If you know that a call option will be profitably exercised then the Black-Scholes model price will simplify to _______. A) S₀ - X B) X - S₀ C) S₀ - PV(X) D) PV(X) - S₀

Question

Quizplus · Accepted Answer

When a call option is profitably exercised, the holder of the option will buy the underlying asset at the strike price X and sell it at the market price S. Therefore, the profit from exercising the option is S - X. In the Black-Scholes model, the price of the option is represented by S₀. To get the profit from exercising the option, we need to subtract the strike price X from S₀, which gives us S₀ - X. However, we also need to take into account the time value of money, so we need to discount the strike price X by the risk-free rate to get the present value of X, which is PV(X). Therefore, the simplified Black-Scholes model price when a call option is profitably exercised is S₀ - PV(X), which is equivalent to choice C.

If You Know That a Call Option Will Be Profitably