Options autohedging for Hegic LPs (Part 1):

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 lover. I don’t aim to give any financial advice.

This is Part 1 of 2 of my notes and analysis.

In Part 1, I will introduce the problem to be solved and explore 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.

Context: I’m thinking about a way to hedge Hegic LPs, who at the moment short options on request of option buyers in exchange for a premium. Currently LPs are not automatically hedged at the pool level. The analysis was first done on Jan 23rd 2021 and re-run on Jan 25th 2021.

Problem to be solved: I want to ideally look for a way to find suitable options on a centralized exchange (CEX) that could hedge perfectly (1:1) the options sold by Hegic LPs. LPs will automatically invest X% of the premiums collected by selling options in Hegic into hedging. (I used X = 80% as starting point).

Assumptions & Limitations:
(i) I based my analysis in the current version of Hegic at the time of writing, any changes may affect the results of the analysis (say longer dated options become available, for example).
(ii) I assume that, in case a secondary market is developed for Hegic options, the pool buying those options in secondary will not be the same pool as the one we are trying to hedge. Therefore, the pool we are trying to hedge will never pay option buyers more than intrinsic value (either at expiry or because of early exercise).
(iii) Currently, puts sold in Hegic are actually put spreads with strikes X and X/2 (I have explained this in Twitter). I have not taken this into account, I have treated them as actual puts, as the change in risk is not very relevant in the tenors available in Hegic (=< 28 days) and as in any case, I am being over conservative .
(iv) Relative changes in skew and term structure vs 1m ATM for options listed in CEX (vs the situation at the moment of analysis) can impact the results of the analysis in Part 2, as Hegic uses 1 single vol input across tenors and strikes.
(v) Also regarding Part 2, it would be ideal to change the option initially bought as a hedge to another listed option that matches as close as possible the strike and expiry of the Hegic option, whenever that option becomes available in CEX.
(vi) Increasing Theoretical Value — ask spreads in CEX would affect the results of Part 2.

I believe an explanation on ways to hedge an option exposure would be quite valuable, so I’ll go ahead and share with you my thoughts on this. If you prefer to go directly to the solution of the problem raised (“How could Hegic Liquidity Providers (LPs) automatically hedge themselves in a centralized exchange (CEX)?”), you can wait for Part 2. I believe Part 1 provides a good base for understanding the limitations of the solution explained in Part 2, though.

1. Introduction to ways of hedging an option exposure:

Hedging consists on balancing your risk profile, most of the time by mirroring the existing risks in your portfolio with some other risks that counter effect the first ones.

One can think of two main categorizations regarding how to hedge option risk profiles:
(i) Hedging at a trade by trade level vs Hedging at a portfolio level
(ii) Hedging by trading the entire asset in the opposite direction vs Hedging by managing and trading each of the risk factors in the option(s)

There are many ways to hedge but all respond to each of these 2 categorizations (at least all the ways that come to my mind now).

Now I will focus on 2 possible ways in which LPs could hedge their exposures, and I will describe their pros and cons in relation to our “mission” of hedging Hegic’s LPs:

- Trading the same option in the opposite direction, 1 to 1. Ex: Every time you sell a call, immediately hedge it buying a call, ideally the same call. I will call this “The Mirror Approach”. Each option is hedged with another option.
- Synthetically replicating the risk factors of the original position (note position is used here as you can replicate a position consisting of several options in the same expiry bucket, for example), in the opposite direction. Ex: Hedging a short call buying X amount of underlying (mirroring 1 of the risk factors here: delta). I will call this “The Aggregated Risk Factors Approach”. In this approach you can also hedge by trading options if you not only want to hedge against delta, but also want to hedge your vega, gamma, theta exposure. The key here is that you don’t hedge each option in a vacuum, but the overall position instead.

1.1 “The Mirror Approach” — Basics and Pros&Cons for Hegic LPs hedging:

Using this approach, you look for the most similar option that you can trade in opposite direction, so that you pay a premium for that option and the risks of both options “cancel” each other, so that you are hedged. More specifically, I have looked at the case where LPs go to a CEX, such as Deribit Exchange looking for the “mirroring option”. For more detail, please wait for Part 2.

