# -*- coding: utf-8 -*-
"""
py_vollib.ref_python.black_scholes_merton.greeks.numerical
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A library for option pricing, implied volatility, and
greek calculation. py_vollib is based on lets_be_rational,
a Python wrapper for LetsBeRational by Peter Jaeckel as
described below.
:copyright: © 2023 Larry Richards
:license: MIT, see LICENSE for more details.
py_vollib.ref_python is a pure python version of py_vollib without any dependence on LetsBeRational. It is provided purely as a reference implementation for sanity checking. It is not recommended for industrial use.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
"""
# -----------------------------------------------------------------------------
# IMPORTS
# Standard library imports
# Related third party imports
# Local application/library specific imports
from py_vollib.ref_python.black_scholes_merton import black_scholes_merton
from py_vollib.helpers.numerical_greeks import delta as numerical_delta
from py_vollib.helpers.numerical_greeks import vega as numerical_vega
from py_vollib.helpers.numerical_greeks import theta as numerical_theta
from py_vollib.helpers.numerical_greeks import rho as numerical_rho
from py_vollib.helpers.numerical_greeks import gamma as numerical_gamma
from py_vollib.ref_python.black_scholes_merton.greeks.analytical import gamma as agamma
from py_vollib.ref_python.black_scholes_merton.greeks.analytical import delta as adelta
from py_vollib.ref_python.black_scholes_merton.greeks.analytical import vega as avega
from py_vollib.ref_python.black_scholes_merton.greeks.analytical import rho as arho
from py_vollib.ref_python.black_scholes_merton.greeks.analytical import theta as atheta
# -----------------------------------------------------------------------------
# FUNCTIONS - NUMERICAL GREEK CALCULATION
f = lambda flag, S, K, t, r, sigma, b: black_scholes_merton(flag, S, K, t, r, sigma, r-b)
[docs]def delta(flag, S, K, t, r, sigma, q):
"""Returns the Black-Scholes-Merton delta of an option.
:param flag: 'c' or 'p' for call or put.
:type flag: str
:param S: underlying asset price
:type S: float
:param K: strike price
:type K: float
:param t: time to expiration in years
:type t: float
:param r: annual risk-free interest rate
:type r: float
:param sigma: volatility
:type sigma: float
:param q: annualized continuous dividend yield
:type q: float
:returns: float
"""
return numerical_delta(flag, S, K, t, r, sigma, r-q, f)
[docs]def theta(flag, S, K, t, r, sigma, q):
"""Returns the Black-Scholes-Merton theta of an option.
:param flag: 'c' or 'p' for call or put.
:type flag: str
:param S: underlying asset price
:type S: float
:param K: strike price
:type K: float
:param t: time to expiration in years
:type t: float
:param r: annual risk-free interest rate
:type r: float
:param sigma: volatility
:type sigma: float
:param q: annualized continuous dividend yield
:type q: float
:returns: float
"""
return numerical_theta(flag, S, K, t, r, sigma, r-q, f)
[docs]def vega(flag, S, K, t, r, sigma, q):
"""Returns the Black-Scholes-Merton vega of an option.
:param flag: 'c' or 'p' for call or put.
:type flag: str
:param S: underlying asset price
:type S: float
:param K: strike price
:type K: float
:param t: time to expiration in years
:type t: float
:param r: annual risk-free interest rate
:type r: float
:param sigma: volatility
:type sigma: float
:param q: annualized continuous dividend yield
:type q: float
:returns: float
"""
return numerical_vega(flag, S, K, t, r, sigma, r-q, f)
[docs]def rho(flag, S, K, t, r, sigma, q):
"""Returns the Black-Scholes-Merton rho of an option.
:param flag: 'c' or 'p' for call or put.
:type flag: str
:param S: underlying asset price
:type S: float
:param K: strike price
:type K: float
:param t: time to expiration in years
:type t: float
:param r: annual risk-free interest rate
:type r: float
:param sigma: volatility
:type sigma: float
:param q: annualized continuous dividend yield
:type q: float
:returns: float
"""
return numerical_rho(flag, S, K, t, r, sigma, r-q, f)
[docs]def gamma(flag, S, K, t, r, sigma, q):
"""Returns the Black-Scholes-Merton gamma of an option.
:param flag: 'c' or 'p' for call or put.
:type flag: str
:param S: underlying asset price
:type S: float
:param K: strike price
:type K: float
:param t: time to expiration in years
:type t: float
:param r: annual risk-free interest rate
:type r: float
:param sigma: volatility
:type sigma: float
:param q: annualized continuous dividend yield
:type q: float
:returns: float
"""
return numerical_gamma(flag, S, K, t, r, sigma, r-q, f)
[docs]def test_analytical_vs_numerical():
"""Test by comparing analytical and numerical values.
>>> S = 49
>>> K = 50
>>> r = .05
>>> q = .05
>>> t = 0.3846
>>> sigma = 0.2
>>> flag = 'c'
>>> epsilon = .0001
>>> v1 = delta(flag, S, K, t, r, sigma, q)
>>> v2 = adelta(flag, S, K, t, r, sigma, q)
>>> abs(v1-v2)<epsilon
True
>>> v1 = gamma(flag, S, K, t, r, sigma, q)
>>> v2 = agamma(flag, S, K, t, r, sigma, q)
>>> abs(v1-v2)<epsilon
True
>>> v1 = rho(flag, S, K, t, r, sigma, q)
>>> v2 = arho(flag, S, K, t, r, sigma, q)
>>> abs(v1-v2)<epsilon
True
>>> v1 = vega(flag, S, K, t, r, sigma, q)
>>> v2 = avega(flag, S, K, t, r, sigma, q)
>>> abs(v1-v2)<epsilon
True
>>> v1 = theta(flag, S, K, t, r, sigma, q)
>>> v2 = atheta(flag, S, K, t, r, sigma, q)
>>> abs(v1-v2)<epsilon
True
"""
pass
if __name__ == "__main__":
from py_vollib.helpers.doctest_helper import run_doctest
run_doctest()