Risk Neutral Pricing API

Risk-neutral valuation for derivatives pricing.

risk_neutral_valuation(payoff_function, underlying_price, risk_free_rate, volatility, time_to_expiry, steps=100, simulations=1000, dividend_yield=0.0, seed=None)

Price a derivative using risk-neutral valuation with optimized NumPy vectorization.

Parameters:

Name	Type	Description	Default
payoff_function	callable	Function that takes the final underlying price and returns the payoff	required
underlying_price	float	Current price of the underlying asset	required
risk_free_rate	float	Risk-free interest rate (annualized)	required
volatility	float	Volatility of the underlying asset (annualized)	required
time_to_expiry	float	Time to expiration in years	required
steps	int	Number of time steps in the simulation, by default 100	100
simulations	int	Number of Monte Carlo simulations, by default 1000	1000
dividend_yield	float	Continuous dividend yield, by default 0.0	0.0
seed	int	Random seed for reproducibility, by default None	None

Returns:

Type	Description
dict	Derivative price and details

Raises:

Type	Description
ValueError	If the payoff function is not callable, underlying price is not positive, time to expiry is not positive, volatility is not positive, steps is not a positive integer, or simulations is not a positive integer.