This is a short bridge lesson. The Greeks do not change because the underlying is Bitcoin — if you understand them from the Options Trading course, you understand them here. But a few things about the crypto environment change how they feel and how you use them, so let us cover just the differences.
Same maths, bigger and faster
Delta, gamma, theta and vega are the same sensitivities, computed from the same Black-Scholes. What differs is scale and context:
- Dollar values are large. Because crypto IV is ~50–70% (Lesson 6), the Greeks are big in dollar terms. That 30-day ATM BTC call has theta ≈ −$94/day and vega ≈ $103 per 1% IV. A small move in IV or a day of decay is real money. Respect the magnitudes.
- Theta runs 24/7. There is no overnight pause and no weekend break. Time decay is continuous. A weekend is simply three more days of theta ticking away while the market stays wide open — unlike equities, where the weekend is “closed”. For option sellers this is a steady drip; for buyers it is relentless.
- Gamma near expiry is even wilder. ATM gamma spikes near expiry everywhere, but combine that with crypto’s capacity for 10–20% moves and expiry-day positions can swing violently. Treat crypto expiry with extra caution.
The crucial addition: perps are pure delta
Here is the one genuinely new idea. In crypto your book usually is not just options — it includes spot and perps. And a perpetual future (or spot) is pure delta: being long 1 BTC perp is +1 delta per coin, with no gamma, theta or vega. This matters enormously:
- Your true delta is the sum across everything: options + perps + spot. A “delta-neutral” options position is not neutral if you are also holding a perp.
- This is exactly what makes delta-hedging work (Lesson 9): you sell an option (which gives you some delta and lots of theta/vega), then buy or sell a perp to cancel the delta, leaving you holding mostly the theta/vega bet you actually wanted.
# net delta of a mixed crypto book
def book_delta(option_positions, perp_qty, spot_qty):
opt_delta = sum(p.qty * p.greeks["delta"] for p in option_positions)
return opt_delta + perp_qty + spot_qty # perp & spot are +1 delta each per coin
# to be delta-neutral: perp_qty = -(opt_delta + spot_qty)So the programmer’s job is the same as in equities but with a richer book: compute the net Greeks across options, perps and spot, and you always know your true exposure. The perp is your cheapest, most liquid delta-adjustment tool — use it.
Pitfalls
- Forgetting the perp/spot delta. An options book that looks neutral can be very directional once you add the perp you’re also holding. Always net everything.
- Underestimating 24/7 theta. Decay doesn’t pause on weekends. Three days of theta over a weekend is real, and there’s no “closed market” to hide in.
- Treating crypto gamma like equity gamma. With 10–20% daily moves possible, gamma risk near expiry is larger than your equity instincts expect.
Recap
The Greeks are identical maths in crypto; what changes is scale and context. Dollar values are large (IV ~55%), theta runs continuously 24/7 (weekends included), and your true delta must include perps and spot, which are pure delta. Compute net Greeks across your whole book — that netting, with the perp as the delta tool, is the foundation of delta-hedging later.
Next: Lesson 6 — Crypto Volatility, the single biggest practical difference from equity options.