Mean Inversion Models API

Mean inversion pricing model for asset pricing.

This module implements the Ornstein-Uhlenbeck process for mean-reverting assets such as commodities, interest rates, and volatility.

analytical_mean_inversion_option(current_price, long_term_mean, mean_reversion_rate, volatility, time_to_expiry, risk_free_rate, strike_price, option_type='call')

Price European options on mean-reverting assets using an analytical approximation.

This function implements an analytical approximation for pricing European options on mean-reverting assets based on the Ornstein-Uhlenbeck process.

Parameters:

Name	Type	Description	Default
current_price	float	Current price of the underlying asset	required
long_term_mean	float	Long-term mean level that the asset price reverts to	required
mean_reversion_rate	float	Speed at which the asset price reverts to the long-term mean (annualized)	required
volatility	float	Volatility of the asset price (annualized)	required
time_to_expiry	float	Time to option expiration in years	required
risk_free_rate	float	Risk-free interest rate (annualized)	required
strike_price	float	Strike price of the option	required
option_type	str	Type of option ('call' or 'put'), by default 'call'	'call'

Returns:

Type	Description
dict	Option price and details

Raises:

Type	Description
ValueError	If Current price, volatility, time to expiry, mean reversion rate, or strike price are not positive. If option type is not 'call' or 'put'.

mean_inversion_pricing(current_price, long_term_mean, mean_reversion_rate, volatility, time_to_expiry, risk_free_rate, strike_price, option_type='call', simulations=10000, time_steps=252, seed=None)

Price options on mean-reverting assets using Monte Carlo simulation.

This function implements the Ornstein-Uhlenbeck process to model mean-reverting assets and prices options using Monte Carlo simulation.

Parameters:

Name	Type	Description	Default
current_price	float	Current price of the underlying asset	required
long_term_mean	float	Long-term mean level that the asset price reverts to	required
mean_reversion_rate	float	Speed at which the asset price reverts to the long-term mean (annualized)	required
volatility	float	Volatility of the asset price (annualized)	required
time_to_expiry	float	Time to option expiration in years	required
risk_free_rate	float	Risk-free interest rate (annualized)	required
strike_price	float	Strike price of the option	required
option_type	str	Type of option ('call' or 'put'), by default 'call'	'call'
simulations	int	Number of Monte Carlo simulations, by default 10000	10000
time_steps	int	Number of time steps in each simulation, by default 252	252
seed	int	Random seed for reproducibility, by default None	None

Returns:

Type	Description
dict	Option price and details

Raises:

Type	Description
ValueError	If Current price, volatility, time to expiry, mean reversion rate, or simulations are not positive. If option type is not 'call' or 'put'. If time steps is not a positive integer.