Note: This piece is only for educational purposes and does not constitute a piece of investment advice.
I’d like to thank the developers at @RealHxro for helping me understand the different products and time-saving techniques to retrieve TIX contract data with their API. It’s always a pleasure to work with such a responsive and knowledgeable team! Using this TIX data, we are able to build out relatively liquid implied volatility curves not only for BTC and ETH but also for alt-coins such as LINK, UNI, and YFI.
In this analysis, I looked at TIX contracts as “cash-or-nothing binary options”. For a call, this means that at expiry if the spot is greater than the strike, then we get paid out a certain amount (the odds multiplied by the amount bet). At maturity, if the spot price is less than or equal to the strike the payout is zero. As an example, consider the March 26, 2021 $30,500 TIX contract. The odds for this contract are 2.215x which means if BTC is greater than $30,500 on March 26, 2021, then a $1 bet on this TIX will payout $2.215 at maturity. We can also look at this from a probabilistic standpoint — the market is implying a 45.1% chance that BTC will be above $30,500 by the option’s maturity. If we think the market is significantly undervaluing the probability we would want to purchase this TIX contract.
Pricing TIX contracts is fairly straightforward as it requires us to only look at the second term of the Black-Scholes model. As shown below, N(d) represents the probability of the option expiring in the money, and multiplying this by the payoff (K) gives us the expected value of the TIX. The formula below is taken from Espen Haug’s excellent book, “The Complete Guide to Option Pricing Formulas”.
The HXRO dataset has all of the inputs except the volatility term, therefore, we can build a function that will converge to the market-implied volatility. Similar to finding the implied volatility for vanilla options, there isn’t a nice closed-form solution so we need to use a numerical approach. For example, let’s look at the following option (values will change from the time this is published): BTC TIX 2021–01–29 ABOVE $18,500.
Spot = $25,823 | Strike = $18,500 | Days Left = 33.5 | Option Type = Call | Market Price = $0.922
We can iterate across thousands of implied volatility values and see which one gives us the closest value to the market price. With this approach, we can find implied volatility of 68.9% will give us a theoretical value equivalent to the TIX contract’s price.
Despite iterating over a wide range of volatilities, there were several instances where regardless of whichever value we chose, the model wasn’t able to converge to the actual market-price. As an example, consider an ETH TIX option which has a market price of 0.36. After searching over thousands of implied volatilities, a value of around 106% gives us the closest possible theoretical price of 0.29. In this case we have a theoretical price of 0.29 compared to a market price of 0.36. I’m guessing this is due to illiquidity which should smooth out over time as we see more participants enter this market.
We can run this same analysis for all TIX contracts across various maturities and cryptocurrencies as shown below:
Overall, we can see that short-term TIX contracts are fairly well priced but there may be some opportunities to arbitrage farther-dated contracts (especially among the alt-coins) given the wider differences between the theoretical and market price.
The key point to think about is how we can hedge the risk of buying or selling this binary option. Theoretically, we could use a tight call-spread to replicate the binary but we need more granularity in strikes on @DeribitExchange to make this an accurate hedge. As new market-makers enter this space I’d expect the differences we see between the theoretical and market TIX prices to converge closer to zero. Nevertheless, it’s amazing to see @RealHxro is a first-mover in exotic derivatives within the cryptocurrency space — looking forward to new products ahead!