Source code for py_vollib.black_scholes.greeks.numerical

# -*- coding: utf-8 -*-

"""
py_vollib.black_scholes.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: © 2017 Gammon Capital LLC
:license: MIT, see LICENSE for more details.

About LetsBeRational:
~~~~~~~~~~~~~~~~~~~~~

The source code of LetsBeRational resides at www.jaeckel.org/LetsBeRational.7z .

::

    ========================================================================================
    Copyright © 2013-2014 Peter Jäckel.

    Permission to use, copy, modify, and distribute this software is freely granted,
    provided that this notice is preserved.

    WARRANTY DISCLAIMER
    The Software is provided "as is" without warranty of any kind, either express or implied,
    including without limitation any implied warranties of condition, uninterrupted use,
    merchantability, fitness for a particular purpose, or non-infringement.
    ========================================================================================


"""


# -----------------------------------------------------------------------------
# IMPORTS

# Standard library imports

# Related third party imports

# Local application/library specific imports
from py_vollib.black_scholes import black_scholes
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.black_scholes.greeks.analytical import gamma as agamma
from py_vollib.black_scholes.greeks.analytical import delta as adelta
from py_vollib.black_scholes.greeks.analytical import vega as avega
from py_vollib.black_scholes.greeks.analytical import rho as arho
from py_vollib.black_scholes.greeks.analytical import theta as atheta


# -----------------------------------------------------------------------------
# FUNCTIONS - NUMERICAL GREEK CALCULATION

f = lambda flag, S, K, t, r, sigma, b: black_scholes(flag, S, K, t, r, sigma)


[docs]def delta(flag, S, K, t, r, sigma): """Return Black-Scholes delta of an option. :param S: underlying asset price :type S: float :param K: strike price :type K: float :param sigma: annualized standard deviation, or volatility :type sigma: float :param t: time to expiration in years :type t: float :param r: risk-free interest rate :type r: float :param flag: 'c' or 'p' for call or put. :type flag: str """ b = r return numerical_delta(flag, S, K, t, r, sigma, b, f)
[docs]def theta(flag, S, K, t, r, sigma): """Return Black-Scholes theta of an option. :param S: underlying asset price :type S: float :param K: strike price :type K: float :param sigma: annualized standard deviation, or volatility :type sigma: float :param t: time to expiration in years :type t: float :param r: risk-free interest rate :type r: float :param flag: 'c' or 'p' for call or put. :type flag: str """ b = r return numerical_theta(flag, S, K, t, r, sigma, b, f)
[docs]def vega(flag, S, K, t, r, sigma): """Return Black-Scholes vega of an option. :param S: underlying asset price :type S: float :param K: strike price :type K: float :param sigma: annualized standard deviation, or volatility :type sigma: float :param t: time to expiration in years :type t: float :param r: risk-free interest rate :type r: float :param flag: 'c' or 'p' for call or put. :type flag: str """ b = r return numerical_vega(flag, S, K, t, r, sigma, b, f)
