vp.finance.bs_greeks

Black-Scholes delta, gamma and vega of one option. Delta and vega are grad of bs_price; gamma is vega / (S^2 sigma T), which holds for Black-Scholes calls and puts alike.

Part of the distribution vipyr; it runs from a checkout of the repository. Planned on PyPI as pip install vipyr.

Signature

vp.finance.bs_greeks(S, K, T, r, q, sigma, is_call)

Parameters

S : float, required

K : float, required

T : float, required

r : float, required

q : float, required

sigma : float, required

is_call : bool, required

Returns

A frozen BsGreeksResult. Iterating it gives the fields below in order; it also has params, tests, log and check().

delta : float

DV/dS.

gamma : float

D2V/dS2, per unit of S.

vega : float

DV/dsigma.

Raises

TypeError

An argument of the wrong type, or an unknown keyword.

vipyr.VivBuildError

An ImportError: no C compiler, or the program's C does not build.

Examples

import vipyr as vp
r = vp.finance.bs_greeks(S=100.0, K=100.0, T=1.0, r=0.05, q=0.0, sigma=0.2, is_call=True)
print(r.delta, r.gamma, r.vega)
assert r.check()

0.6368306511756193 0.01876201734584689 37.524034691693785

Each example ran as written when these pages were generated, and the output shown is what it printed.

Checked against

Reference

The closed-form Black-Scholes Greeks (examples/options/test_options.py, test_bs_greeks_by_autodiff); delta and vega come from Viv's reverse-mode grad.

Source

• Viv: examples/options/greeks.viv
• The defs it reaches and the calls between them: map of the code