option-pricing

Use the bs2 mode for a closed-form Bjerksund-Stensland/BAW approximation at about 3.6 microseconds per option, or the binomial mode with steps=2000 for about 0.1% error. For custom payoffs, the lsm mode implements Longstaff-Schwartz Monte Carlo.

Black-Scholes runs at roughly 419,000 options per second for European options, and BAW (bs2) at about 276,000 per second for American options. Both are O(1) closed-form methods, roughly 2000x faster than a binomial tree with 500 steps.

Use the iv mode with the observed market price, spot, strike, time to expiry, and rate. It solves via bisection in about 82 microseconds for European options using Black-Scholes, and uses a binomial engine for American options.

Yes, it implements Heston 1993 via Fourier integration at about 400 microseconds per option, capturing volatility smile through the rho parameter. Bates 1996 adds Merton jump diffusion for crash risk at about 6 milliseconds per option.

Black-Scholes assumes constant volatility and lognormal returns, so it misses the volatility smile and underestimates tail risk. It also only prices European options; use BAW or binomial trees for American exercise, and Heston or Bates when skew matters.

Path-dependent exotics like Asian, barrier, and lookback options are not implemented out of the box, though the Monte Carlo framework is extensible. Multi-asset options, discrete dividends, and rough volatility models are also unsupported.