基于分数O U过程的几何亚式-再装股票期权定价模型

通过将几何亚式期权应用到再装期权中,解决了传统再装期权在再装日按B-S模型执行时所产生的经理激励问题,建立了几何亚式-再装股票期权的定价模型,并在股价服从分数O-U过程下得到了相应的定价公式.通过模拟分析发现,与传统再装期权相比,几何亚式-再装期权的价值要低一些,这说明几何亚式-再装股票期权能更好地降低代理成本.     

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 .     

幂型支付的欧式期权定价公式

在等价鞅测度框架下,讨论了(在到期时刻)期权处于实值状态时支付函数为幂型的股票欧式期权定价公式.这里我们假设无风险利率,股票预期收益率和股价波动率都是时间的确定性函数.本文结果不但包含了原始的Black-Scholes公式,而且可用于上封顶与下保底(幂型)欧式看涨期权的定价.     

债券受布朗运动驱动时幂型支付重置期权的定价

考虑完全的无套利市场环境下,基础股票支付连续红利,债券价格满足由布朗运动驱动的随机微分方程,对具有幂型支付的一种创新重置期权,以鞅论和随机分析为工具,得到了期权的定价公式.     

具有连续红利的幂型欧式期权定价

在等价鞅测度框架下,讨论了在期权到期时刻具有连续红利支付的幂型股票欧式期权的定价公式.这里我们假设市场无风险利率,股票预期收益率,股价波动率以及股票红利率都是时间的确定性函数.     

混合高斯模型下带红利的永久美式期权定价

本文建立混合高斯模型下支付连续红利的永久美式期权定价模型.利用自融资策略和分数伊藤公式,得到永久美式期权价值所满足的偏微分方程.其次,由永久美式期权的实施条件与看涨-看跌期权的对称关系,获得看涨与看跌期权的定价公式与最佳实施边界.最后,利用平安银行的日收盘价对标的资产进行实证分析,结果表明:用混合高斯模型模拟出的股票价格与真实股票价格比较接近,能够反映股票的整体走势.     

基础股票有分红及配股的期权定价与套期保值

给出了有分红及配股的股票价格运动规律,并讨论了以定期分红及配股的股票为标的资产的美式看涨期权的定价与套期保值问题．通过对有凸支付函数的美式期权执行时间的讨论得到美式看涨期权的最优执行时间只可能在每次分红或送配股除权除息之前．证明了在各次分红或送配股之间,期权的值满足熟知的Black-Scholes方程。     

基于跳-分形模型的美式看涨期权定价

假设股票变化过程服从跳一分形布朗运动,根据风险中性定价原理对股票发生跳跃次数的收益求条件期望现值推导出M次离散支付红利的美式看涨期权解析定价方程,并使用外推加速法求出当M趋于无穷时方程的二重、三重正态积分多项式表达,依此计算连续支付红利美式看涨期权价值.数值模拟表明通常仅需二重正态积分多项式能产生精确价值,而在极实值状态下则需三重正态积分多项式才能满足,结合两种多项式可以编出有效数字程序评价支付红利的美式看涨期权.     

不对称信息下技术员工股票期权管理激励的博弈分析

分析了技术员工偷懒“囚徒困境”的形成过程,构建了技术员工股票期权管理激励的博弈模型,进行ESS博弈均衡分析,得出了防范技术员工偷懒行为的惩罚力度与股票期权管理激励因子之间的关系,在此基础上得出结论：股票期权与偷懒惩罚力度相结合,能有效预防技术员工偷懒行为．     

支付股利的跳跃-扩散过程下美式看涨期权定价

讨论了当基础资产遵循跳跃-扩散过程时支付股利美式看涨期权定价问题。在等价鞅测度下,导出在风险中性定价模型中,标的股票服从跳跃-扩散过程并且在期权有效期支付一次股利时美式看涨期权的解析定价公式,然后将其扩展到期权有效期多次支付股利的美式看涨期权,其价值在期权有效期等间隔支付股利次数趋于无穷时将收敛于连续支付股利的美式看涨期权,在此基础上,提供了便于实践应用的外推加速法以减少计算复杂性。     

高管个人特征对股权激励模式选择的影响研究

上市公司股权激励模式的选择问题一直受社会各界关注。本文利用2006年到2017年期间实施股权激励的上市公司数据,研究了高管个人特征如何对股权激励模式的选择产生影响。结果表明,被激励高管的个人特征如高管年龄、任期、学历与社会资本显著影响公司股权激励模式的选择,年龄越大、任期越久、学历越高、社会资本越丰富的高管,公司更倾向选择限制性股票激励模式;男性高管越多的公司,越倾向选择股票期权激励模式,然而性别对其影响并不显著。本文在经过一系列的稳健性和内生性检验后,研究结论依然成立。本文研究结果丰富了股权激励相关理论,并为上市公司科学合理地选择股权激励模式提供参考。     

Valuing executive stock options: A quadratic approximation

This paper develops a continuous-time model for valuing executive stock options (ESOs) with features of early exercise, delayed vesting and forfeiture. Applying the quadratic approximation established for valuing American options into ESOs, we obtain an explicit formula for the fair ESO value at its grant date. We show that the approximation formula is consistent with the exact results for two special cases either with no dividend or infinite maturity, and also that the perpetual value for the latter case gives an upper bound of the ESO value. To see the performance of the formula, we numerically examine it with benchmark results generated by a binomial-tree model for some particular cases. Numerical experiments show that there is a complementary relation between the vesting and trading periods with respect to exit rate of ESO holders.     

