随机执行日经理股票期权的定价及激励效用分析

针对标准支付型经理股票期权执行日确定的问题,提出具有随机执行日的支付型经理股票期权的定价公式;选择期权价值对股票价格的敏感性(delta)、期权价值对股票收益波动率的敏感性(vega)对经理股票期权进行激励效用分析;并通过改变部分参数的值,分析期权对经理激励作用的变化.     

Option pricing under joint dynamics of interest rates, dividends, and stock prices

This paper proposes a unified framework for option pricing, which integrates the stochastic dynamics of interest rates, dividends, and stock prices under the transversality condition. Using the Vasicek model for the spot rate dynamics, I compare the framework with two existing option pricing models. The main implication is that the stochastic spot rate affects options not only directly but also via an endogenously determined dividend yield and return volatility; consequently, call prices can be decreasing with respect to interest rates.     

再装股票期权的Esscher变换定价

近年来,公司为了吸引和激励股票的执行者而引入了一系列的非传统期权.本文将讨论其中的一种:再装期权,运用Esscher变换给出了再装期权(只装一次)的闭式解,并提供了数值计算的例子,为实践者提供了理论上的参考价格.     

Stochastic equity volatility related to the leverage effect II: valuation of European equity options and warrants

We propose a general framework to assess the value of the financial claims issued by the firm, European equity options and warrantsin terms of the stock price. In our framework, the firm's asset is assumed to follow a standard stationary lognormal process with constant volatility. However, it is not the case for equity volatility. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firm's assets on the financial leverage. In a previous paper we studied the stochastic process for equity volatility, and proposed analytic approximations for different capital structures. In this companion paper we derive analytic approximations for the value of European equity options and warrants for a firm financed by equity, debt and warrants. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities either as a function of the stock price, or as a function of the firm's total assets. Since stock prices are observable, then for practical purposes, traders prefer to use the stock as the underlying instrument, we concentrate on valuation models in terms of the stock price. Second, we derive an exact solution for the valuation in terms of the stock price of (i) a European call option on the stock of a levered firm, i.e. a European compound call option on the total assets of the firm, (ii) an equity warrant for an all-equity firm, and (iii) an equity warrant for a firm financed by equity and debt. Unfortunately, to compute these solutions we need to specify the function of the stock price in terms of the firm's assets value. In general we are unable to specify this expression, but we propose tight bounds for the value of these options which can be easily computed as a function of the stock price. Our results provide useful extensions of the Black-Scholes model.     

Fixed versus flexible production systems: A real options analysis

In this work, we address investment decisions in production systems by using real options. As is standard in literature, the stochastic variable is assumed to be normally distributed and then approximated by a binomial distribution, resulting in a binomial lattice. The methodology establishes a discrete-valued lattice of possible future values of the underlying stochastic variable (demand in our case) and then, computes the project value. We have developed and implemented stochastic dynamic programming models both for fixed and flexible capacity systems. In the former case, we consider three standard options: the option to postpone investment, the option to abandon investment, and the option to temporarily shut-down production. For the latter case, we introduce the option of corrective action, in terms of production capacity, that the management can take during the project by considering the existence of one of the following: (i) a capacity expansion option; (ii) a capacity contraction option; or (iii) an option considering both expansion and contraction. The full flexible capacity model, where both the contraction and expansion options exist, leads, as expected, to a better project predicted value and thus, investment policy. However, we have also found that the capacity strategy obtained from the flexible capacity model, when applied to specific demand data series, often does not lead to a better investment decision. This might seem surprising, at first, but it can be explained by the inaccuracy of the binomial model. The binomial model tends to undervalue future decreases in the stochastic variable (demand), while at the same time tending to overvalue an increase in future demand values.     

A Pricing Model for American Options with Gaussian Interest Rates

In this paper we introduce a new methodology to price American put options under stochastic interest rates. We derive an analytic approximation that can be evaluated very fast and is fairly accurate. The method uses the so-called forward risk adjusted measure to derive analytic prices. We show that for American puts the correlation between the stock price and the interest rate has different influences on European option values and early exercise premiums.     

