# A story on how an options secondary automated market maker (AMM) should work

As I once told a friend of mine: “I believe that markets are born with primary markets, but really take off when efficient secondary markets are developed”. Think about it. When a secondary market is developed, that translates into being able to do much more with the asset apart from holding it. At the same time, this makes the asset and the primary market more valuable. Suddenly, the value of the asset is not only equal to the value for the asset holder, but the value for any potential holder out there (who might value the asset even more than the original holder).

This is why I think the **creation of efficient secondary markets is key for the development of many protocols in general and AMMs in particular**, in the crypto scene.

So I decided to share my thoughts on how I think an options secondary AMM should be built (not from a dev perspective, but from a risk and structural persepective). **I am not a freaking guru nor I die for community recognizement. Writing things down hepls me tidying-up my thoughts. **If at the same time anyone out there finds this interesting, that’s cool.

“Markets are born with primary markets, but really take off when efficient secondary markets are developed”

As I said in Twitter a few days ago, in general, there are three possible ways of making money being an options secondary market maker (both for AMMs and traditional MMs):

**Buying an option bidding vol at X and selling that same option to someone else at vol X+Y, ceteris paribus.**This is basically “brokering”, so the market maker makes money while limiting risk as it tries to hold the asset for the smaller amount of time possible. This adds value by offering a counterparty for the seller who was looking for a buyer and afterwards, for the buyer who was looking for a seller.**The problem?**It is not always so easy to have simoultaneusly 2 sides, plus there is a chance of making more money if you keep the asset in your book…if you embrace that risk.**Buying an option bidding vol at X and hoping for the underlying to move past the breakeven point.**This strategy can create good profits, the problem is that those profits are the result of a gamble…(I still haven’t met the guy who knows if ETH is going up or down in the next few days).**The problem**here is that the P&L of this strategy comes mainly from the underlying price in t0 and tn, as you are relying on a spot movement translating in an appreciation of the option (Delta unhedged).**No one can control the underlying price in t0 and tn**, so with this strategy the only way of having consistent chances of making money is bidding very low for the option, so that the breakeven is relatively close vs expected move of the underlying.

Again, the problem there is that bidding super low doesn’t add much value for those in the market willing to sell. This strategy can be pretty much like a monkey driving a school bus, specially if the option pool is clearly skewed towards calls or puts.**Buying an option bidding vol at X and managing this exposure, so that directional risk of underlying going up or down is limited, while the Realized Vol- Implied Vol (bid) spread can be monetized.**This is a smart way of making money in a consistent way, taking risk but “embracing” and managing that risk. The big difference with 2. is that in this case, the P&L comes from the spread between Implied Vol in your bid and Realized Vol of the underlying until expiry (or secondary sale) of the option. The Implied Vol in your bid is directly controlled by you. With this strategy, you are long volatily: you want the underlying to realize as much volatility as possible. At the same time, you have your delta exposure mostly hedged.**The problem?**Realized vol could result to be lower than your expectations, even lower than the realized vol extrapolated from the Implied Vol in your bid. If that happens, you would have lost this game of “Realized- Implied Vol”.

So, as a recap, IMO the ideal Options Secondary AMM should be:

- **Promoting liquidity and high volumes, in order to enhance the chances of making money by following strategy 1**. One example for this is that the Secondary AMM enables to buy and sell amounts of options that are different to the other side (so, the AMM could buy 120 options, and sell 1 option in 120 different transactions…no need to find in the other side someone matching the size of the original block of options).

- **Performing strategy 3. so that while the option is holded in the pool, LPs can monetize it in a risk-controlled way.**

In this last section I will explain how strategy 3. can be done by a AMM and I will show some results of this strategy, which I have modeled.

**Delta Hedging and Gamma Scalping:**

These are two very related methods, as Gamma is “scalped” with Delta rebalances.

**Starting from the begining**: every option has a Delta. Delta is the marginal rate of change in the price of an option for a given move in the underlying. The Delta of an option changes as the price of the underlying changes and moves away or closer from the strike, or as time passes, or as volatily changes. This second derivative is called Gamma. So, Gamma is the rate of change of Delta for given move in the underlying, ceteris paribus. See graphs below (they are my own and not perfect, I know).

Delta can be hedged, as if you hold a call with Delta +0.5, you can sell 0.5 underlying and you are hedged. But as delta changes, you will need to rebalance your hedge (buy or sell more of the underlying, to stay balance).

