Dynamic Hedging & Option P/L Decomposition

Friends,

Last week, in Connecting Vol Surfaces To Option P/L, we showed how a position in the 6-month 25d put or 25d call in IWM would have performed if you:

• bought the option and hedged the delta on the close of 7/10/24 with the stock at $202.97 and went on vacation
• returned on 7/16/24 and liquidated both you stock and options position near the close with the stock at $224.32

With the stock up over 10% and IVs higher on the 185-strike put and 223-strike call you made money both on the vol expansion and because you were long gamma — although you started market-neutral, you had a net long delta when you looked at your account.

This week we will examine the same trade but instead of going on vacation we will see what happens if you hedge each day.

The most valuable part of this exercise will be the option p/l decomposition.

The 185 put and the 223 call have a negative and positive delta respectively. Since we are sterilizing the delta or directional p/l of the option with shares we want to ignore that portion of the p/l.

We care about the p/l that we don’t attribute to delta. That’s our vol p/l. We can decompose that p/l into 2 primary buckets:

1. Vega: how much of the p/l is coming from the change in implied vol
2. Realized p/l: what is p/l due to gamma or the change in delta which was not continuously hedged minus the cost of the optionality aka theta.

The p/l decomposition will contain some error. We will give that error a sense of proportion and discuss its source.

In the process, you will learn some trickery around the calculation of realized vol and the concept of “sampling”.

Onwards…

You can read the rest of this post here ($)