Market calibration under a long memory stochastic volatility model

In this article, we study a long memory stochastic volatility model (LSV), under which stock prices follow a jump-diffusion stochastic process and its stochastic volatility is driven by a continuous-time fractional process that attains a long memory. LSV model should take into account most of the observed market aspects and unlike many other approaches, the volatility clustering phenomenon is captured explicitly by the long memory parameter. Moreover, this property has been reported in realized volatility time-series across different asset classes and time periods. In the first part of the article, we derive an alternative formula for pricing European securities. The formula enables us to effectively price European options and to calibrate the model to a given option market. In the second part of the article, we provide an empirical review of the model calibration. For this purpose, a set of traded FTSE 100 index call options is used and the long memory volatility model is compared to a popular pricing approach – the Heston model. To test stability of calibrated parameters and to verify calibration results from previous data set, we utilize multiple data sets from NYSE option market on Apple Inc. stock.     

The pricing of Asian options under stochastic interest rates

The purpose of this paper is to analyse the effect of stochastic interest rates on the pricing of Asian options. It is shown that a stochastic, in contrast to a deterministic, development of the term structure of interest rates has a significant influence. The price of the underlying asset, e.g. a stock or oil, and the prices of bonds are assumed to follow correlated two-dimensional Itô processes. The averages considered in the Asian options are calculated on a discrete time grid, e.g. all closing prices on Wednesdays during the lifetime of the contract. The value of an Asian option will be obtained through the application of Monte Carlo simulation, and for this purpose the stochastic processes for the basic assets need not be severely restricted. However, to make comparison with published results originating from models with deterministic interest rates, we will stay within the setting of a Gaussian framework.     

Pricing currency options under two-factor Markov-modulated stochastic volatility models

This article investigates the valuation of currency options when the dynamic of the spot Foreign Exchange (FX) rate is governed by a two-factor Markov-modulated stochastic volatility model, with the first stochastic volatility component driven by a lognormal diffusion process and the second independent stochastic volatility component driven by a continuous-time finite-state Markov chain model. The states of the Markov chain can be interpreted as the states of an economy. We employ the regime-switching Esscher transform to determine a martingale pricing measure for valuing currency options under the incomplete market setting. We consider the valuation of the European-style and American-style currency options. In the case of American options, we provide a decomposition result for the American option price into the sum of its European counterpart and the early exercise premium. Numerical results are included.     

双边敲出障碍期权定价模型

本文针对经理通过操纵股价牟利和非公司经营业绩下滑 ,股价下跌给经理期权收益造成损失两方面的问题 ,提出采用限制股票价格变化的方式 ,计算经理股票期权收益 ,构建了双障碍敲出期权用于经理激励 ,并给出了与 Black- Scholes公式的对比分析 .     

A closed form solution for vulnerable options with Heston’s stochastic volatility

Over-the-counter stock markets in the world have been growing rapidly and vulnerability to default risks of option holders traded in the over-the-counter markets became an important issue, in particular, since the global finance crisis and Eurozone crisis. This paper studies the pricing of European-type vulnerable options when the underlying asset follows the Heston dynamics. In this paper, we obtain a closed form analytic formula of the option price as a stochastic volatility extension of the classical Heston formula and find how the stochastic volatility effect on the Black–Scholes price as well as on the decreasing speed of the option price with credit risk depends on moneyness.     

Computational Methods for Pricing American Put Options

This work develops computational methods for pricing American put options under a Markov-switching diffusion market model. Two methods are suggested in this paper. The first method is a stochastic approximation approach. It can handle option pricing in a finite horizon, which is particularly useful in practice and provides a systematic approach. It does not require calibration of the system parameters nor estimation of the states of the switching process. Asymptotic results of the recursive algorithms are developed. The second method is based on a selling rule for the liquidation of a stock for perpetual options. Numerical results using stochastic approximation and Monte Carlo simulation are reported. Comparisons of different methods are made. This research was supported in part by the National Science Foundation and in part by the Wayne State University Research Enhancement Program.     

Binary option pricing using fuzzy numbers

A binary option is a type of option where the payout is either fixed after the underlying stock exceeds the predetermined threshold (or strike price) or is nothing at all. Traditional option pricing models determine the option’s expected return without taking into account the uncertainty associated with the underlying asset price at maturity. Fuzzy set theory can be used to explicitly account for such uncertainty. Here we use fuzzy set theory to price binary options. Specifically, we study binary options by fuzzifying the maturity value of the stock price using trapezoidal, parabolic and adaptive fuzzy numbers.     