Pros:

+ With Hegic’s current pricing, this would work (again, wait for Part 2 for more detail)
+ It is the closest thing to fully cover the short option risk at any time during the life of the short option (as long as you keep the option and you have chosen the long “hedge” option properly)
+ With Hegic’s current primary offering, this approach would be always buying options, not selling them, in order to hedge. This can be good in terms of margin required for these trades in CEX
+ It could allow to make some extra profit if the short option is exercised, as it will be exercised at intrinsic and your long position will most likely have some time value (again, as long as you have chosen the long “hedge” option properly)
+ Cost of hedging is known upfront and it is limited to the option bought premium

Cons:

— Identical option most likely will not be found in CEX, so you will have to go for the next best thing, always making sure that the option used as hedge is covering the risk as well as possible and aim for that 1:1. This implies that you will be most of the times “overpaying” upfront for optionality you don’t really need
— As Hegic pricing becomes more in line with that of CEX, this approach will become less feasible, until it will become not possible to perform having 1:1 hedge + profit. In a perfect market, two identical options have identical prices
— Liquidity and slippage issues: this is actually one of the reasons why I like Hegic so much… In Hegic there is no slippage and there is always liquidity no matter the strike (as long as there is enough collateral in the LP). If someone bought a big and/or weird option in HEGIC, you might not be able to trade the “hedging” mirror option in any CEX without moving the market, or what is worse, maybe there is no one willing to sell you that option…The hedge might not work when it is most needed
— By hedging on a one to one basis, it could happen that very similar options in opposite directions (in terms of delta) make you hedge more times that it is actually needed
— Increasing Bid-Ask spreads would decrease the feasibility of this trade
— Potential front runs for options with low liquidity in CEX
— In order to avoid risk mismatches, it would be ideal to change the option initially bought as a hedge to another listed option that matches as close as possible the strike and expiry of the Hegic option, whenever that option becomes available.

Why? Well, for example, it could happen that if the Hegic option is very close to ATM when close to expiring (big gamma) and you have bought as hedge a slightly longer dated or slightly more OTM option, the price of the Hegic option will be more sensitive to changes in spot than the price of the option you bought as hedge (CEX one).

1.2 “The Aggregated Risk Factors Approach’’ — Basics and Pros&Cons for Hegic LPs hedging:

In this case, you aggregate your risk factors and you hedge those that you want to. In the current status of Hegic and even when a secondary market develops, as far as the pool buying the options in secondary was a different one from this main pool, it would be ok to focus on hedging delta.

So, in this case, you would look at your aggregated delta of the options you have sold as LP and you would hedge directly buying or selling futures in a CEX. For example, if the pool sells a call with delta 0.5 and sells a put with delta 0.3, the overall delta would be -0.2 and you could just do 1 single trade, buying 0.2 futures. You could aggregate your short options by expiry and hedge each bucket with the corresponding future.

Pros:

+ Liquidity will be easier to find in futures than in specific options. Also execution could be potentially easier with less slippage
+ Way harder for anyone to front run you
+ If you don’t aim to be at every single time perfectly hedged 1:1, the number of transactions would most likely be lower vs “The Mirror Approach”
+ This works also as Hegic pricing evolves to being more in line with that of CEX
+ You could make money in the hedge, if you manage it well

Note that here you are playing a game of Implied Volatility (IV) vs Realized Volatility (RV): IV you have received as premium for the short Hegic option vs RV you will be suffering in your delta rebalancings buying and selling futures

Cons:

- It is not possible to ensure being 1:1 hedged at every single moment while limiting the cost to X% of the premium received from selling the option in Hegic
- If you try to be all the time perfectly hedged, you would be buying futures high and selling them low with every single tiny movement in the underlying (this is the consequence of being short gamma, happy to elaborate on this). You would be paying for every single bit of RV. Therefore, the cost of this is not limited and can be high
- Even if you decide that being 1:1 hedged at every single time is not so important, path dependency is relevant
- When hedging short puts sold by LPs, you would be selling futures, which might not be great in terms of margin requirements in CEX
- Slippage might still occur if a big rebalancing is needed

And…that’s all for Part 1.

In Part 2 I will go into detail as of how “The Mirror Approach” could be implemented and show you some pretty encouraging simulations.