<aside> ⚙ A refresher on what a batch is

A set of 500 simulations in which we:

1. Buy a 1-year ATM call for 25% implied vol. The call’s initial value is $9.95 and has a vega of $.396
   1. This implies our daily breakeven move is 1.5%
2. Hedge the delta daily
3. Each batch is seeded with an expected realized volatility that governs the stock diffusion process. Any single 1-year run is a sample that can differ from the batch realized vol </aside>

In this section, instead of zooming in a particular run we will look examine what happens in a batch in aggregate. The format will be:

1. Description of notable stats
2. Observations from charts
3. Summary table to compare batches

Description of notable stats

Let’s explore the batch of runs for 25% realized volatility.

For the 500 runs:

• Mean realized volatility is 24.77% with a standard deviation of 1.09%
  • Therefore the realized underperformed the IV on average by .23% or less than a quarter vol point.
• The average P/L as a percentage of the initial option price of $9.95 over the 500 runs is -.5%. This makes sense since the RV slightly underperformed the IV.
• The initial vega is $.396. You would expect to make about $.40 per option for every 1 vol point of outperformance. Since we lost -.5% of our premium on average we can convert this to the statement: We lost .12 vol points on average with a standard deviation of 1.38 vol points.

This forms the basis of a simple, handy chart.

Observations from charts

We can see how our P/L varies in vol points as a function of RV-IV in vol points.

• When RV-IV is positive, the RV outperformed the 25% IV and vice versa

About the chart:

• The black line is a fabricated slope of 1 line. It’s a useful visual reference because it’s the line you’d get if your P/L in vol points simply comes down to “I win or lose vol points in direct proportion to the spread between RV and IV.”
• The red line is the regression line from the sample data. The R-square is for the red line.