Option payoff and net profit
Call payoff = max(S - X, 0) x quantity
Put payoff = max(X - S, 0) x quantity
Buyer net profit = payoff - total premium
Writer net profit = total premium - payoff
quantity = number of lots x lot size
Every option numerical. Compute the number of shares first, because both the premium and the payoff are quoted per share. Read whether the question wants payoff or profit.
- S
- Spot price of the underlying at exercise or expiry
- X
- Strike or exercise price
- total premium
- Premium per share times the number of shares
Intrinsic value and time value
Intrinsic value (call) = max(S - X, 0)
Intrinsic value (put) = max(X - S, 0)
Time value = premium - intrinsic value
When a question gives a premium and asks how much of it is real value. Time value is zero at expiry, so the premium then equals the intrinsic value.
- intrinsic value
- Cash flow from exercising immediately, floored at zero
- time value
- What the market charges for the chance of a further favourable move
Break-even spot price
Long call: S = X + premium per share
Long put: S = X - premium per share
Whenever the question asks where the buyer starts to profit. The lot size cancels, so work in per-share terms.
- premium per share
- The quoted premium, not the total paid
Put-call parity
C + X / (1 + r)^t = P + S
To price one option from the other three quantities, or to spot an arbitrage. Not derived in either section's material, so confirm it against your class slides.
- C
- Price of a European call, strike X, expiry t
- P
- Price of a European put, same strike and expiry
- r
- Risk-free rate for the tenor t