Options and volatility · O8 · 9 min
Strategies
Match an option strategy to a view, and work out where it breaks even and what it can lose.
In the news: “Traders bought straddles before the results”: a bet on a big move, whichever way it goes.
The essentials
- Choosing a strategy
- Three questions set the strategy: which way the price will go, whether it will move more or less than options price, and how much you can lose. Bought options cap the loss at the premium; sold ones can lose far more.
- Vertical spreads
- A buys one option and sells another of the same type at a further strike: cheaper, with capped gains. A 100/110 bull call spread costing 3.50 breaks even at 103.50 and makes at most 6.50.
- Collars and covered calls
- A holds the share, buys a put below and sells a call above to pay for it, capping both loss and gain; with matched premiums it costs nothing. Selling the call alone against shares you own is a covered call.
- Straddles and strangles
- A buys the at-the-money call and put and pays on a big move either way: at a 100 strike, costing 8, it needs the price below 92 or above 108. A uses out-of-the-money strikes: cheaper, but it needs a bigger move.
- Butterflies and calendars
- A long butterfly buys the 90 and 110 calls and sells two 100 calls: a cheap bet that the price ends near 100. A sells a near-dated option and buys a later one: short gamma, long vega.
Straddle breakevens
Breakevens = K ± (C + P); at the money, C + P ≈ 0.8 × σ × √T × S
- K
- the strike
- C + P
- total premium paid for the call and the put
- σ, T, S
- volatility a year (as a decimal), years to expiry and the share price
How it works
1. Three questions first
Before choosing a strategy, answer three questions. Which way do you expect the price to go? Will it move more or less than the options are pricing? How much can you afford to lose? Buying options limits the loss to the premium; selling them earns the premium but can lose much more.
2. The call spread
Buy the 100 call for 5 and sell the 110 call for 1.50. You pay 3.50 instead of 5, but give up any gain above 110. This is a bull call spread, one kind of . It breaks even at 100 + 3.50 = 103.50, and the most it can make is 10 − 3.50 = 6.50.
3. The put spread
For a fall, do the mirror image: buy the 100 put and sell the 90 put. It costs less than the put alone, and the gain stops at 90. This is a bear put spread.
4. The collar
You own a share at 100 and fear a fall. Buy the 90 put for protection and pay for it by selling the 115 call: you can’t lose more than 10 or make more than 15. This is a ; when the two premiums match it costs nothing. Selling the call alone, against a share you own, is a covered call.
5. The straddle
Buy the 100 call and the 100 put together: a . It pays if the price moves a lot either way. If the two cost 8 in total, you need the price below 92 or above 108 at expiry: the strike plus or minus the total premium.
6. What a straddle prices in
An at-the-money straddle costs about 0.8 × volatility × √time × price. So premium ÷ strike is the move the market is pricing: a straddle costing 6.65 on a share at 100 prices a move of about 6.7% by expiry. Buy it if you expect more; sell it if you expect less.
7. The strangle
Buy an out-of-the-money put and call instead, say the 90 put and the 110 call: a . It is cheaper than a straddle but needs a bigger move. Sellers of straddles and strangles are betting on calm, and their losses on a big move can be large.
8. Butterflies and calendars
A long butterfly buys the 90 and 110 calls and sells two 100 calls: a cheap bet that the price ends near 100, with a small, known loss. A sells a near-dated option and buys a later one at the same strike: it earns time decay while the price sits still.
9. The Greeks of a strategy
Add up the Greeks of the legs. Bought options have positive gamma and vega and negative theta, so a bought straddle wants big moves and rising volatility, and pays decay every day. A sold strangle is the reverse. A calendar is short gamma but long vega, because its later-dated leg has more vega.
Try it
Choose Straddle to see two breakevens, one each side of the strike. Switch between Long and Short: the same breakevens, opposite risks.
P&L per share against the stock priceAt expiryToday, 1 year to expiry
- Premium paid
- 7.97
- time value 7.97
- Breakeven
- 107.97
- Delta
- +0.54
- Gamma
- +0.020
- per 1 point
- Theta
- −0.011
- per day
- Vega
- +0.40
- per vol point
| Stock price | P&L at expiry | P&L today |
|---|---|---|
| 70 | −7.97 | −7.72 |
| 80 | −7.97 | −6.78 |
| 90 | −7.97 | −4.38 |
| 100 | −7.97 | 0.00 |
| 110 | 2.03 | 6.33 |
| 120 | 12.03 | 14.18 |
| 130 | 22.03 | 23.04 |
Worked example
A share at 100 reports results tomorrow. One-week at-the-money implied volatility is 60%. You are deciding whether to buy the 100 straddle.
- One week is 7 ÷ 365 of a year, and √(7/365) = 0.138.
- 0.8 × 0.60 = 0.48.
- 0.48 × 0.138 × 100 = 6.65 (Black–Scholes gives 6.63).
- Breakevens: 100 − 6.65 = 93.35 and 100 + 6.65 = 106.65.
- So the market prices a move of about 6.7% either way: the straddle is cheap if you expect more, dear if you expect less.
About 6.65, so the share must move more than about 6.7% by expiry for the buyer to profit.
Check yourself
9 quick questions on the explanation above.
Practice
New numbers every set. Misses and guesses go into your review deck.
In the interview
Answer out loud in under a minute, then compare.
You think a stock will move a lot but don’t know which way. What do you buy?
Why would someone sell a strangle?
Explain a calendar spread and its main risk.
Remember
Straddle ≈ 0.8 × σ × √T × S
Pick a strategy by direction, movement and risk; premium ÷ strike is the move a straddle buyer needs.