Value a European call or put option under the CEV model.

Value a European call option under the CEV model. For beta < 1 the exact European CEV formula is expressed in terms of non-central chi-square distribution functions. For beta = 1 the model reduces to Black-Scholes.

Value a European put option using put-call parity.

Return the instantaneous percentage local volatility sigma_loc(S) = sigma S^(beta - 1).

Return the absolute diffusion coefficient sigma S^beta appearing in dS = (r-q)S dt + sigma S^beta dW.

Return the Black-Scholes implied volatility corresponding to the CEV European call price.

Return the Black-Scholes implied-volatility curve across strikes.

Alias for implied_volatility_curve(). For beta < 1 the basic CEV model generally produces a negative implied-volatility skew.

Monte Carlo valuation using a full-truncation Euler scheme. This is primarily intended as a numerical cross-check of the analytic European pricing formula.

Return the Black-Scholes implied-volatility surface generated by the CEV model. Parameters ---------- stock_price : float Current stock price. expiries : array_like Times to expiry in years. strikes : array_like Strike grid. interest_rate : float Continuously compounded risk-free rate. dividend_yield : float Continuously compounded dividend yield. Returns ------- vols : ndarray Matrix of implied volatilities with shape (len(expiries), len(strikes)) so that vols[i, j] is the implied volatility for expiries[i] and strikes[j].