`vp.finance.crr_price`

The CRR value with N steps: u = exp(sigma sqrt(dt)), d = 1/u, the risk-neutral up probability p = (exp((r - q) dt) - d) / (u - d), values rolled back from maturity; an American option takes the larger of continuing and exercising at every node.

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

Signature

vp.finance.crr_price(S, K, T, r, q, sigma, N, is_call, american)

Parameters

S : float, required
K : float, required
T : float, required
r : float, required
q : float, required
sigma : float, required
N : int, required
is_call : bool, required
american : bool, required

Returns

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

price : float: The option's value on an N-step Cox-Ross-Rubinstein tree.

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.crr_price(S=50.0, K=50.0, T=5 / 12, r=0.1, q=0.0, sigma=0.4, N=5,
                            is_call=False, american=True)
print(r.price)                            # Hull: 4.49
assert r.check()

4.488458534725913

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

Checked against

Reference: Hull's printed American put values 4.49, 4.263, 4.272, 4.278 and 4.283 (N = 5 to 500), within half a unit of the last printed digit; the European value at N = 4000 within 2 × 10⁻³ of Black-Scholes.

Source

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