How Does the Black-Scholes Model Use Implied Volatility to Price Options?
The Black-Scholes-Merton model is a mathematical formula used to estimate the theoretical price of European-style options. It takes five inputs: the asset price, strike price, time to expiration, risk-free interest rate, and volatility.
Since the market price of an option is known, the model is run in reverse to solve for the volatility input, which is the implied volatility (IV). IV is thus a variable derived from the option's current market price.
Glossar
Implied Volatility
Expectation ⎊ This value represents the market's consensus forecast of future asset price fluctuation, derived by reversing option pricing models using current market premiums.
Black-Scholes-Merton Model
Valuation ⎊ The Black-Scholes-Merton Model, initially conceived for European-style options on non-dividend-paying stocks, provides a theoretical estimate of the price of derivative instruments, adapting to cryptocurrency options through adjustments for continuous compounding and volatility estimation.
Option Pricing
Framework ⎊ Option pricing within cryptocurrency derivatives necessitates a framework extending beyond traditional Black-Scholes assumptions, primarily due to the unique characteristics of digital assets.
Market Price
Valuation ⎊ Market price represents the most recent, observable valuation at which an asset, such as a cryptocurrency or a derivative contract, was traded on an open exchange.
The Black-Scholes Model
Foundation ⎊ The Black-Scholes model serves as the cornerstone for modern options pricing theory, providing a continuous-time framework for calculating the fair value of derivatives.
Risk-Free Rate
Determinant ⎊ A risk-free rate, within cryptocurrency derivatives, represents the theoretical return on an investment with zero risk of financial loss over a given period, often proxied by yields on highly-rated sovereign debt denominated in a stable currency like the US Treasury yield.