Which of the two options is correct and why?

Question: Consider a stock priced at $33 with a standard deviation of 0.3. The risk-free rate is 0.05. There are put and call options available at exercise prices of 35 and a time to expiration of six months. The calls are priced at $2.39 and the puts cost $2.05. There are no dividends on the stock and the options are European. Assume that all transactions consist of 100 shares or one contract (100 options). Suppose the investor constructed a covered call. If the transaction is closed out when the option has three months to go and the stock price is at $39,

what is the investor's profit?

Option A: Current stock price, So = 33

Std deviation = 0.30

risk free rate = 0.05

Exercise price, X = 35

Call option price, c = 2.39

Put option price, p =2.05

Stock price at expiry, ST = 39

One contract = 100 options

Investor's profit;

Profit = (Expiration price of stock - strike price-call premium) * quantity

= (39-33-2.39) *100

= $ 361

Option B: 1. The option is European option and hence it can be exercised only in maturity

2. For ascertaining PV we have taken 5% for discounting purpose

3. The option price is compounded continuously. However, for the sake of calculation I have ignored it.

Now coming to calculation part :-

Since it is a call covered then it is S+ and C-

Profit is calculated for 1 share as follows :

= Profit of Stock + Present value of Loss of call + Premium money of call

= (39-33) + PV of (35 - 39) for 3 month + 2.39

= 6 + 4*1/(1+0.05)^3/13+2.39

=6-3.95+2.39

= $ 4.44

Profit for 100 share = 4.44 * 100 = $ 444 at the end of 3 month