Simulating Dynamically Hedged Option Positions

The heart of vol trading

Friends,

Yesterday’s preamble, Introduction to Dynamically Hedged Option Positions, explains what a derivatives trader does and even more specifically a volatility trader.

In a sentence:

Most investors look for mispriced underlying securities and assume the options are “fair” while volatility traders look for mispriced options and assume the underlying is fair.

The moontower.ai application hands you vol trader goggles so you parse option decisions better. Most option users have a directional view already. Their source of edge is “upstream” of the options expression. The vol trader lens is a funnel to help you decide if options make sense for your directional/timing thesis (and if so what part of the surface). With practice you will be able to narrate if and why options were the right implementation. [I tried to suppress my meat-head accent to explain all this in my interview with Corey Hoffstein]

However, if you are in the much smaller set of traders who start with a volatility thesis, you are in the realm of “vol trading”. If you are vol trading, you want to isolate the mispriced volatility by hedging the directional risks (the option’s delta) lest they swamp your source of edge.

Do I advocate for viewers at home to become “vol traders”? Groan. I don’t even recommend college students pursue a life in vol trading. But preaching celibacy is a classic example of a “triumph of hope over experience”. So in the spirit of the Zelda shopkeeper…It's dangerous to go alone! Take this.

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Today, new warrior, you get a wooden sword. It won’t slay the advanced bosses but it’s a massive leap from having the words “delta neutral” wash over you with zero context and the illusion of understanding.

This post is really a document with things to take from it.

It uses simulations to provide intuition for how realized volatility drives the p/l of delta-hedged position when hedging is done on a regular but discrete interval.

It answers questions of the variety:

“If I buy an ATM option for 20% and the stock realizes 25% what does my p/l look like?”

It includes:

• code

• plenty of pictures

• lots of explanations (sometimes scraping more advanced topics)

It’s appropriate for the vol-curious, aspiring traders, and professional trainees.

Senior traders will find thoughts they already have articulated in a different or useful way. A lot of practitioners tell me the writing gives them another way to communicate concepts they try to teach their assistants (that’s if they don’t just tell the trainees to read it and grok by the next day).

That’s my pitch.

Let’s hit it.