Options Pricing · Lesson 9 of 11

Option Strategies

Spreads, straddles, and how to use the Greeks · 20 min

Before this lesson

Builds on calls and puts (Lesson 1) and payoff thinking — no new math beyond what's already covered.

From Single Options to Strategies

Almost nobody trading options professionally is just buying or selling one contract in isolation. Real trading combines options — and sometimes the underlying stock itself — into strategies: multi-leg structures built to target a specific payoff shape, a specific risk-to-reward ratio, and a specific set of Greek exposures. Knowing why a given strategy exists, and exactly when it's the right tool, is what separates deliberate positioning from just placing a bet and hoping.

Every strategy is worth analyzing on two separate axes: its payoff at expiration — a function purely of where the stock ends up — and its Greeks profile — how it behaves right now as S, σ, and t shift underneath it. You need both. The payoff diagram tells you where the money is at the finish line; the Greeks tell you what the ride there actually feels like.

Covered Call: Selling Upside for Income

The covered call is the single most common strategy among equity investors who dabble in options. You already own the stock, and you sell a call against it:

Long 100 shares + Short 1 call (K = strike above current price)

Payoff at expiration: if ST < K, you keep the stock at its current value plus the premium you collected. If ST > K, you're forced to sell at K, but you keep both the premium and the sale proceeds — your upside is simply capped there.

Why bother? You were holding the stock anyway and don't expect a huge move soon, so collecting premium against it lowers your effective cost basis. The tradeoff is explicit: if the stock rips well past K, you leave real money on the table. You're deliberately trading some upside for income today.

Greek profile: net delta lands around (1 − Δ_call) per share. Short vega — you want implied vol to fall, since that makes buying back the short call cheaper. Positive theta — time decay on that short call works in your favor every day.

Vertical Spreads: Defined Risk, Defined Reward

A vertical spread buys one option and sells another at a different strike, same expiry, same underlying. Structuring it this way caps both your risk and your reward — exactly what you want when you have a directional view but don't want to pay full price for a naked option, or take on its unlimited downside.

Bull Call Spread: buy a call at K₁, sell a call at K₂ > K₁, same expiration on both.

  • Max profit: (K₂ − K₁) − net premium paid, reached once ST ≥ K₂
  • Max loss: just the net premium paid, if ST ≤ K₁
  • Breakeven: K₁ + net premium paid

You pay less up front than a naked call — the short leg subsidizes the long one — but you give up anything above K₂. Reach for this when you're moderately bullish and don't need a home run, just a move past K₂.

Bear Put Spread: buy a put at K₂, sell a put at K₁ < K₂, same expiry.

  • Max profit: (K₂ − K₁) − net premium paid, reached once ST ≤ K₁
  • Max loss: the net premium paid, if ST ≥ K₂

The mirror image, for when you're moderately bearish — the cheaper lower-strike short put subsidizes the higher-strike long put you actually want.

Straddle: Trading Pure Volatility

A long straddle buys a call and a put at the same strike and expiry:

Long call (K, T) + Long put (K, T) — same strike and expiry

This position profits from a big move in either direction — the call catches the upside, the put catches the downside. The one scenario that actually hurts is the stock going nowhere: both legs expire close to worthless and you lose the combined premium you paid for both.

Break-even points: K ± total premium paid. A straddle at K = 100 with $8 total premium breaks even at $92 and $108.

Greek profile: delta starts near zero — the call's positive delta and put's negative delta cancel out at initiation. Long gamma, since any large move helps. Short theta, since you're paying decay on two options simultaneously. Long vega — the whole position is fundamentally a bet that implied vol is currently priced too low.

Traders reach for long straddles ahead of known catalysts — earnings, Fed meetings — when they expect a big move but have no edge on direction. They sell straddles instead when they think IV is overpriced and the stock is going to sit still.

Strangle: A Cheaper Straddle

A strangle is the same idea as a straddle, just built with OTM strikes instead of ATM ones:

Long OTM put (K₁ < S) + Long OTM call (K₂ > S)

Since both legs start out-of-the-money, the total premium is lower than an equivalent straddle — but the stock has to travel further to reach either break-even point. Cheaper entry, bigger move required.

Iron Condor: Selling the Tails

An iron condor stitches together a bull put spread and a bear call spread:

Short put at K₂ + Long put at K₁ (K₁ < K₂) + Short call at K₃ + Long call at K₄ (K₃ < K₄)

with K₁ < K₂ < S < K₃ < K₄. The position collects premium up front and stays profitable as long as the stock finishes between K₂ and K₃ — the "condor body." The long options out at K₁ and K₄ exist purely to cap the damage if the stock makes a genuinely large move.

Max profit: the net premium collected, if K₂ ≤ ST ≤ K₃.

Max loss: the width of one spread minus that premium, if ST ≤ K₁ or ST ≥ K₄.

Greek profile: short vega, so falling IV helps you. Positive theta, so time passing helps you too. Net delta sits close to zero if you build it symmetrically. In short, the iron condor is a pure volatility-selling play — you're betting the stock stays inside its range through expiration.

Choosing the Right Strategy

Every strategy above is, at bottom, a specific market view wearing a different outfit:

  • Moderately bullish: bull call spread
  • Moderately bearish: bear put spread
  • Big move coming, direction unclear: long straddle or strangle
  • Stock likely flat, IV feels too high: short straddle, strangle, or iron condor
  • Already own the stock, want income: covered call

Whichever you pick, its Greek profile needs to actually match your time horizon and risk appetite. Long straddles bleed theta every single day, so you need your catalyst to actually arrive on schedule. Short iron condors collect theta slowly and steadily, rewarding patience but punishing you hard if the stock breaks out of its range. Matching the position to the view — not just the view to the trade idea — is what separates systematic options trading from gambling with extra steps.

Try it

Build any of the strategies above with the tool below and watch its payoff shape change in real time.

Coding ExercisePython · runs in browser
+100 XP
Implement `bull_call_spread_payoff(S_T, K1, K2, premium_paid)` — returns the P&L at expiration for a bull call spread.
Write your solution, then run