This calculator uses the Nobel Prize winning Black Scholes calculator to value put and call options. Options give you the right to buy or sell something at a specific price during a specific time period. Call options give you an option to buy and put options give you an option to sell. You buy calls when you expect prices to increase and puts and you expect prices to decline.
1. Black-Scholes Model Foundation
Calculates the theoretical value of European-style call and put options based on five parameters: underlying asset price, strike price, time to expiration, risk-free interest rate, and volatility.
2. Implied Volatility (IV)
Represents the market's expected future volatility of the underlying asset, solved backward from the current option market price using the Brent numerical solver.
3. Moneyness (ITM vs. OTM)
In-The-Money (ITM) options have intrinsic value. Calls are ITM when the asset price is above the strike price. Puts are ITM when the asset price is below the strike price.
4. High Volatility Sensitivity
Under extremely high volatility, the call option price converges to the underlying asset price, while the put option price approaches the discounted strike price.
5. Parameter Conventions
The risk-free rate is entered as an annual percentage (e.g. 5.0%), and the expiration term is entered in months, which is automatically converted to annualized time.
6. Solver Minimum Bounds
If the option's market price is below its theoretical minimum intrinsic value, the solver caps the implied volatility at 0.00% to indicate that no premium exists.
It uses the Black-Scholes model to value put and call options — call options give you the right to buy at a set price, while put options give you the right to sell, and this calculator estimates what either should be worth given your inputs.
A call option gives you the right to buy at a specific price, which is valuable if you expect the price to rise; a put option gives you the right to sell at a specific price, which is valuable if you expect the price to decline.
Implied volatility reflects the market's expectation of how much the underlying asset's price will fluctuate — since option value is highly sensitive to volatility, small changes in this input can meaningfully change the calculated price.
An option is "in the money" (ITM) when exercising it immediately would be profitable, and "out of the money" (OTM) when it wouldn't be — this moneyness affects both the option's current value and how sensitive that value is to further price moves.
The Bond Calculator and Fixed Income Dashboard can help with fixed-income analysis, while Portfolio Valuation lets you track how any options or other positions fit into your broader portfolio.
