# Options autohedging for Hegic LPs (Part 2):

**A few days ago, I started thinking about: “How could ****Hegic**** Liquidity Providers (LPs) automatically hedge themselves in a centralized exchange (CEX)?”** After thinking of a solution to this question, I decided that my notes and analysis could be useful for Hegic LPs, for the Hegic community as a whole and for anyone interested in options.

These are just the notes and analysis of a derivatives enthusiast and crypto learner. I don’t aim to give any financial advice.

This is Part 2 of 2 of my notes and analysis.

In Part 1, I introduced the problem to be solved and explored a couple of general ways to solve it. In part 2, I will go into the details of how Hegic LPs could hedge in an automated way, from an options pricing and risk management perspective.

Please read the Context, Problem to be solved and Asumptions & Limitations in Part 1. **Part 1 provides a good base for understanding the limitations of the solution explained in Part 2.**

# 2. Detail on “The Mirror Approach” applied to hedging Hegic’s LPs — explanation and calcs:

If you are anxious to know the outcome: **yes, looks like it is currently possible for Hegic LPs to hedge each option with a mirror option bought in CEX, investing around 80% of the premium received by selling the option in Hegic**. At least for underlying = ETH (I have only done ETH for the moment). There are however, some limitations to this approach (please read Part 1).

So, I have done a pretty simple (but kind of cool, imho) model describing what an “autohedging machine” could do in order too hedge Hegic LPs each time they sell an option. I have called this machine **“The Mirror”** (yes, based on the “Mirror Approach” and yes, I like giving names to stuff…).

The Mirror **looks for the most appropriate option in a CEX to hedge an option sold in Hegic**, returns its theoretical value and also takes into account an average theoretical value - ask spread, **giving you a pretty good aproximation of the “mirroring option” ask in a CEX** such as Deribit Exchange. The Mirror model allows you to play around with the % of premium from the sold option LP could use to hedge that option with the CEX option. The Mirror also **calculates the initial P&L** (the difference between the amount available for hedging and price you pay for the “hedging” option in CEX) you are making **on that pair of trades (short Hegic option + long CEX option)**.

Lastly, I have run a basic sensitivity analysis in order to see how the initial P&L would change for several expiries and strikes.

Let’s dig into the details…

**2.1 The Mirror — Inputs:**

- Updated underlying IV ATM term structure for listed expiries

- Updated underlying futures ref for listed expiries

- LPs premiums invested in Hedge (% of total premium received)

- Updated underlying price (Spot) in Hegic at the moment of trading

- Hegic option strike

- Hegic option size

- Updated Hegic Vol Rate

- Time to maturity of the option traded in Hegic

**2.2 The Mirror — Outputs:**

With these inputs, The Mirror **calculates the price of the option in Hegic** (also the premium received by LPs and the **premium invested in buying a hedge**), looks for a **“mirroring option” in CEX **and returns **its price**. Lastly, The Mirror **compares** the “mirroring” CEX option ask with the amount of premium received by LPs that is invested by them to hedge their short Hegic options.

**2.3 The Mirror — Hegic calcs:**

I will not explain in detail the calcs in order to get to Hegic’s option price in this post (it is pretty simple, DYOR). The Mirror calculates the premium of any Hegic option and the amount that LPs receive (and the amount LPs are willing to invest in the hedge). It looks like this:

**2.4 The Mirror — Looking for the best “mirroring option” in CEX:**

The Mirror **takes the option details from the Hegic option inputs and returns the best available expiry and strike for a mirroring option**. In order to do this, The Mirror returns the closest larger listed expiry. Similar thing is done with the strike: it returns the closest higher listed strike for puts and the closest lower listed strike for calls.

Knowing the listed expiry, The Mirror can “search” in its data base for the related ATM IV and futures reference. Actually, **it will return an interpolated IV for any expiry**, even if it wasn’t listed. If we used a full implied volatility surface (instead of using only ATM IV for simplicity purposes), The Mirror could look in that 3 dimensional space for the most accurate IV.

This looks like the following:

**2.5 The Mirror — Calculating the “mirroring option” price in CEX:**

Next, **The Mirror calculates** (pretty accurately when you compare to CEX) the **option TV, **using the interpolated volatility, listed expiry and strike we just got**, with Black Scholes**. Notice that this TV calculation worsens as strikes are further away from ATM, as for this first version of The Mirror I am using only ATM IV for the calcs.

The Mirror **then adds an average Ask — TV spread** to get to a close approximation of the Ask you could find for that listed option in CEX, say Deribit Exchange for example.

This part of The Mirror looks like the following:

Lastly, The Mirror compares the amount available for hedging (X% of premium received by HEGIC LPs) with the listed option Ask it just calculated and **returns the “edge” you as LP would be making.**

**2.6 The Mirror — Observations on the t0 P&L when investing 80% of premium received by LPs:**

After the previous calcs, we can observe the difference between the amount Hegic LPs could invest in hedging and the price the LP would pay for the “hedging” option in CEX. Main takeaways:

- On average **t0 P&L= c. 0.07 ETH per 1 option for the maturities and strikes observed**, therefore a hedge at a trade by trade level (The Mirror Approach from Part 1), could be done

- On average **t0 P&L for OTM options **(I believe the ones most people would buy in Hegic) **= 0.055 ETH**, however please note that as stated before, the calcs for very OTM stuff are less accurate in this v1 due to the fact that I’m using ATM IV for all strikes

- The Mirror was most profitable for longer dated options the two times I ran it. In general, **The Mirror could struggle for those expiries where the IV in CEX is larger than Hegic’s IV Rate.** There were actually some cases with expiry = 1 day, where The Mirror lost money (marginal, though). Inverted IV term structure at the time of analysis was key to this, as Hegic IV Rate is based on 1m ATM IV as per what I have seen until now

Full **sensitivity analysis of t0 P&L** for ETH options (in ETH, option size = 1) vs Hegic option strike and expiry, if LPs invested 80% of the premium they received for selling Hegic options:

**Please note the limitations listed at the very beginning of Part 1 under “Assumptions & Limitations”.**

So after all this analysis, someone asked me: “Is The Mirror your favourite way to hedge Hegic LPs?” …No, it isn’t

.This approach has some big limitations, most of them related to potential lack of liquidity in CEX to cover Hegic options (that is one of the reasons why Hegic is a game changer!!).

Actually, given the limitations of this approach, I may dig deeper on how to automate “The Aggregated Risk Factors Approach”. Would be fun…we’ll see, maybe there is a Part 3.

That’s all folks. Hope you found this useful. Let me know if you have any comments!