What Alternative Options Pricing Models Are Sometimes Preferred for Highly Volatile Assets like Crypto?
Alternative models are preferred because Black-Scholes assumes a normal distribution of returns, which crypto violates with its 'fat tails' (extreme price movements). Models like the Merton Jump-Diffusion model account for sudden, unexpected price jumps.
Another is the Heston model, which allows for stochastic volatility (volatility that changes over time), offering a more realistic representation of the crypto market's price dynamics.
Glossar
Options Models
Pricing ⎊ Options models are mathematical frameworks used to calculate the theoretical fair value of a derivative contract.
Heston Model
Modeling ⎊ This framework describes the evolution of an asset's price and its instantaneous variance through coupled stochastic differential equations.
Options Pricing Models
Models ⎊ Options Pricing Models are mathematical frameworks, such as Black-Scholes or binomial trees, adapted to calculate the theoretical fair value of derivative contracts based on underlying asset dynamics and market parameters.
Stochastic Volatility
Volatility Model ⎊ Stochastic Volatility describes a class of mathematical models where the volatility itself is treated as a random process rather than a constant, which is often necessary to accurately price and hedge options on highly erratic crypto assets.
Highly Volatile Assets
Exposure ⎊ Highly volatile assets, within cryptocurrency, options, and derivatives, represent instruments exhibiting pronounced price fluctuations over short durations, demanding sophisticated risk quantification.
Merton Jump-Diffusion Model
Calibration ⎊ The Merton Jump-Diffusion Model, when applied to cryptocurrency options, necessitates careful calibration of its parameters ⎊ volatility, drift, and jump intensity ⎊ using observed market prices, often employing techniques like maximum likelihood estimation or implied volatility surface fitting.