Options Simulator

Imagine a security that follows a simple discrete process: starting from a price of $100, it randomly goes +1/-1/+1 etc., such that its expected net change is 0.

We can follow this security across 1,000 trading days, roughly 4 years (click to randomize):

Suppose that our security goes up by +1, but goes down by -4. The expected change is still 0, so there are four times as many +1s as there are -4s. Now there are large gaps down and steady climbs back up.

What does it look like?

What if it went up by 1 and down by n? Standard deviation/skewness/kurtosis might change for the run, but if we average several runs together, skew will go to 0 and kurtosis will go to 3, by the Central Limit Theorem.

Now suppose we made a portfolio by buying a European call and put with strike prices equal to the initial price of the security, $100. Let's assume that there's no interest and no dividend, and that spot price = $100, and time to expiry = 4 years.

Let's analyze the +1/-4 series above using Black-Scholes:

Delta: The change in the value of the option, as the underlying security's price changes.
Vega: The change in the value of the option, as the volatility of the underlying security changes.
Theta: The change in the value of the option, as time passes.
Gamma: Second order Greek. The change in the value of the option, as its delta changes.

We can play around with this model!

Tweak your underlying security and build your portfolio of options below. We assume that the interest rate and dividend are 0. Click "Generate!" to draw a chart of the security, and click "Graph Option!" to draw a graph of your option's value (without adding it to your portfolio):
(We assume that we buy the option long at time step 0)

The portfolio must have a single "Price at Time:" value, which is the spot price at a certain time step of the chart (from 0 to 999).

All values must be filled in to add the option. Click "Calculate!" to finalize the portfolio.