Most people who own stock eventually want insurance on it. The options market sells it, and the price it charges is set by the same volatility you have been reading all course. This lesson looks at the three ways stock owners use options and reads each one through the smile: puts below the market trade at a higher implied volatility than calls above it, so protection is dear and upside is cheap.
The protective put: insurance with a premium
You own 100 shares at $100. You buy one $95 put with 60 days to run for $2.03. Whatever happens, you can sell at $95 until expiration, so the most you can lose is $5 on the stock plus $2.03 of premium, $703 on the position. The put is the insurance, $2.03 is the premium, $95 is the floor. Your breakeven also moves up to $102.03, because the stock has to earn back what the insurance cost.
P&L on 100 shares and one put, bought at $100 with 60 days to run. The chart prices the put at one flat 24%, about $1.61, rather than the $2.03 it costs on a skewed smile. The floor sits at $95 less the premium; above the strike you trail the stock by what the insurance cost. Drag volatility up and watch the green line lift below the strike: the put is worth more today when the market expects bigger moves.
Look at the green line with 60 days left. Above the strike it runs just under the plain stock, trailing by the premium. Below the strike it bends flat well before expiry, because the put gains value as the stock falls. That bend is the insurance working, and it is long gamma: the further and faster the stock drops, the more the put pays.
What the insurance really costs
In vol terms the cost is not $2.03, it is the implied volatility you paid. Say the at-the-money option is priced at 24% and the $95 put at 27%. You paid three vol points over the middle of the smile for the right to sell below the market. That is the skew premium. At a flat 24% the same put would be worth about $1.61, so the skew is adding about 42 cents, a quarter of the price.
That is why rolling protection every month is expensive. Buy a fresh two-month put six times a year and you spend about $12 on a $100 stock, 12% a year, before the stock has done anything. The vol you pay is usually above the vol the stock goes on to deliver, so on average the insurer wins. People buy it anyway for the same reason they insure a house: the bad year is the one that matters.
The collar: sell the upside to pay for it
A collar adds one leg. You keep the stock and the $95 put, and you sell a $105 call. The call premium pays for most of the put. In exchange you have capped your gain at $105. The put is the floor and the call is the ceiling, and between them the position behaves like a smaller amount of stock.
Floor at $95, ceiling at $105, a straight line between. Every leg is priced at one flat 24% here, so the entry note shows about $9,943 for the shares and both options, less than the $10,000 the shares alone cost: at flat vol the collar pays you about $0.57 a share. The skew in the next chart is what makes a real collar cost money. Drag days down to see the position harden into its expiry shape.
This chart prices both options at one flat volatility, and at one flat vol the $105 call is worth more than the $95 put, because interest pushes the forward price up: the collar comes out at a small credit. Real markets do not trade at one vol. The skew lifts the put and lowers the call, and that is what turns the collar into a debit.
Put value by strike priced off a skewed smile (green) against the same put at one flat 24% (dashed). At the 95% strike the skewed put is worth about $2.03 against $1.61. Switch to calls: at 105% the skewed call is worth less than at flat vol. Set skew to zero and the gap disappears.
Put numbers on it. With a 24% at-the-money vol, a put wing at 27% and a call wing at 21%, the $95 put costs $2.03 and the $105 call brings in $1.75, so the collar costs $0.28. At flat vol the same trade would have paid you about $0.57. The skew moved the price of the collar by roughly 85 cents. To get back to zero cost you have to bring the call strike closer to the money than the put strike, giving up more upside than the put protects.
The covered call: short volatility on stock you own
Drop the put and keep the short call and you have a covered call: stock plus a short call. By put-call parity that has the same payoff as a short put at the call's strike. You collect the premium, you keep it if the stock stays below the strike, and you give away every dollar above it. Because you are short an option you are short vega and short gamma: you are paid for time passing, you still lose if the stock falls, and above the strike your gain stops while the stock keeps going.
The same shape as a short put: a full loss to the downside, cushioned only by the premium, and a flat line above $105. Drag days toward zero with the stock near $100 and the green line rises toward the expiry line; that rise is the theta you collect.
Through the skew, the covered call is selling the cheap side of the smile. The call wing trades at a lower implied volatility than the put wing, so the premium you collect per dollar of upside you give up is smaller than what a put buyer pays for the same distance below the market. It still works whenever realized volatility stays under the call's implied, which is often, but you are collecting the thinner premium.
| Structure | Legs | Vol position | Where it sits on the smile |
|---|---|---|---|
| Protective put | Stock + long put | Long vol | Buys the expensive wing |
| Collar | Stock + long put + short call | Roughly flat | Buys expensive, sells cheap |
| Covered call | Stock + short call | Short vol | Sells the cheap wing |
The maths: the cost of protection in vol points
Near a given vol, an option's price moves by its vega for each vol point, so the extra you pay for skew is about vega × (IV of your strike - ATM IV). For the 60-day $95 put, vega is about 0.137 per point, and 0.137 × 3 points is $0.41. The model gives $2.03 at 27% and $1.61 at 24%, a difference of $0.42, so the rule holds.
The same rule prices the collar. The call's vega is about 0.15, so selling it three points under the at-the-money vol gives up about 0.15 × 3 = $0.45. Add the $0.41 paid on the put and the skew costs the collar about $0.86 against flat vol, which is the gap between a $0.57 credit and a $0.28 debit.
Over the life of the hedge, what you get back depends on the volatility the stock actually delivers. If it realizes 20%, the put was worth about $1.10 on that path in model terms: you paid $2.03 for $1.10 of protection. Protection pays for itself only when realized volatility, or a single large drop, beats the implied you paid.
Your turn
Open the AAPL chain and find the put with a delta nearest minus 0.25. Read its mid and type it into the Protective Put Calc as the premium. Then switch to MSFT, find the 25-delta call, and compare its IV with the 25-delta put's. The gap is the skew you have just paid, or been paid.