Tools

Monte Carlo

Monte Carlo here is not a forecast and not a live chain. You type a spot, strike, premium, vol, expected return, and days. The lab draws many random stock paths (geometric Brownian motion), then at expiration prices a long call or put as intrinsic minus that premium, one contract, and discounts that P/L. Each path is one possible ending print from the numbers you typed. Volatility is the width of those draws; expected return is drift, not a quote.

Example POP, mean, median, and the 5th–95th band come from that same cloud. This page does not load Journal or Practice.

Example math. Not financial advice.

Simulation

Volatility %

Annualized

Expected return %

Drift, not a quote

Days to expirationNumber of simulations

100–10,000 streamed paths

Interest rate %

Discount only

Shock %

SpotStrikePremium

Per share, one contract

Right

Example POP

17.2%

Mean P/L

-$122.36

Median P/L

-$208.83

5th–95th

-$245.14 · $537.00

P/L histogram

This is a P/L histogram. Each bar is how many paths landed in that dollar band. Taller means more paths, not “more likely in the market.” The gold line is P/L = 0 — breakeven on the premium you typed. Left of gold those paths lost money; right of gold they made money. Example POP is the share of paths to the right of gold. Mean and median average the same cloud; 5th–95th is the thin tails. Bars are counts of streamed paths (100–10,000), never a stored cloud, never Journal or Practice.