# Options mechanics of the colosal $22m LUNA bet

### Stablekwon x Algodtrading x Gigantic Rebirth

Many traders didnāt survive the death of the open-outcry pits. Their edge disappeared, and their previous spending habits left them with little. (In this case, ātrickle-downā economics was correct, as profits from market-making trickled down to prostitutes, strippers, and cocaine dealers. At least it wasnāt fully wasted. It went to somethingā¦

On the 14th of March 2022, three people struck a bet on what the price of LUNA was going to be exactly a year from the said date. The bet between the parties was that the price of LUNA would be below or above $88 in a yearās time.

If LUNA > $88 , stablekwon wins and and takes home the entire $22m while donating $1m to any charity of his choice. But if LUNA < $88, Gigantic Rebirth gets to take home $20m and Algodtrading takes $2m while stablekwon and Gigantic Rebirth still has to donate $1m to charity. (well, it was all his choice. No one forced him to). But what happens if price equals $88 at the end of the period stipulated? I guess stablekwon takes it because itās synonymous to his bet. Looks like a 100% profit for the winner innit?

Today, Iāll take you on the Options mechanics of this bet. This post was inspired by Lily Francus one of the gigabrains that just seem to know a lot about the options market. So, letās get on with it.

**Options Trading**

Options are financial derivatives that give the buyer the right to buy or sell the underlying asset at a stated price within a specified period.

If you trade Options already, youāll know that this bet is a fixed payout regardless of its distance. It is a type of options contract in which the payout will depend entirely on the outcome of a yes/no proposition. This means that if it trades at $87.99 at maturity, Algod and Gigantic rebirth wins but if it trades at $88.01, Stablekwon wins and gets his entire prize money. This is similar to a binary or digital options struck with a 1 year tenor.

A binary option is an option that pays out a fixed coupon if the spot price at maturity is higher than the barrier level. This translates to mean that Algodtrading and Gigantic Rebirth is basically short a binary call to Stablekwon which is struck 1 year forward at $88. This makes the maths and hedging a bit straightforward.

In a limiting case, this binary call option can be replicated using a call spread. If i bought an equivalent amount of $88/88.5 call spreads as the amount i covered in my bet. i would be fully hedged. But if at maturity, LUNA ends up between $88 and $88.5, the limits breaks and i become unhedged. However, intuitively, as the call spread strikes starts getting closer and closer, iāll be getting better hedged. As the distance becomes 0, i would have replicated my exact payoff.

Interestingly enough, itās very likely that Stablekwon overpaid for his call option. Given Black-Scholes model which is a differential equation widely used to price options contracts,

this is approximately where C is the coupon ($11m), r is the risk free, T is the time to maturity. Now, N(d2) gets a bit more interesting here. It essentially gives the risk adjusted probability that the option is exercised i.e the probability that in a years time LUNA would be trading above $88 per coin. As Lily Francus suggested, thereās something akin to staking here. If thereās a risk free 2% APY, weād get something more like $1.02m*N(d2). This means that realistically, this should have been like a 1:2 kinda bet where stablekwon puts up half of whatever Algodtrading and Gigantic Rebirth puts. Thereās also another way to look at this using risk reversal; digital call and digital put. But in both the digital call only and riskie methods, the conventional BSM pricing model implies the premium can be invested at risk-free rates.

Remember, Algodtrading and Gigantic rebirth essentially sold a digital call option here and as professional gamblers, would probably want to hedge their bets. The traditional approach would be to hedge using call spreads. They buy an $86/88 1 year call spread and hold enough notional to hedge the bet completely. If this is the case, then you can see that Stablekwon overpaid for the binary option.

Gigantic Rebirth had probably calculated this already before he made the bet because he actually implied that it was +EV for him and actually wanted to bet $50m but decided that the escrow part was risky.

Like how would he even lose right? Maybe if Cobie and the two other signatories decides to the multisig steal the money. If that isnāt the case, he could just twap 10m of LUNA on a crash. Price drops, he buys equivalent of $10m LUNA and has a risk free 40% and only lose if he doesnāt hedge the bet or LUNA never goes below the agreed upon price right? Also, if a liquid enough market existed, itāll be highly likely that both algod and gigantic rebirth could actually lock in a risk free profit. But hmmm there might be a twist somewhere.

Now, letās look at the Greeks of this digital position

As we all know, options traders often refer to the delta, gamma, vega, and theta of their option positions. Collectively, these terms are known as the Greeks, and they provide a way to measure the sensitivity of an option's price to quantifiable factors. They are the key factors that can influence options pricing. They're used to predict price movements. The cool rule of thumb is that binary greeks are just like vanilla greeks but differentiated again with regards to S. This follows from the fact that you can replicate a binary as an infinitesimally narrow call spread.

Stablekwon clearly has long delta as he is long the forward price of LUNA. But unlike a normal option, the delta is the highest at the barrier ($88) and decreases as you move above it for intuitive reasons. Hence, at expiry, he doesnāt care if LUNA is $100 or $5,000. He still wins.

Interestingly, the gamma here behaves differently from a normal option because the sign flips the barrier. As you get closer to the barrier from below, you get longer delta and are more likely to win. But if you move away from the barrier, you get lesser delta as gamma becomes negative.

Up to a scaling, the payoff of such a call spread is equal to the derivative of a vanilla payoff. If you look at how the binary delta changes approaching expiry, it becomes clear that this position is hard to dynamically hedge as delta goes to infinity at expiry.

What are the takeaways?

This bet is really interesting because of itās (digital options) nature.

Stablekwon overpaid for the bet but this is offset because of he has asymmetric information on the price of LUNA due to factors like the UST burn mechanism, the bitcoin collateralization taking place right now and the Anchor rate especially if anchor maintains APY. These events have high probability of creating more demand and thereby boosting the price of LUNA.

Algodtrading and GiganticRebirth canāt properly hedge this bet as there isnāt really a LUNA options market that is liquid enough.

BSM (Black-Scholes-Merton) model might not really work well for crypto because no one can really argue that the price of LUNA is a derivative process of UST issuance.

This bet can be +EV vs selling as Gigantic rebirth and Algodtrading can actually buy the options and resell it via OTC at a slightly less favourable term but still bagging the difference.

**Conclusion:**

Crypto is highly volatile and most people trading it, have the attention span of babies. This causes rapid periods of high volume and volatility and sometimes low volume/volatility based on what the hype of the moment currently is. Hence, it is very difficult to generalize forward-looking, the IV of the past maybe 6 months for LUNA to go forward.

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