Black-Scholes Option Pricing API

Black-Scholes option pricing model implementation.

black_scholes(option_type, underlying_price, strike_price, time_to_expiry, risk_free_rate, volatility, dividend_yield=0.0)

Calculate option price using the Black-Scholes model.

Parameters:

Name	Type	Description	Default
option_type	str	Type of option ('call' or '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
dividend_yield	float	Continuous dividend yield, by default 0.0	0.0

Returns:

Type	Description
dict	Option price and Greeks

Raises:

Type	Description
ValueError	If option_type is not 'call' or 'put' If underlying_price or strike_price is not positive If time_to_expiry is not positive If volatility is not positive

implied_volatility(option_type, market_price, underlying_price, strike_price, time_to_expiry, risk_free_rate, dividend_yield=0.0, precision=0.0001, max_iterations=100, initial_vol=0.2)

Calculate implied volatility from option market price using the Black-Scholes model.

Parameters:

Name	Type	Description	Default
option_type	str	Type of option ('call' or 'put')	required
market_price	float	Market price of the option	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
dividend_yield	float	Continuous dividend yield, by default 0.0	0.0
precision	float	Desired precision for implied volatility, by default 0.0001	0.0001
max_iterations	int	Maximum number of iterations, by default 100	100
initial_vol	float	Initial volatility guess, by default 0.2	0.2

Returns:

Type	Description
dict	Implied volatility and option details

Examples:

>>> from pypulate.asset import implied_volatility
>>> result = implied_volatility(
...     option_type='call',
...     market_price=10.5,
...     underlying_price=100,
...     strike_price=100,
...     time_to_expiry=1.0,
...     risk_free_rate=0.05
... )
>>> print(f"Implied Volatility: {result['implied_volatility']:.2%}")
Implied Volatility: 20.12%