Understanding N ( d 1 ) and N ( d 2 ) : Risk - Adjusted Probabilities in the Black - Scholes Model 1 Lars
نویسنده
چکیده
This paper uses risk-adjusted lognormal probabilities to derive the BlackScholes formula and explain the factors N(d1) and N(d2). It also shows how the one-period and multi-period binomial option pricing formulas can be restated so that they involve analogues of N(d1) and N(d2) which have the same interpretation as in the Black-Scholes model. Cet article utilise les probabilités lognormaux corrigées du risque pour dériver la formule de Black-Scholes et expliquer les facteurs N(d1) et N(d2). Il montre aussi comment les modèles binomiaux des prix d’options d’une et de plusieurs périodes peuvent être exprimés d’une façon telle qu’ils impliquent des analogues de N(d1) et N(d2) qui ont la même interprétation que dans le modèle de Black-Scholes.
منابع مشابه
Option Valuation with Sinusoidal Heteroskedasticity
Ito drift-diffusion process (1) can be used to derive the Black Scholes formula (2). [1] dS = σSdX + µdt (1) ∂f ∂t + 1 2 σ 2 S 2 ∂ 2 f ∂S 2 + rS ∂f ∂S − rf = 0 (2) By applying boundaries conditions V (S, T) = max{S − K, 0} and V (S, T) = max{0, S − K} to (2) we can solve the PDE to find its closed form solution for European calls and puts, the Black-Scholes Model. [7] C(s, t) = SN (d 1) − Ke r(...
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