We will step through the case where buy the 1 year ATM call for 25% vol, and simulate a stock path that realizes an expected vol of 25%.

<aside> 💡 Sampling

Because our daily moves are sampled from a distribution with a 25% realized vol, the actual realized vol for any single run will differ from exactly 25%. The average realized vol over all 500 runs of 250 days in the batch is of course 25% even though any particular 1-year sim differs slightly.

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Exposition

  1. We will step through several charts with explanations and interpretations for a single run randomly chosen from the batch of 500 runs seeded with a 25% realized vol.
  2. That template will help you step through other examples in the chartbooks below on your own to get a feel of how p/l paths look for various realized vols. Remember, in every case in this entire document we are assuming the implied vol of the option is 25% at all times.

A Tour Through A Single Run

The Code

The Feeder Tables

Charts & Interpretations

Chartbooks for other realized vol paths

<aside> âš™ The same setup every time

  1. Buy a 1-year ATM call for 25% implied vol
    1. This implies our daily breakeven move is 1.5%
  2. Hedge the delta daily </aside>

Realized Vol: 10%

Realized Vol: 20%

Realized Vol: 25%

Realized Vol: 26%

Realized Vol: 27%