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Optionssensitivitäten Rechner (Greeks)

Berechnen Sie die Kennzahlen Delta, Gamma und Vega zur Risikoanalyse Ihres Optionsportfolios.

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Berechnungsparameter

Geben Sie Ihre Parameter ein.

Aktienkurs (€)

Basispreis (Strike) (€)

Restlaufzeit (Jahre)

Volatilität (%)

Risikofreier Zinssatz (%)

Berechnetes Ergebnis

Call Delta (Δ) 0,62

Gamma (Γ) 0,03

Vega (ν) 0,27

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Expertentipp

Delta misst die Kursänderung des Optionsscheins bei 1 € Kursänderung des Basiswerts. Gamma beschreibt die Dynamik von Delta.

Funktionsweise des Rechners

Leitet die Black-Scholes-Gleichung mathematisch nach den Parametern Kurs und Volatilität ab.

Formel & Methodik

Delta = N(d1) Gamma = N'(d1) / (S * v * sqrt(t)) Vega = S * sqrt(t) * N'(d1)

Schritt-für-Schritt-Rechenbeispiel

Hier ist ein Schritt-für-Schritt-Beispiel zur Veranschaulichung der Berechnungen:

Bei Aktienkurs = 100 €, Strike = 98 €, Laufzeit = 0,5 Jahre und Volatilität = 25 %: - Delta = 0,62, Gamma = 0,03

Detailed Insights & Expert Guide

ℹ️ About this Calculation

This derivatives and options pricing calculator evaluates theoretical option premiums, implied volatility (IV), option Greeks (Delta, Gamma, Theta, Vega, Rho), multi-leg strategy risk profiles, and futures margin requirements using Black-Scholes and Cox-Ross-Rubinstein binomial models.

Variable Glossary

Input

Option Parameters

Underlying stock price (S), strike price (K), expiration days (T), volatility (σ %), and risk-free interest rate (r %).

Parameter

Greeks & Premium

Theoretical Call/Put price ($), Delta sensitivity (Δ), Theta daily decay (Θ), and maximum profit/loss boundaries.

How to Calculate Step-by-Step

Step 1

Input current asset price, option contract strike price, and target expiration date.

Step 2

Specify implied or historical volatility percentage, dividend yield %, and risk-free treasury yield.

Step 3

Review calculated fair value option price, Greek risk sensitivities, break-even stock price, and payoff diagram matrix.

FAQ

What are the primary Option Greeks and what do they measure?

Delta (Δ) measures price sensitivity to underlying asset moves; Gamma (Γ) measures rate of Delta change; Theta (Θ) measures daily time decay; Vega (ν) measures sensitivity to 1% volatility changes.

What is Put-Call Parity?

Put-Call Parity defines the static equilibrium relationship: Call Price - Put Price = Spot Price - Present Value of Strike Price. It prevents arbitrage between options and European spot markets.

Can option pricing models guarantee trading profits?

No. Black-Scholes and Binomial models assume continuous trading, constant volatility, and lognormal price distributions. Options trading involves substantial risk of capital loss due to leverage and volatility expansion.