Black-Scholes Option Pricing
The Black-Scholes Option Pricing calculation calculates the price of European style call and put options. Furthermore it calculates the so called "Greeks" which represent market sensitivities of options.
An option is an agreement that gives the option holder the right, but not the obligation, to buy or sell specified securities at a given price (the strike price) from or to the option writer or issuer.
Two common types of options exist:
- call options, which give the holder the right to buy an underlying stock at a specified price
- put options, which give the holder the right to sell an underlying stock at a specified price
With American style options,
the option can be excercised at any time up
to the expiration date of the option.
With European style options, the option can be excercised only
on the expiration date. Please note FinKit calculates European style
options.
The Black–Scholes model, published by Fischer Black and Myron Scholes in 1973, is a mathematical model that calculates the theoretical value of European style put and call stock options.
For more info on the Black-Scholes model and its key assumptions, please visit the Wikipedia page on the subject.
Input
| • risk free rate | |
| • duration in years | |
| • underlying stock price | |
| • option strike price | |
| • volatility |
Tip: the duration in years between any two given days can be easily calculated using FinKit's Year Fraction calculation.
Results
| • call option price |
| • put option price |
Details
FinKit also calculates the "Greeks" which are quantities representing market sensitivities of options.
The delta is the rate of change of the option price with respect to the price of the underlying stock. It measures sensitivity to price.
The gamma is the rate of change of the option's delta with respect to the price of the underlying stock. It measures measures second order sensitivity to price.
The vega is the rate of change of the option price with respect to volatility. It measures sensitivity to volatility. It is scaled down to a 1 point (0.01 %) change in volatility.
The theta is the rate of change of the option price with respect to the duration of the option. It measures the sensitivity to the passage of time and is scaled down to a one-day change.
The rho is the rate of change of the option price with respect to the interest rate. It measures the sensitivity to market rate changes. It is scaled down to a 1 point (0.01 %) change in the interest rate.
Examples
| • | Stock from the ABC company has a current price of $25 and a volatility of 30 %. The risk free rate is at 10 %. The annual dividend is 2 %. What is the price of a 3-month call option at a strike price of $28?
Answer: $0.634987 |
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| • | Stock from the ABC company has a current price of $25 and a volatility of 30 %. The risk free rate is at 10 %. There is no dividend. What is the price of a 3-month put option at a strike price of $28?
Answer: $2.980808 |
Related topic
| Black-Scholes Implied Volatility |