双随机跳扩散模型下亚式期权的定价

研究了双随机跳扩散模型下的亚式期权的定价问题.首先引入一个双随机跳扩散过程.然后通过测度变换消除了亚式期权定价中的路经依赖性问题.最后利用鞅定价方法和Ito引理得到了跳扩散模型下的亚式期权价格必须满足的一个积微分方程.通过数值求解该积微分方程就可以得到了亚式期权的价格,供投资者参考.     

Static super-replicating strategies for a class of exotic options

In this paper, we investigate static super-replicating strategies for European-type call options written on a weighted sum of asset prices. This class of exotic options includes Asian options and basket options among others. We assume that there exists a market where the plain vanilla options on the different assets are traded and hence their prices can be observed in the market. Both the infinite market case (where prices of the plain vanilla options are available for all strikes) and the finite market case (where only a finite number of plain vanilla option prices are observed) are considered. We prove that the finite market case converges to the infinite market case when the number of observed plain vanilla option prices tends to infinity.We show how to construct a portfolio consisting of the plain vanilla options on the different assets, whose pay-off super-replicates the pay-off of the exotic option. As a consequence, the price of the super-replicating portfolio is an upper bound for the price of the exotic option. The super-hedging strategy is model-free in the sense that it is expressed in terms of the observed option prices on the individual assets, which can be e.g. dividend paying stocks with no explicit dividend process known. This paper is a generalization of the work of Simon et al. [Simon, S., Goovaerts, M., Dhaene, J., 2000. An easy computable upper bound for the price of an arithmetic Asian option. Insurance Math. Econom. 26 (2–3), 175–184] who considered this problem for Asian options in the infinite market case. Laurence and Wang [Laurence, P., Wang, T.H., 2004. What’s a basket worth? Risk Mag. 17, 73–77] and Hobson et al. [Hobson, D., Laurence, P., Wang, T.H., 2005. Static-arbitrage upper bounds for the prices of basket options. Quant. Fin. 5 (4), 329–342] considered this problem for basket options, in the infinite as well as in the finite market case.As opposed to Hobson et al. [Hobson, D., Laurence, P., Wang, T.H., 2005. Static-arbitrage upper bounds for the prices of basket options. Quant. Fin. 5 (4), 329–342] who use Lagrange optimization techniques, the proofs in this paper are based on the theory of integral stochastic orders and on the theory of comonotonic risks.     

A BLACK－SCHOLES FORMULA FOR OPTIONPRICINGWITHDIVIDENDS

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Catastrophe equity put options with target variance

In this study, we consider a new class of catastrophe equity put options, whose payoff depends on the ratio of the realized variance of the stock over the life of the option and the target variance, which represents the insurance company’s expectation of the future realized variance. This kind of options could help insurance companies raise more equity capital when a large number of catastrophic events occur during the life of the option. We employ a compound doubly stochastic Poisson process with lognormal intensity to describe accumulated catastrophe losses and assume the volatility varies stochastically. Finally, numerical results are presented to investigate the values of this class of options.     

A Delayed Black and Scholes Formula

Abstract

In this article we develop an explicit formula for pricing European options when the underlying stock price follows nonlinear stochastic functional differential equations with fixed and variable delays. We believe that the proposed models are sufficiently flexible to fit real market data, and yet simple enough to allow for a closed-form representation of the option price. Furthermore, the models maintain the no-arbitrage property and the completeness of the market. The derivation of the option-pricing formula is based on an equivalent local martingale measure.     

The Herd Behavior Index: A new measure for the implied degree of co-movement in stock markets

We introduce a new and easy-to-calculate measure for the expected degree of herd behavior or co-movement between stock prices. This forward looking measure is model-independent and based on observed option data. It is baptized the Herd Behavior Index (HIX).The degree of co-movement in a stock market can be determined by comparing the observed market situation with the extreme (theoretical) situation under which the whole system is driven by a single factor. The HIX is then defined as the ratio of an option-based estimate of the risk-neutral variance of the market index and an option-based estimate of the corresponding variance in case of the extreme single factor market situation.The HIX can be determined for any market index provided an appropriate series of vanilla options is traded on this index as well as on its components. As an illustration, we determine historical values of the 30-days HIX for the Dow Jones Industrial Average, covering the period January 2003 to October 2009.