Call option

Call option gives owner the right, not obligation, buyer or the holder of long position
seller, writer, holder of short position

Payoff
C_T=S_T-X if ST▷X, C_T=0 if S_T≦X
=> C_T=max(0,S_T-X)
Profit = max (0, X_T-X)-C₀ = C_T-C_o
If S_T◁X+C_o, call buyer profit ◁0◁call seller profit
If S_T=X+C_o, call buyer profit =0=call seller profit
If S_T▷X+C_o, call buyer profit ▷0▷call seller profit
Breakeven at X+C₀, or X+premium

Where:
◁ - smaller than
▷ - greater than
C_o - premium