vp.finance.bs_price

The Black-Scholes price of a European option on a stock with continuous dividend yield q. An in-the-money option is priced as the out-of-the-money one plus the discounted forward intrinsic value (put-call parity).

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

Signature

vp.finance.bs_price(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 BsPriceResult. Iterating it gives the fields below in order; it also has params, tests, log and check().

price : float

The option's value, in the currency of S and K.

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_price(S=42.0, K=40.0, T=0.5, r=0.1, q=0.0, sigma=0.2, is_call=True)
print(r.price)                            # Hull's example: 4.76
assert r.check()

4.759422392871536

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

Checked against

Reference

The SciPy closed form on 2000 random quotes: worst relative error 1.0 × 10⁻¹³, tolerance 10⁻¹² (examples/options/test_options.py).

Source

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