Now, **the beauty of this: every time you are long an option, whenever you delta rebalance, you are buying low and selling high the underlying**. The higher the realized vol and Gamma, the more feasible it is for this delta rebalances to make more money than what the we paid for the option.

I will explain this with a call, but it works with puts in the same way.

**Simplified example (dummy numbers here, wait for last part for accurate modeling):**

t0: We buy an ETH call Delta 0.5, we hedge it by selling 0.5 ETH at current ETH price = 2600. Delta rebalance cashflow = 2600*0.5 =+1300 USD

t1: ETH goes up to 2800, our call’s Delta goes up to 0.8. We will have to sell additional 0.3 ETH …at current ETH price = 2800. Delta rebalance cashflow = 2800*0.3 = +840 USD

t2: ETH goes down to 2400, our call’s Delta goes down to 0.2. We will have to buy (0.8–0.2) = 0.6 ETH at current ETH price = 2400. Delta rebalance cashflow = 2400*0.6 = -1440 USD

t3: ETH goes back to its original price of 2600, our call’s Delta goes up to 0.5. We will have to sell (0.2–0.5) = 0.3 ETH at current ETH price = 2600. Delta rebalance cashflow = 2600*0.3 = 780 USD

Let’s assume at this point the option expires or we sell the option, and buy the remaining delta we had. Delta rebalance cashflow = 2600*0.5 = -1300USD

Total profit = 180 USD. I haven’t cared at all about what the strike was. **I only cared about how much the underlying moved, not how far ITM the option gets. **At the same time, I was at all times trying to have my Delta exposure as close to 0 as possible. In other words,** my P&L did not depend on a rally or crash in the spot. It relied on realized volatility being larger than the implied volatility in the bid paid for the option**.

**Modeling how an Options Secondary AMM should manage its position in the options pool:**

In my opinion, an Options Secondary AMM should have a LP that allows it not only to buy options, but to buy and sell the necesary underlying to be hedged and extract value from realized volatility.

In my model:

- I **calculate the options price** (I can use BS for this or any other input such as Hegic pricing formula)

- I **calculate the options delta** (Black-Scholes based) for several prices of underlying and several points in time, building a matrix. It is relevant that even for options that do not follow in primary markets the Black-Scholes formula (such as Hegic options), I do believe that using Black-Schole as “probabilistic tool” for calculating the option Delta is accurate enough…we could always calculate some alternative Delta for Hegic options, but I don’t find it necessary for this purpose

- I **calculate the implied expected realized movements in the underlying** from the Implied Vol in Deribit

- The **model assumes the underlying moves between “simulation windows”** in a random way, limited by a “Realized Period Maximum Move”, which at the same time can be stress tested vs the “Implied expected realized movements”.

- “Realized Period Maximum Move” is an **input that makes the magnitude of realized moves in underlying to be larger or smaller**

- **Simulation period** is an input in hours (you can choose the hours in the simulation period)

- The model **calculates for every single point in time the necessary delta rebalance that would have to be done**, as well as the **cash flow** generated by each of those delta rebalances

- The model aggregates the **P&L from the delta rebalances, together with the option price paid and the option’s payout at expiry**. In this way, the model returns the expected P&L for the whole strategy as well as the ROI (%)

Results (ran c.100 simulations, so the sample isn’t huge but std devs look ok):

**In high implied vol scenarios (130v), bidding vol X% lower than the marks in Deribit and using Y hours observation windows:**- When realized vol is in line with that implied by marks in Deribit’s implied vol:

Average ROI = 63%

- When realized vol is 30% lower than that implied by marks in Deribit’s implied vol:

Average ROI = 12%

- When realized vol is 50% lower than that implied by marks in Deribit’s implied vol:

Average ROI = -17%

**In low implied vol scenarios (50v), bidding vol X% lower than the marks in Deribit and using Y hours observation windows:**- When realized vol is in line with that implied by marks in Deribit’s implied vol:

Average ROI = 30%

- When realized vol is 30% lower than that implied by marks in Deribit’s implied vol:

Average ROI = -4%

- When realized vol is 50% lower than that implied by marks in Deribit’s implied vol:

Average ROI = -31%

Ps: X% and Y are mine…not everything can be completely for free haha. Happy to share this via DM in Twitter.

I hope you found this useful, as much as I hope Secondary AMMs to grow and support the whole crypto scene.

Let’s build rad shittttttt