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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?
a. USD 1.61
b. USD 1.78
c. USD 1.95
d. USD 2.11
Answer as per GARP is (C).
But how can a call price increase when there is a dividend announcement?
The dividend need to be discounted and reduced from the current stock price:
New S0* N(d1)= 40- (0.5*EXP(-3%*1/12)*0.299828= 11.8219
Before the dividend the So*N(d1)= 40*0.29123= 11.6492.
Hence the change 11.8219-11.6492= 0.1727 should be reduced from existing call price of 1.78.
Please help me understand where am I going wrong with this.
Thanks,
Anir.
Request help with this question.
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?
a. USD 1.61
b. USD 1.78
c. USD 1.95
d. USD 2.11
Answer as per GARP is (C).
But how can a call price increase when there is a dividend announcement?
The dividend need to be discounted and reduced from the current stock price:
New S0* N(d1)= 40- (0.5*EXP(-3%*1/12)*0.299828= 11.8219
Before the dividend the So*N(d1)= 40*0.29123= 11.6492.
Hence the change 11.8219-11.6492= 0.1727 should be reduced from existing call price of 1.78.
Please help me understand where am I going wrong with this.
Thanks,
Anir.