Crypto Newbie / Simulators / Options Pricing
Black-Scholes Options Pricing Simulator (Crypto)
Deribit lists $20B+ in BTC + ETH option open interest. Lyra, Dopex, Stryke offer on-chain alternatives. Pricing all of them uses the Black-Scholes model from 1973, with adjustments for crypto's high implied volatility (50-150% annualised vs equity's 15-30%). This simulator runs the exact BSM formula plus all Greeks (delta, gamma, vega, theta) so you can see how option premiums move with spot, time, and IV.
Option setup
Pricing
Premium
$7.00k
Intrinsic value
$0.00
Extrinsic value (time value)
$7.00k
Moneyness
ATM (0.00%)
Greeks
Delta
0.5369
Premium change per $1 spot move. 0.5 = call price moves ~50¢ per $1 ETH move. Range: 0 to 1 for calls, -1 to 0 for puts.
Gamma
0.000018
Delta's rate of change. High gamma = delta swings fast as spot moves. Highest at ATM near expiry.
Vega (per 1% IV)
$107.94
Premium change per 1% absolute change in IV. ATM options are most vega-sensitive.
Theta (per day)
-$143.92
Time decay — premium lost per day as expiry approaches. Always NEGATIVE for option BUYERS, positive for sellers. Accelerates near expiry.
Counterpart (put at same strike)
Premium: $7.00k
Delta: -0.4631
Theta (per day): -$143.92
Intrinsic + extrinsic — the two halves of premium
Premium = intrinsic + extrinsic. Intrinsic = how much the option is IN the money RIGHT NOW (call: max(0, spot − strike); put: max(0, strike − spot)). Extrinsic = the rest — time value + IV value. ATM options have ZERO intrinsic and maximum extrinsic. Deep ITM options are nearly all intrinsic (the extrinsic shrinks because there's little chance the option goes back OTM). Deep OTM options are pure extrinsic — they have NO chance of being intrinsic unless spot moves a lot.
Why crypto IV is so high
BTC's 30-day realised volatility averages 60-80%; ETH 70-100%; altcoins 100-200%. For comparison: S&P 500 averages 15-20%, FAANG tech stocks 25-35%. Crypto's high vol comes from 24/7 markets (no overnight cool-down), thin order books vs equity markets, high speculative demand from retail, and structural regime changes (halvings, ETF approvals, regulatory events). Higher IV makes options more EXPENSIVE relative to spot — a 30-day ATM BTC call at 80% IV costs ~10% of spot, vs ~4% for an equivalent S&P call.
The four Greeks in plain terms
DELTA: 'how much does premium move per $1 of spot move?' Call delta is 0 to 1; put delta is -1 to 0. ATM call delta ≈ 0.5. GAMMA: 'how much does delta change per $1 of spot move?' Highest at ATM near expiry. Long gamma = you profit from big moves (in either direction). Short gamma = you profit from small moves. VEGA: 'how much does premium move per 1% IV change?' Long vega = you profit when IV rises. Short vega = you profit when IV falls. Vega is highest at ATM. THETA: 'how much premium decays per day?' Always NEGATIVE for buyers (you lose money holding); positive for sellers (you collect decay). Accelerates near expiry — gamma sellers harvest the most theta in the final week.
What the simulator does (and doesn't)
DOES: compute the exact BSM premium + all four Greeks for any strike/DTE/IV combination. Lets you compare call vs put at the same strike to see put-call parity in action (calls + puts at same strike have related prices). DOESN'T: model the volatility smile (real options at far OTM/ITM strikes have higher IV than ATM — the simulator assumes flat IV across strikes). For accurate market pricing, real traders use SVI smile fits or volatility surface models. The simulator is the right starting point for understanding mechanics; production trading uses extensions.
Frequently asked questions
+Why don't crypto options use risk-free rate?
Traditional options use the risk-free rate (e.g., 3-month T-bill yield) because option pricing assumes you can borrow + lend at that rate. Crypto has no equivalent — you can earn 4-8% on USDC via DeFi, but that's not 'risk-free'. Most crypto options pricing uses r=0 for simplicity, which slightly under-prices ITM calls and over-prices ITM puts vs theoretical fair value. For short-DTE options the impact is < 1% — fine for most use cases.
+What's the difference between ATM, ITM, and OTM?
ATM (at-the-money): strike ≈ spot. ITM (in-the-money): the option HAS intrinsic value right now (call with strike < spot; put with strike > spot). OTM (out-of-the-money): zero intrinsic value (call with strike > spot; put with strike < spot). ATM options are typically the most LIQUID; OTM options are typically the CHEAPEST (lowest premium); ITM options are typically the LEAST liquid (higher cost, fewer buyers).
+How do option SELLERS make money — isn't selling unlimited risk?
Sellers collect the premium UPFRONT and profit if the option expires worthless. Naked option selling DOES have unlimited risk (selling a call: theoretically infinite loss if spot moons). COVERED strategies limit risk: sell a call against ETH you already hold ('covered call') → if called away, you sell ETH at the strike. Sell a put with cash collateral ('cash-secured put') → if exercised, you buy ETH at the strike. Most retail option sellers use covered strategies; pros use complex multi-leg spreads to define risk while collecting theta.
+What's IV crush and when does it happen?
IV crush = sudden drop in implied volatility, dragging option premiums down sharply. Happens after expected events resolve: earnings (for stocks), CPI prints (for crypto), token unlocks. Buyers of options before the event get hurt because even if spot moved in their favour, IV collapsed by 30-50% wiping out vega gains. Sellers of options before events profit DOUBLE: from theta decay + IV crush. This is why 'sell volatility before predictable events' is a common pro strategy.
+Are on-chain options (Lyra, Dopex) accurately priced vs Deribit?
Mostly. Lyra uses an AMM-based market maker that adjusts IV based on order flow. Deribit uses a traditional order book with market makers quoting. Pricing converges within 1-2% for liquid pairs (BTC + ETH near-term ATM). For long-dated or deep OTM strikes, on-chain options can be 5-20% off Deribit fair value due to thinner LP capital. Most arbers profit from these spreads — fewer than expected because gas + slippage eats most opportunities.