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Sem 5 Prep
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Formulas for this chapter

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
Step 3 of 27
The real wordsTheory

Call and put

Call optionThe right to buy the underlying at the strike price. Buy a call when you expect the price to rise.
Put optionThe right to sell the underlying at the strike price. Buy a put when you expect the price to fall.

The memory hook: you call the asset in to you, you put the asset out to somebody else.

Because a right has value, the owner pays for it. That payment is the premium.

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