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EmilyZhou · 2025年05月07日

老师这道题用画图大法如何理解?

NO.PZ2025040202000082

问题如下:

Under the Black–Scholes–Merton option valuation model, for equity options with an exercise price equal to the current stock price, an increase in a stock's dividend yield will:

选项:

A.A.lower the value of a call option and lower the value of a put option. B.B.lower the value of a call option and raise the value of a put option. C.C.lower the value of a put option and raise the value of a call option.

解释:

A Incorrect because carry benefits will have the effect of lowering the expected future value of the underlying. The carry benefit adjusted BSM model can be described as having two components, a stock component and a bond component. For call options, the stock component is Se–γTN(d1) and the bond component is again e–rTXN(d2). For put options, the stock component is Se–γTN(–d1) and the bond component is again e–rTXN(–d2). Although both d1 and d2 are reduced by carry benefits, the general approach to valuation remains the same. An increase in carry benefits will lower the value of the call option and raise, not lower, the value of the put option.

B Correct because carry benefits will have the effect of lowering the expected future value of the underlying. The carry benefit adjusted BSM model can be described as having two components, a stock component and a bond component. For call options, the stock component is Se–γTN(d1) and the bond component is again e–rTXN(d2). For put options, the stock component is Se–γTN(–d1) and the bond component is again e–rTXN(–d2). Although both d1 and d2 are reduced by carry benefits, the general approach to valuation remains the same. An increase in carry benefits will lower the value of the call option and raise the value of the put option.

C Incorrect because carry benefits will have the effect of lowering the expected future value of the underlying. The carry benefit adjusted BSM model can be described as having two components, a stock component and a bond component. For call options, the stock component is Se–γTN(d1) and the bond component is again e–rTXN(d2). For put options, the stock component is Se–γTN(–d1) and the bond component is again e–rTXN(–d2). Although both d1 and d2 are reduced by carry benefits, the general approach to valuation remains the same. An increase in carry benefits will lower, not raise, the value of the call option and raise, not lower, the value of the put option.

从公式上可以选出答案,但是逻辑上想不太明白

1 个答案

李坏_品职助教 · 2025年05月07日

嗨,从没放弃的小努力你好:


这个题目没有给出任何具体条件或者时间,所以画图不合适。


股票分红比率变大,你想想,股票分红的出处是公司的税后净利润,公司出钱,会导致净资产下降,股价下跌。所以call option价值下降。


反过来,put option价值上升。


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