Under these settings, firms face the risk of demonopolization, that can occur as a random or a certain event. We show that these new settings produce significantly different results when compared to the canonical monopolistic and duopolistic models. In a certain-lived monopoly, the leader invests sooner than in a duopoly if there is a risk of being preempted, and later than in a monopoly if the leader role is pre-assigned. In a random-lived monopoly, entry occurs somewhere between the duopoly and monopoly cases. Higher uncertainty delays investment in all cases.     

Some problems in actuarial finance involving sums of dependent risks

A trend in actuarial finance is to combine technical risk with interest risk. If Y_t , t = 1, 2, denotes the timevalue of money (discount factors at time t ) and X_t the stochastic payments to be made at time t , the random variable of interest is often the scalar product of these two random vectors V = X_t Y_t . The vectors X and Y are supposed to be independent, although in general they have dependent components. The current insurance practice based on the law of large numbers disregards the stochastic financial aspects of insurance. On the other hand, introduction of the variables Y ₁, Y ₂, to describe the financial aspects necessitates estimation or knowledge of their distribution function.
We investigate some statistical models for problems of insurance and finance, including Risk Based Capital/Value at Risk, Asset Liability Management, the distribution of annuities, cash flow evaluations (in the framework of pension funds, embedded value of a portfolio, Asian options) and provisions for claims incurred, but not reported (IBNR).     

基于期权博弈的战略投资决策分析

基于期权博弈的战略投资一般通过两阶段（战略研发投资阶段和商业化阶段）进行。企业战略投资的最佳时机选择本质上是对投资期权的灵活性价值与竞争战略占先价值之间进行权衡，从而实现企业价值的最大化。而企业的战略选择根据研发是竞争还是合作，研发投资的利益为竞争企业独占还是共享，以及商业化竞争是战略替代还是战略互补而有所不同。不确定性、不对称信息以及学习效应等都对企业的投资时机及投资价值产生一定的影响。     

Maturity and volatility effects on UK smiles

The smile effect is a result of an empirical observation of the options implied volatility with the same expiration date, across different exercise prices. However, its shape has been under discussion seeming to be dependent on the option underlying security. In this paper, and filling up a scarce empirical research on the topic, we used liquid equity options on 9 stocks traded on the London International Financial Futures and Options Exchange (LIFFE) between August 1990 and December 1991. We tested two different hypothesis for testing two different phenomena: (1) the increase of the smile as maturity approaches; (2) and the association between the smile and the volatility of the underlying stock. In order to estimate implied volatilities for unavailable exercise prices, we modelled the smile using cubic B-spline curves. We found empirical support for the smile intensification (the U-shape is more pronounced) as maturity approaches as well as when volatility rises. However, we found two major sources of disagreement with the literature on stochastic volatility models. First, as maturity approaches, out-of-the-money options implied volatility tends to be higher than the implied volatility of in-the-money options. Second, as the volatility of the underlying asset increases, the implied volatility of in-the-money options tends to be higher than implied volatility of out-of-the-money options.Received: September 2001, Accepted: September 2003, JEL Classification: G13Correspondence to: João L. C. DuqueWe thank Professor Dean A. Paxson (University of Manchester), António Sousa Câmara (University of Strathclyde), Ser-Huang Poon (University of Lancaster) and the attendees of the 26th EFA Annual Conference for helpful comments on previous versions of this paper. We also want to thank to two anonymous referees for their relevant comments and suggestions. Financial support granted by the Fundação para a Ciência e a Tecnologia (FCT) and the Programa Praxis XXI is gratefully acknowledged.     

薪酬激励差异分析:工资薪金与股票期权

工资薪金和股票期权是现代企业员工薪酬激励的两种重要形式。两种薪酬激励在属性、效应、适用的税收政策等方面存在着多项差异。了解并掌握这些差异,有利于企业所有者从两种薪酬激励的风险程度、激励效应和税负水平出发,结合企业实际运营情况和目标水平,建立最有效的薪酬激励体系。     

Valuation of options on the maximum of two prices with default risk under GARCH models

In this paper, we work under GARCH models to value options on the maximum or the minimum of two prices. In addition, we consider not only two underlying asset prices but also geometric average ones. Further, default risk is also incorporated in a reduced-form model. In the proposed framework, closed-form pricing formulae of options on the maximum with or without default risk are derived and then used to perform numerical examples.     

Put-call parity revisited: intradaily tests in the foreign currency options market

We test exchange-traded (PHLX) German mark options for conformance to put-call parity (PCP). Puts and calls are matched to the nearest minute, and the relative impact of competing spot exchange rate sources (Reuters vs. Telerate) is assessed. We find that PCP usually holds (roughly 96% of put-call pairs), with the exception of a notable incident in the European options pits. In those instances in which PCP is violated, we find sharp intradaily and intraweekly seasonalities for American options, with disproportionate PCP violations occurring during the relatively light trading periods in early evening and on Fridays. We also conclude that the Telerate prices as recorded by the PHLX are not as accurate as the Reuters exchange rates provided by Olsen and Associates, probably because of time lags in the Telerate data.