`vp.finance.heston_cos`

Heston prices of European options on one stock for an array of strikes, with N cosine terms and the truncation half-width L standard deviations. The put comes from the series (its payoff is bounded) and the call from put-call parity, as Fang and Oosterlee recommend. is_call: 1 call, 0 put.

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

Signature

vp.finance.heston_cos(S, K, T, r, q, v0, kappa, theta, eta, rho, N, L, is_call)

Parameters

S : float, required
K : ndarray[float64], required
T : float, required
r : float, required
q : float, required
v0 : float, required
kappa : float, required
theta : float, required
eta : float, required
rho : float, required
N : int, required
L : float, required
is_call : ndarray[float64], required

Returns

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

prices : ndarray[float64]: One price per strike.

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 numpy as np
import vipyr as vp
r = vp.finance.heston_cos(S=100.0, K=np.array([100.0]), T=1.0, r=0.0, q=0.0, v0=0.0175,
                             kappa=1.5768, theta=0.0398, eta=0.5751, rho=-0.5711,
                             N=1024, L=32.0, is_call=np.array([1.0]))
print(r.prices)                           # Fang-Oosterlee: 5.785155450
assert r.check()                          # the program's own test, at this N and L

[5.78515543]

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

Checked against

Reference: Fang and Oosterlee (2008): 5.785155450 at T = 1 (error 1.6 × 10⁻⁸, tolerance 2 × 10⁻⁸); SciPy quad of the Gil-Pelaez integrals on 21 options, within 2.0 × 10⁻¹³ (tolerance 10⁻⁹).

Source

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