BlackScholesPreis
BlackScholesPreis refers to the theoretical value of a European option as determined by the Black-Scholes pricing model. The model provides closed-form formulas for call and put prices when the underlying asset follows a lognormal process under a risk-neutral measure. For a non-dividend-paying stock, the European call price is C = S0 N(d1) − K e^(−rT) N(d2), and the put price is P = K e^(−rT) N(−d2) − S0 N(−d1), where N(·) is the standard normal cumulative distribution function. The terms d1 and d2 are defined as d1 = [ln(S0/K) + (r + 0.5 σ^2) T] / (σ sqrt(T)) and d2 = d1 − σ sqrt(T). For stocks that pay a continuous dividend yield q, the formulas adjust to C = S0 e^(−qT) N(d1) − K e^(−rT) N(d2) and P = K e^(−rT) N(−d2) − S0 e^(−qT) N(−d1), with d1 and d2 defined using (r − q + 0.5 σ^2) in place of r.
Parameters include S0 (current spot price), K (strike), T (time to maturity), r (risk-free interest rate), σ
History and use: the model was introduced in 1973 by Fischer Black, Myron Scholes, and Robert Merton,