NO.PZ2023091802000137
问题如下：
A non-dividend-paying stock is currently trading at USD 40 and has
an expected return of 12% per year. Using the Black-Scholes-Merton (BSM) model,
a 1-year, European-style call option on the stock is valued at USD 1.78.
The parameters used in the model are:
N(d1) = 0.29123
N(d2) = 0.20333
The next day, the company announces that it
will pay a dividend of USD 0.5 per share to holders of the stock on an
ex-dividend date 1 month from now and has no further dividend payout plans for
at least 1 year. This new information does not affect the current stock price,
but the BSM model inputs change, so that:
N(d1) = 0.29928
N(d2) = 0.20333
If the risk-free rate is 3% per year, what is the new BSM call price? (Practice Exam)
选项：
A.USD 1.61
B.USD 1.78
C.USD 1.95
D.USD 2.11
解释：
The value of a European call is equal to SN(d1) – Ke – rTN(d2), where S is the
current price of the stock. In the case that dividends are introduced, S in the
formula is reduced by the present value of the dividends. Furthermore, the
announcement would affect the values of S, d1 and d2. However, since we are given
the new values, and d2 is the same, the change in the price of the call is only dependent
on the term S × N(d1).
Previous S × N(d1) = 40 × 0.29123 = 11.6492
New S × N(d1) = (40 – (0.5 × exp(-3%/12))
× 0.29928 = 11.8219
Change = 11.8219 – 11.6492 = 0.1727
So the new BSM call price would increase in
value by 0.1727, which when added to the previous price of 1.78 equals 1.9527.
解析里，3%哪里来的，应该是12%/12吗？
