Pricing

{
  "eth_spot": 2450.50,
  "eth_iv": 0.65,
  "protocol_fee_bps": 400,
  "gas_price_gwei": 0.01,
  "available_otokens": [
    {
      "address": "0x...",
      "strike_price": 2400.0,
      "expiry": 1741200000,
      "is_put": true
    }
  ]
}

from math import log, sqrt, exp
from scipy.stats import norm

def bs_price(is_put, spot, strike, T, r, sigma):
    """T = time to expiry in years, r = risk-free rate, sigma = IV."""
    if T <= 0:
        return max(strike - spot, 0) if is_put else max(spot - strike, 0)
    d1 = (log(spot / strike) + (r + 0.5 * sigma**2) * T) / (sigma * sqrt(T))
    d2 = d1 - sigma * sqrt(T)
    if is_put:
        return strike * exp(-r * T) * norm.cdf(-d2) - spot * norm.cdf(-d1)
    return spot * norm.cdf(d1) - strike * exp(-r * T) * norm.cdf(d2)

def bs_delta(is_put, spot, strike, T, r, sigma):
    """Returns delta: [-1, 0] for puts, [0, 1] for calls."""
    if T <= 0:
        if is_put:
            return -1.0 if spot < strike else 0.0
        return 1.0 if spot > strike else 0.0
    d1 = (log(spot / strike) + (r + 0.5 * sigma**2) * T) / (sigma * sqrt(T))
    return norm.cdf(d1) - 1.0 if is_put else norm.cdf(d1)

def bid_price(is_put, spot, strike, T, r, sigma, spread_bps=300):
    theo = bs_price(is_put, spot, strike, T, r, sigma)
    return max(theo * (1 - spread_bps / 10000), 1e-6)