When a European call option is deep in-the-money (the stock price is much greater than the strike price, $S \gg K$), both $d_1$ and $d_2$ in the Black-Scholes-Merton model become very large, meaning $N(d_1)$ and $N(d_2)$ approach 1.

The price of a European non-dividend-paying call option can then be approximated by its lower bound: $c \approx S - K e^{-rT}$

Given:

• $S = 200$
• $K = 50$
• $r = 8\% = 0.08$
• $T = 3 \text{ months} = 3 / 12 = 0.25 \text{ years}$

$c \approx 200 - 50 \times e^{-0.08 \times 0.25}$ $c \approx 200 - 50 \times e^{-0.02}$ $c \approx 200 - 50 \times 0.9802$ $c \approx 200 - 49.01 = 150.99$

The closest option is $151.