Monte Carlo Simulation API

Monte Carlo option pricing model implementation.

hybrid_price_action_monte_carlo(option_type, underlying_price, strike_price, time_to_expiry, risk_free_rate, volatility, support_levels, resistance_levels, mean_reversion_params=None, jump_params=None, price_action_weight=0.4, mean_reversion_weight=0.3, jump_diffusion_weight=0.3, respect_level_strength=0.7, volatility_near_levels=1.3, simulations=10000, time_steps=252, dividend_yield=0.0, antithetic=True, seed=None)

A hybrid option pricing model that combines price action Monte Carlo with mean reversion and jump diffusion models.

This function creates a weighted average of three pricing models: 1. Price action Monte Carlo (respects support/resistance) 2. Mean reversion (if parameters provided) 3. Jump diffusion (if parameters provided)

Parameters:

Name	Type	Description	Default
option_type	str	Type of option ('european_call', 'european_put', 'asian_call', 'asian_put', 'lookback_call', 'lookback_put')	required
underlying_price	float	Current price of the underlying asset	required
strike_price	float	Strike price of the option	required
time_to_expiry	float	Time to expiration in years	required
risk_free_rate	float	Risk-free interest rate (annualized)	required
volatility	float	Base volatility of the underlying asset (annualized)	required
support_levels	List[float]	List of price levels that act as support	required
resistance_levels	List[float]	List of price levels that act as resistance	required
mean_reversion_params	Dict	Parameters for mean reversion model: {'long_term_mean': float, 'mean_reversion_rate': float}	None
jump_params	Dict	Parameters for jump diffusion: {'jump_intensity': float, 'jump_mean': float, 'jump_std': float}	None
price_action_weight	float	Weight for the price action model (0-1)	0.4
mean_reversion_weight	float	Weight for the mean reversion model (0-1)	0.3
jump_diffusion_weight	float	Weight for the jump diffusion model (0-1)	0.3
respect_level_strength	float	How strongly the price respects support/resistance levels (0-1)	0.7
volatility_near_levels	float	Volatility multiplier when price is near support/resistance levels	1.3
simulations	int	Number of Monte Carlo simulations	10000
time_steps	int	Number of time steps in each simulation	252
dividend_yield	float	Continuous dividend yield	0.0
antithetic	bool	Whether to use antithetic variates for variance reduction	True
seed	int	Random seed for reproducibility	None

Returns:

Type	Description
dict	Dictionary containing the option price, standard error, and other information

Raises:

Type	Description
ValueError	If weights do not sum to 1.0, or missing required parameters

monte_carlo_option_pricing(option_type, underlying_price, strike_price, time_to_expiry, risk_free_rate, volatility, simulations=10000, time_steps=252, dividend_yield=0.0, antithetic=True, jump_intensity=0.0, jump_mean=0.0, jump_std=0.0, seed=None)

Price options using Monte Carlo simulation.

This function implements Monte Carlo simulation for pricing various types of options, including European, Asian, and lookback options. It also supports jump diffusion for modeling assets with sudden price jumps like cryptocurrencies.

Parameters:

Name	Type	Description	Default
option_type	str	Type of option ('european_call', 'european_put', 'asian_call', 'asian_put', 'lookback_call', 'lookback_put')	required
underlying_price	float	Current price of the underlying asset	required
strike_price	float	Strike price of the option	required
time_to_expiry	float	Time to expiration in years	required
risk_free_rate	float	Risk-free interest rate (annualized)	required
volatility	float	Volatility of the underlying asset (annualized)	required
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
dividend_yield	float	Continuous dividend yield, by default 0.0	0.0
antithetic	bool	Whether to use antithetic variates for variance reduction, by default True	True
jump_intensity	float	Expected number of jumps per year (lambda in Poisson process), by default 0.0	0.0
jump_mean	float	Mean of the jump size distribution, by default 0.0	0.0
jump_std	float	Standard deviation of the jump size distribution, by default 0.0	0.0
seed	int	Random seed for reproducibility, by default None	None

Returns:

Type	Description
dict	Option price and details

Raises:

Type	Description
ValueError	If option_type is not valid, or prices are non-positive, or time to expiry is non-positive, or volatility is non-positive, or number of simulations or time steps are non-positive, or jump intensity or jump standard deviation are negative

price_action_monte_carlo(option_type, underlying_price, strike_price, time_to_expiry, risk_free_rate, volatility, support_levels, resistance_levels, respect_level_strength=0.7, volatility_near_levels=1.3, simulations=10000, time_steps=252, dividend_yield=0.0, jump_intensity=0.0, jump_mean=0.0, jump_std=0.0, antithetic=True, seed=None)

Price options using Monte Carlo simulation with price action considerations.

This function extends the standard Monte Carlo simulation by incorporating technical analysis elements such as support and resistance levels. The price paths are adjusted to respect these levels, with increased volatility near levels and potential bounces or breakouts.

Parameters:

Name	Type	Description	Default
option_type	str	Type of option ('european_call', 'european_put', 'asian_call', 'asian_put', 'lookback_call', 'lookback_put')	required
underlying_price	float	Current price of the underlying asset	required
strike_price	float	Strike price of the option	required
time_to_expiry	float	Time to expiration in years	required
risk_free_rate	float	Risk-free interest rate (annualized)	required
volatility	float	Base volatility of the underlying asset (annualized)	required
support_levels	List[float]	List of price levels that act as support (in ascending order)	required
resistance_levels	List[float]	List of price levels that act as resistance (in ascending order)	required
respect_level_strength	float	How strongly the price respects support/resistance levels (0-1) 0 = no respect (standard Monte Carlo), 1 = strong respect	0.7
volatility_near_levels	float	Volatility multiplier when price is near support/resistance levels	1.3
simulations	int	Number of Monte Carlo simulations	10000
time_steps	int	Number of time steps in each simulation	252
dividend_yield	float	Continuous dividend yield	0.0
jump_intensity	float	Expected number of jumps per year (lambda in Poisson process)	0.0
jump_mean	float	Mean of the jump size distribution	0.0
jump_std	float	Standard deviation of the jump size distribution	0.0
antithetic	bool	Whether to use antithetic variates for variance reduction	True
seed	int	Random seed for reproducibility	None

Returns:

Type	Description
dict	Dictionary containing the option price, standard error, and other information

Raises:

Type	Description
ValueError	If prices are non-positive, or time to expiry is non-positive, or volatility is non-positive, or number of simulations or time steps are non-positive, or jump intensity or jump standard deviation are negative, or respect level strength is not between 0 and 1, or volatility multiplier is non-positive