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asm第5版mfe
243页
EXAMPLE 118 You are given:
(i) A stock with price 50 will pay a dividend of 5 at time 0.25.
(ii) An American call option on the stock with strike price 45 will expire at time 0.4.
(iii) The volatility of a pre-paid forward on the stock is 0.3.
(iv) r =0.06.
(v) CallOnPut(50, 45, 4.5968,0.3, 0.06, 0.25, 0.4, 0) =0.1748
(vi) CaiIOnPut(50, 45,9.5968,0.3,0.06,0.25,0.4,0) =0.0134
I. Determine whether it is optimal to exercise the option if the stock price is 45 before payment of the dividend.

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关键词：MFE Volatility determine Dividend American 朋友 MFE

ANSWER: I. As we just discussed, it is optimal to exercise the American option if the value of the put is less
than D - K (I - e-r(T-/1»). D - K(I- e-r(T-/,») =5 - 45 (I - e-o.06(o.IS») =4.5968. The ex-dividend price of the
stock is 40 if the cum-dividend price is 45. The price of the put is
d, = In(40/45) + [0.06 + 0.5(0.32)J(0.15) =-0.8782
0.3 "0.15
d2 =-0.8782 - 0.3 VO.15 =-0.9944
P(40, 45, 0.3, 0.06, 0.15, 0) = 45e-o.15(O.06)N(0.99) -. 40N(O.88)
=44.5968(0.8389) - 40(0.8106) =4.988
which is greater than 4.5968, so the put should be purchased, which is equivalent to not exercising the option. By
iterative techniques, it can be shown that the price of the stock ex-dividend should be greater than 40.58 to make
exercise optimal.
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这是手册的解答

请问提前执行美式call option的条件是什么？
是不是：当未来分红的折现值大于结算价利息的折现值时

It is optimal to excercise the American call option if the present value of the dividends recieved is greater than that of the interest lost on the strike price.

这种说法对不对？

这道题的分红折现值是5，结算价利息只有0.4
应该提前执行啊
大家说我错在哪里了？

On the day before an ex-dividend date, you should exercise an equity call option early in order to collect the dividend.

To early exercise an American call option, you need to consider  whenever the benefits of being long the underlier outweigh the costs of surrendering the option early. In general, equity call options should only be exercised early on the day before an ex-dividend date, and then only for deep in-the-money options.