Black-Scholes Calculator

To calculate Black and Scholes, enter stock price, strike price, time to expiration in years, risk-free rate as a percentage, and volatility as a percentage in calculator. Select option type (Call/Put). The calculator will compute theoretical option price and Greeks (Delta, Gamma, Theta, Vega).

• Inputs: Stock price = $100, Strike price = $100, Time = 1 year, Risk-free rate = 5%, Volatility = 20%
• Process: Enter all values and select “Call” option
• Result: The call option price is $10.45

How to Calculate Black Scholes

To easily calculate Black Scholes, compute d1 and d2 using the formulas: d1 = (ln(S/K) + (r + (σ²/2)) T) / (σ √T), d2 = d1 – σ * √T. Find N(d1) and N(d2) and Substitute into the call or put option formulas: Call: C = S N(d1) – K e^(-rT) * N(d2), Put: P = K e^(-rT) N(-d2) – S * N(-d1)

• Inputs: Stock price = $150, Strike = $145, Time = 0.5 years, Rate = 3%, Volatility = 25%
• Calculations: d1 = 0.5673, d2 = 0.3906, N(d1) = 0.7148, N(d2) = 0.6520
• Result: The call option value is $15.24

Black Scholes Formula

Call Option Price = S × N(d1) - K × e^(-rT) × N(d2)
Put Option Price = K × e^(-rT) × N(-d2) - S × N(-d1)

Where:

d1 = [ln(S/K) + (r + σ²/2)T] / (σ√T)
d2 = d1 - σ√T

S = Stock price
K = Strike price
T = Time to expiration
r = Risk-free rate
σ = Volatility
N() = Cumulative normal distribution

Tech Stock Option

• Inputs: Stock = $200, Strike = $210, Time = 0.25 years, Rate = 2%, Volatility = 30%
• Calculations: d1 = -0.0944, d2 = -0.2444, N(d1) = 0.4624, N(d2) = 0.4035
• Result: The call option price is $7.32

Bank Stock Option

• Inputs: Stock = $50, Strike = $45, Time = 1 year, Rate = 4%, Volatility = 15%
• Calculations: d1 = 0.8544, d2 = 0.7044, N(d1) = 0.8035, N(d2) = 0.7594
• Result: The call option price is $8.21

Index Fund Option

• Inputs: Stock = $300, Strike = $300, Time = 0.5 years, Rate = 3%, Volatility = 18%
• Calculations: d1 = 0.1915, d2 = 0.0642, N(d1) = 0.5759, N(d2) = 0.5256
• Result: The call option price is $15.87

Growth Stock Option

• Inputs: Stock = $75, Strike = $70, Time = 2 years, Rate = 5%, Volatility = 40%
• Calculations: d1 = 0.6234, d2 = 0.0575, N(d1) = 0.7335, N(d2) = 0.5229
• Result: The call option price is $19.64

Value Stock Option

• Inputs: Stock = $40, Strike = $40, Time = 0.75 years, Rate = 3%, Volatility = 22%
• Calculations: d1 = 0.1531, d2 = 0.0625, N(d1) = 0.5609, N(d2) = 0.5249
• Result: The call option price is $4.12

What is Black Scholes?

Black-Scholes Model: A mathematical formula for calculating the theoretical price of European-style stock options, developed by Fischer Black and Myron Scholes in 1973. The model considers five key variables in its calculation.

Key Variables:

Stock Price (S): Current market price
Strike Price (K): Option's exercise price
Time (T): Time until expiration
Risk-free Rate (r): Treasury yield
Volatility (σ): Stock price variation