Black-Scholes call price

easyFinanceacceptance —~15 min

Implement call_price(S, K, T, r, sigma) — the Black-Scholes price of a European call on a non-dividend stock: spot S, strike K, time to expiry T in years, continuously compounded rate r, volatility sigma. Use the standard normal CDF N from statistics.NormalDist.

This is the formula every options desk still reaches for first, and the one the workbench's Black-Scholes bot runs on every chain. Get the discounting right: the strike is paid at expiry, so it is worth less today.

Return the price rounded to 4 decimal places.

example 1

input

S=100.0, K=100.0, T=1.0, r=0.0, sigma=0.2

output

7.9656

example 2

input

S=100.0, K=100.0, T=1.0, r=0.05, sigma=0.2

output

10.4506

note

With r = 5% the strike is discounted; the undiscounted price would read 7.7213.

constraints

0 < S, K ≤ 10_000
0 < T ≤ 5
0 ≤ r ≤ 0.2
0.01 ≤ sigma ≤ 2

teacher · 3 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 log, sqrt, exp
from statistics import NormalDist

N = NormalDist().cdf


def call_price(S: float, K: float, T: float, r: float, sigma: float) -> float:
    """European call, no dividends. Return the price rounded to 4 dp."""
    d1 = (log(S / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * sqrt(T))
    d2 = d1 - sigma * sqrt(T)
    # TODO: the strike leg is paid at expiry — it is not discounted yet
    return round(S * N(d1) - K * N(d2), 4)

ln 1, col 1tab indent · esc leave editor

python 3.13 · pyodide

+ 6 hidden on submit

input · keyword arguments to call_price()

S=100.0, K=100.0, T=1.0, r=0.0, sigma=0.2

expected

7.9656

the judge calls call_price() 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