By taking on a long position in a stock and combining it with a short call we create a covered call option. This allows to earn income from the short call, caps the upside from gains on the stock itself.
Covered calls can be used to generate income (writing calls as long as price does not exceed strike price), improve on the market prices (using in-the-money call options to realize better prices on exiting a position) and similarly realize a target price.
S0 and ST = stock price at time 0 and T respectively
T = option maturity
X = exercise price
C0 and P0 = time 0 call and put option values respectively
The convention for quoting options is the month of expiration followed by the exercise price. For example ‘Sep 25 call’ indicates a call option that expires in September and has an exercise price of $25.
For a covered call, important relationships are:
investment at inception = S0 − C0
value at expiration = ST − max(ST − X, 0)
profit at expiration = min(X, ST) − (S0 − C0)
maximum gain = X – S0 + C0
maximum loss = S0 − C0
breakeven point = S0 − C0