[docs]def rho(flag, S, K, t, r, sigma): """Return Black-Scholes rho of an option. :param S: underlying asset price :type S: float :param K: strike price :type K: float :param sigma: annualized standard deviation, or volatility :type sigma: float :param t: time to expiration in years :type t: float :param r: risk-free interest rate :type r: float :param flag: 'c' or 'p' for call or put. :type flag: str """ b = r return numerical_rho(flag, S, K, t, r, sigma, b, f)
[docs]def gamma(flag, S, K, t, r, sigma): """Return Black-Scholes gamma of an option. :param S: underlying asset price :type S: float :param K: strike price :type K: float :param sigma: annualized standard deviation, or volatility :type sigma: float :param t: time to expiration in years :type t: float :param r: risk-free interest rate :type r: float :param flag: 'c' or 'p' for call or put. :type flag: str """ b = r return numerical_gamma(flag, S, K, t, r, sigma, b, f)
[docs]def test(): """Test by comparing analytical and numerical values. >>> flag='c' >>> S=1000.0 >>> K=1000.0 >>> t=0.1 >>> r=0.05 >>> sigma=0.3 >>> epsilon = 0.01 >>> v1 = delta(flag, S, K, t, r, sigma) >>> v2 = adelta(flag, S, K, t, r, sigma) >>> abs(v1-v2)<epsilon True >>> v1 = gamma(flag, S, K, t, r, sigma) >>> v2 = agamma(flag, S, K, t, r, sigma) >>> abs(v1-v2)<epsilon True >>> v1 = rho(flag, S, K, t, r, sigma) >>> v2 = arho(flag, S, K, t, r, sigma) >>> abs(v1-v2)<epsilon True >>> v1 = vega(flag, S, K, t, r, sigma) >>> v2 = avega(flag, S, K, t, r, sigma) >>> abs(v1-v2)<epsilon True >>> v1 = theta(flag, S, K, t, r, sigma) >>> v2 = atheta(flag, S, K, t, r, sigma) >>> abs(v1-v2)<epsilon True Test PUT flag >>> flag = 'p' >>> v1 = delta(flag, S, K, t, r, sigma) >>> v2 = adelta(flag, S, K, t, r, sigma) >>> abs(v1-v2)<epsilon True >>> v1 = gamma(flag, S, K, t, r, sigma) >>> v2 = agamma(flag, S, K, t, r, sigma) >>> abs(v1-v2)<epsilon True >>> v1 = rho(flag, S, K, t, r, sigma) >>> v2 = arho(flag, S, K, t, r, sigma) >>> abs(v1-v2)<epsilon True >>> v1 = vega(flag, S, K, t, r, sigma) >>> v2 = avega(flag, S, K, t, r, sigma) >>> abs(v1-v2)<epsilon True >>> v1 = theta(flag, S, K, t, r, sigma) >>> v2 = atheta(flag, S, K, t, r, sigma) >>> abs(v1-v2)<epsilon True """ pass
[docs]def hull_book_tests(): """ Example 17.1, page 355, Hull: >>> S = 49 >>> K = 50 >>> r = .05 >>> t = 0.3846 >>> sigma = 0.2 >>> flag = 'c' >>> delta_calc = delta(flag, S, K, t, r, sigma) >>> # 0.521601633972 >>> delta_text_book = 0.522 >>> abs(delta_calc - delta_text_book) < .01 True Example 17.2, page 359, Hull: >>> S = 49 >>> K = 50 >>> r = .05 >>> t = 0.3846 >>> sigma = 0.2 >>> flag = 'c' >>> annual_theta_calc = theta(flag, S, K, t, r, sigma) * 365 >>> # -4.30538996455 >>> annual_theta_text_book = -4.31 >>> abs(annual_theta_calc - annual_theta_text_book) < .01 True Example 17.4, page 364, Hull: >>> S = 49 >>> K = 50 >>> r = .05 >>> t = 0.3846 >>> sigma = 0.2 >>> flag = 'c' >>> gamma_calc = gamma(flag, S, K, t, r, sigma) >>> # 0.0655453772525 >>> gamma_text_book = 0.066 >>> abs(gamma_calc - gamma_text_book) < .001 True Example 17.6, page 367, Hull: >>> S = 49 >>> K = 50 >>> r = .05 >>> t = 0.3846 >>> sigma = 0.2 >>> flag = 'c' >>> vega_calc = vega(flag, S, K, t, r, sigma) >>> # 0.121052427542 >>> vega_text_book = 0.121 >>> abs(vega_calc - vega_text_book) < .01 True Example 17.7, page 368, Hull: >>> S = 49 >>> K = 50 >>> r = .05 >>> t = 0.3846 >>> sigma = 0.2 >>> flag = 'c' >>> rho_calc = rho(flag, S, K, t, r, sigma) >>> # 0.089065740988 >>> rho_text_book = 0.0891 >>> abs(rho_calc - rho_text_book) < .0001 True """
if __name__ == "__main__": from py_vollib.helpers.doctest_helper import run_doctest run_doctest()