无风险利率上升，导致折现率上升，价格不是应该下跌吗

问题如下：

Stereo Warehouse is a US retailer that offers employees a defined benefit pension plan and stock options as part of its compensation package. Stereo Warehouse prepares its financial statements in accordance with US GAAP.

Peter Friedland, CFA, is an equity analyst concerned with earnings quality. He is particularly interested in whether the discretionary assumptions the company is making regarding compensation plans are contributing to the recent earnings growth at Stereo Warehouse. He gathers information from the company’s regulatory filings regarding the pension plan assumptions in Exhibit 1 and the assumptions related to option valuation in Exhibit 2.

Exhibit 1. Assumptions Used for Stereo Warehouse Defined Benefit Plan

Exhibit 2. Option Valuation Assumptions

Compared to the assumptions Stereo Warehouse used to value stock options in 2008, earnings in 2009 were most favorably affected by the change in the:

选项：

A.

expected life.

B.

risk-free rate.

C.

dividend yield.

解释：

C is correct.

A higher dividend yield reduces the value of the option and thus option expense. The lower expense results in higher earnings. Higher risk-free rates and expected lives result in higher call option values.

考点：影响option的因素（与衍生相关）

解析：

题目问ABC三个选项都是用来对stock option进行估值的假设。2009相对于2008年，哪个假设的变化会对NI有有利影响。

stock option的会计计量方法是：

1、如果马上就能行权，那么就马上把option的价值作为费用确认在公司的损益表。

2、如果有vesting period，也就是要满足一定的期限或条件才能行权，那么option value就是在服务期内作为费用摊销到损益表。

所以option估计出来的fair value越大，确认到损益表的费用越高，NI就越低。反之，option价值越低，NI越高。这道题我们要找使option价值变低的假设改变。

期权的期限越长（expected life)，时间价值越高，期权fair value上升，费用上升，NI就会变低，所以A选项不正确。

因为FP=S0*e(Rf*T), 如果无风险利率上升了，那么资产的future price就会上升，stock的future price越高，call option赚钱可能性越大，所以option value 上升，NI降低，选项B不正确。

div yield升高，option value下降。因为持有股票的人才能拿到分红long call option的人是拿不到分红的，所以对option持有者来说，分红越多，option就越不吸引人，所以费用下降 ，NI变高，选项C正确。

【提示】注意区分vesting period与期权的expected life

vesting period，是你满足一定条件才能拿到benefit，比如你需要再在公司工作3年。

而option的expected life (maturity)，是option本身的期限，比如5年后可以选择执行，或者3年后可以选择执行。

option的maturity影响对option的估值，期限越长，估值越高。而vesting period影响的是每一期分摊的费用为多少。