问一道题：NO.PZ201702190300000403

问题如下：

3.To determine the long put option value on TCB stock in Exhibit 1, the correct BSM valuation approach is to compute:

选项：

0.4404 times the present value of the exercise price minus 0.6217 times the price of TCB stock.

0.4404 times the present value of the exercise price minus 0.3783 times the price of TCB stock.

0.5596 times the present value of the exercise price minus 0.6217 times the price of TCB stock.

解释：

B is correct.

The formula for the BSM price of a put option is p = e^-rtXN(-d2)-SN(-d₁). N(-d₁) = 1 - N(d₁) = 1 - 0.6217 = 0.3783, and N(-d2) = 1 - N(d₂)= 1 - 0.5596 = 0.4404.

Note that the BSM model can be represented as a portfolio of the stock (n_sS) and zero-coupon bonds (n _bB). For a put, the number of shares is n_s = -N(d₁)< 0 and the number of bonds is n_B =-N(d₂) > 0. The value of the replicating portfolio is n_sS + n_bB = -0.3783(57.03) + 0.4404(54.97) = $2.6343 (the value of the put option with slight rounding error). B is a risk-free bond priced at exp(- rt)(X) = exp(-0.0022 x 0.25)(55) = $54.97.