fyne.blackscholes

fyne.blackscholes.delta(underlying_price, strike, expiry, sigma, put=False)

Black-Scholes Greek delta

Computes the Greek delta of the option – i.e. the option price sensitivity with respect to its underlying price – according to the Black-Scholes model.

Parameters:

• underlying_price (float) – Price of the underlying asset.
• strike (float) – Strike of the option.
• expiry (float) – Time remaining until the expiry of the option.
• sigma (float) – Volatility parameter.
• put (bool, optional) – Whether the option is a put option. Defaults to False.

Returns:

float – Greek delta according to Black-Scholes formula.

Example

>>> import numpy as np
>>> from fyne import blackscholes
>>> sigma = 0.2
>>> underlying_price = 100.
>>> strike = 90.
>>> expiry = 0.5
>>> call_delta = blackscholes.delta(underlying_price, strike, expiry, sigma)
>>> np.round(call_delta, 2)
0.79
>>> put_delta = blackscholes.delta(underlying_price, strike, expiry, sigma,
...                                put=True)
>>> np.round(put_delta, 2)
-0.21

fyne.blackscholes.formula(underlying_price, strike, expiry, sigma, put=False)

Black-Scholes formula

Computes the price of the option according to the Black-Scholes formula.

Parameters:

• underlying_price (float) – Price of the underlying asset.
• strike (float) – Strike of the option.
• expiry (float) – Time remaining until the expiry of the option.
• sigma (float) – Volatility parameter.
• put (bool, optional) – Whether the option is a put option. Defaults to False.

Returns:

float – Option price according to Black-Scholes formula.

Example

>>> import numpy as np
>>> from fyne import blackscholes
>>> sigma = 0.2
>>> underlying_price = 100.
>>> strike = 90.
>>> expiry = 0.5
>>> call_price = blackscholes.formula(underlying_price, strike, expiry,
...                                   sigma)
>>> np.round(call_price, 2)
11.77
>>> put_price = blackscholes.formula(underlying_price, strike, expiry,
...                                  sigma, put=True)
>>> np.round(put_price, 2)
1.77

fyne.blackscholes.implied_vol(underlying_price, strike, expiry, option_price, put=False, assert_no_arbitrage=True)

Implied volatility function

Inverts the Black-Scholes formula to find the volatility that matches the given option price. The implied volatility is computed using Newton’s method.

Parameters:

• underlying_price (float) – Price of the underlying asset.
• strike (float) – Strike of the option.
• expiry (float) – Time remaining until the expiry of the option.
• option_price (float) – Option price according to Black-Scholes formula.
• put (bool, optional) – Whether the option is a put option. Defaults to False.
• assert_no_arbitrage (bool, optional) – Whether to throw an exception upon no arbitrage bounds violation. Defaults to True.

Returns:

float – Implied volatility.

Example

>>> import numpy as np
>>> from fyne import blackscholes
>>> call_price = 11.77
>>> put_price = 1.77
>>> underlying_price = 100.
>>> strike = 90.
>>> expiry = 0.5
>>> implied_vol = blackscholes.implied_vol(underlying_price, strike,
...                                        expiry, call_price)
>>> np.round(implied_vol, 2)
0.2
>>> implied_vol = blackscholes.implied_vol(underlying_price, strike,
...                                        expiry, put_price, put=True)
>>> np.round(implied_vol, 2)
0.2

fyne.blackscholes.vega(underlying_price, strike, expiry, sigma)

Black-Scholes Greek vega

Computes the Greek vega of the option – i.e. the option price sensitivity with respect to its volatility parameter – according to the Black-Scholes model. Note that the Greek vega is the same for calls and puts.

Parameters:

• underlying_price (float) – Price of the underlying asset.
• strike (float) – Strike of the option.
• expiry (float) – Time remaining until the expiry of the option.
• sigma (float) – Volatility parameter.

Returns:

float – Greek vega according to Black-Scholes formula.

Example

>>> import numpy as np
>>> from fyne import blackscholes
>>> sigma = 0.2
>>> underlying_price = 100.
>>> strike = 90.
>>> maturity = 0.5
>>> vega = blackscholes.vega(underlying_price, strike, maturity, sigma)
>>> np.round(vega, 2)
20.23