# Black Scholes Calculator

You can use this Black-Scholes Calculator to determine the fair market value (price) of a European put or call option based on the Black-Scholes pricing model. It also calculates and plots the Greeks – Delta, Gamma, Theta, Vega, Rho.

Enter your own values in the form below and press the "Calculate" button to see the results.

Option Type: Call Put | Values | ||||
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x | Variable | Symbol | Input Value | From | To |

Spot Price | SP |
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Strike Price | ST |
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Expiry Time (Y) | t |
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Volatility (%) | v |
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Rate (%) | r |
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Div. Yield (%) | d |

## Option Type: Call Option

y | Axis | Symbol | Result |
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Value |
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d1 |
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d2 |
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Delta |
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Gamma |
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Theta |
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Vega |
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Rho |

## The Black-Scholes Option Pricing Formula

You can compare the prices of your options by using the Black-Scholes formula. It's a well-regarded formula that calculates theoretical values of an investment based on current financial metrics such as stock prices, interest rates, expiration time, and more. The Black-Scholes formula helps investors and lenders to determine the best possible option for pricing.

The Black Scholes Calculator uses the following formulas:

C = SP *e*^{-dt} N(d_{1}) - ST *e*^{-rt} N(d_{2})

P = ST *e*^{-rt} N(-d_{2}) - SP *e*^{-dt} N(-d_{1})

**d _{1} = ( ln(SP/ST) + (r - d + (σ^{2}/2)) t ) / σ √t**

**d _{2} = ( ln(SP/ST) + (r - d - (σ^{2}/2)) t ) / σ √t = d_{1} - σ √t**

*Where:*

**C** is the value of the call option,

**P** is the value of the put option,

**N (.)** is the cumulative standard normal distribution function,

**SP** is the current stock price (spot price),

**ST** is the strike price (exercise price),

**e** is the exponential constant (2.7182818),

**ln** is the natural logarithm,

**r** is the current risk-free interest rate (as a decimal),

**t** is the time to expiration in years,

**σ** is the annualized volatility of the stock (as a decimal),

**d** is the dividend yield (as a decimal).

You may also be interested in our EPS Calculator or RSI Calculator