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title: Worked Example summary: A full numeric walkthrough of a call option and a protective put.

Worked Example: Long Call

This page walks through a full call contract in one place. Follow the steps and verify each number.

Scenario setup

• $S_0 = 100$
• $K = 105$
• $C_0 = 2.40$ (per share)
• Contract size = 100 shares

Step 1 — Cost of the contract

Premium paid = $2.40 \times 100 = 240$.

Step 2 — Break-even

$$\text{Break-even} = K + C_0 = 105 + 2.40 = 107.40$$

Step 3 — Intrinsic value today

$$\max(S_0 - K, 0) = \max(100 - 105, 0) = 0$$

So the entire premium is time value at entry.

Step 4 — Profit at expiration

• If $S_T = 103$: payoff = 0, profit = $-2.40$ (max loss)
• If $S_T = 110$: payoff = 5, profit = $5 - 2.40 = 2.60$
• If $S_T = 120$: payoff = 15, profit = $12.60$

Interpretation: the buyer needs a meaningful move above $107.40$ by expiration. The seller is paid 2.40 to accept that obligation.

Mini-example: a put as insurance

Suppose you own shares at $S_0 = 100$ and buy a put with $K = 95$ for $P_0 = 1.80$.

• You paid $180$ to guarantee the right to sell at 95.
• If the stock collapses to $80$, your put payoff is $15$.
• That insurance cost 1.80, but it protected you from the tail outcome.

This is why puts are commonly used for hedging.