Put-call parity check

easyFinanceacceptance —~10 min

Implement parity_gap(call, put, S, K, T, r) — the arbitrage gap in put-call parity for European options on a non-dividend stock: C - P - (S - K·e^(-rT)). A perfectly priced pair returns 0.

Parity is the first sanity check a desk runs on a chain: if the gap is not zero, one of the quotes is stale or the pair is mispriced against parity. Return the gap rounded to 4 decimal places.

example 1

input

call=7.9656, put=7.9656, S=100.0, K=100.0, T=1.0, r=0.0

output

example 2

input

call=10.4506, put=5.5735, S=100.0, K=100.0, T=1.0, r=0.05

output

constraints

0 < S, K ≤ 10_000
0 < T ≤ 5
0 ≤ r ≤ 0.2

teacher · 2 hints · the first is free

↗ read the theory

the chapter this problem is cut from

▶ open in the workbench

run the same math on a real tape

●solution.py· utf-8 · spaces:4

from math import exp


def parity_gap(call: float, put: float, S: float, K: float, T: float, r: float) -> float:
    """C - P - (S - PV(K)), rounded to 4 dp. Zero means no arbitrage."""
    # TODO: PV(K) is the strike discounted at r over T, not the strike itself
    pv_strike = K
    return round(call - put - (S - pv_strike), 4)

ln 1, col 1tab indent · esc leave editor

python 3.13 · pyodide

+ 6 hidden on submit

input · keyword arguments to parity_gap()

call=7.9656, put=7.9656, S=100.0, K=100.0, T=1.0, r=0.0

expected

the judge calls parity_gap() with exactly these inputs · outputs are compared to 6 decimal places

● standing bypython 3.13 in your browser · pyodide 0.28.3 · judged on the server to 6 dp⌘↵ run · ⌘⇧↵ submit

paper only · educational · not advice