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 volatility asymptotics of stock loans: Valuation and optimal stopping

A stock loan, or equity security lending service, is a loan which uses stocks as collateral. The borrower has the right to repay the principal with interest and regain the stock, or make no repayment and surrender the stock. Therefore, the valuation of stock loan is an optimal stopping problem related to a perpetual American option with a negative effective interest rate. The negative effective interest rate makes standard techniques for perpetual American option pricing failure. Using a fast mean-reverting stochastic volatility model, we applied a perturbation technique to the free-boundary value problem for the stock loan price. An analytical pricing formula and optimal exercise boundary are derived by means of asymptotic expansion.     

The British Put Option

Abstract

We present a new put option where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Inherent in this is a protection feature which is key to the British put option. Should the option holder believe the true drift of the stock price to be unfavourable (based upon the observed price movements) he can substitute the true drift with the contract drift and minimize his losses. The practical implications of this protection feature are most remarkable as not only can the option holder exercise at or above the strike price to a substantial reimbursement of the original option price (covering the ability to sell in a liquid option market completely endogenously) but also when the stock price movements are favourable he will generally receive higher returns at a lesser price. We derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary and show that the rational exercise boundary itself can be characterized as the unique solution to a nonlinear integral equation. Using these results we perform a financial analysis of the British put option that leads to the conclusions above and shows that with the contract drift properly selected the British put option becomes a very attractive alternative to the classic American put.     

Regularity of the American Put option in the Black–Scholes model with general discrete dividends

We analyze the regularity of the value function and of the optimal exercise boundary of the American Put option when the underlying asset pays a discrete dividend at known times during the lifetime of the option. The ex-dividend asset price process is assumed to follow the Black–Scholes dynamics and the dividend amount is a deterministic function of the ex-dividend asset price just before the dividend date. This function is assumed to be non-negative, non-decreasing and with growth rate not greater than 1. We prove that the exercise boundary is continuous and that the smooth contact property holds for the value function at any time but the dividend dates. We thus extend and generalize the results obtained in Jourdain and Vellekoop (2011) [10] when the dividend function is also positive and concave. Lastly, we give conditions on the dividend function ensuring that the exercise boundary is locally monotonic in a neighborhood of the corresponding dividend date.     

A joint valuation of premium payment and surrender options in participating life insurance contracts

In addition to an interest rate guarantee and annual surplus participation, life insurance contracts typically embed the right to stop premium payments during the term of the contract (paid-up option), to resume payments later (resumption option), or to terminate the contract early (surrender option). Terminal guarantees are on benefits payable upon death, survival and surrender. The latter are adapted after exercising the options. A model framework including these features and an algorithm to jointly value the premium payment and surrender options is presented. In a first step, the standard principles of risk-neutral evaluation are applied and the policyholder is assumed to use an economically rational exercise strategy. In a second step, option value sensitivity on different contract parameters, benefit adaptation mechanisms, and exercise behavior is analyzed numerically. The two latter are the main drivers for the option value.     

离散分红下障碍期权的间接级数展开定价方法

人们投资股票市场的最大动力,除了从股票本身的升值中获利,还包括收益分红.提出了带有离散分红的障碍期权的一种新型的近似方法,以向上敲出看涨障碍期权为例,固定分红的次数,通过泰勒级数展开得到关于关键变量的仿射函数,给出了一个只带有一维积分的定价公式,提高了计算速度.该方法还可以用于回望期权等其它衍生品的定价,对在市场上进行期权交易有一定指导意义.     

Valuation of employee stock options using the exercise multiple approach and life tables

Employee stock options (ESOs) are common in performance-based employee remuneration. Financial reporting standards such as IFRS2 and AASB2 require public corporations to report on the cost of providing ESOs, and mandate the incorporation of voluntary and involuntary early exercise. In this paper we extend the exercise multiple approach of Hull and White (2004) and decompose the attrition unadjusted voluntary exercise ESO into a gap call option and two partial-time barrier options. We use exit probabilities obtained from empirically determined multiple decrement or life tables to model involuntary early exercise or forfeiture. We provide a new analytic valuation formula which expresses the ESO value in terms of a portfolio of exotic European bivariate power options and which correctly accounts for both voluntary exercise and employee attrition. Recent approaches seek to model employee attrition using a constant hazard rate. Our approach uses an empirically driven actuarial method for incorporating employee attrition in the valuation.