What volatility should we use?
We all know implied volatility is one of the key inputs into option pricing. It is simply an expected volatility of a stock over the life of the option based on the standard deviation of log-returns as observed in the options market. Option practitioners typically compare it to the historical or realized volatility over the past “x” days to get a sense as to whether the option is “cheap” or “rich”
At Digital Gamma, we have also previously looked at several methodologies to calculate initial collateral and assess the risk/reward characteristics of bitcoin lending transactions based on the ability to compute or observe such “volatility”, be it using option implied volatility based on observable market option prices, or using historical bitcoin prices to compute realized volatility. Different approaches result in different levels of volatilities, so which one should we use?
In fact, there are many more issues that complicate our thought process, both in terms of using traded option prices or historical data.
Let’s start with the approach where we use traded options to calculate the implied volatility which we then use as an input to calculating collateral. This approach makes intuitive sense as options are being used as hedging instruments. There are a few exchanges which have listed traded options, the biggest of which being Deribit. As you know, Digital Gamma produces a weekly options report where we explore the option analytics primarily based on Deribit data (since it constitutes more than 80% of total listed traded option volume), but we also include some analytics based on CME options, Bit.com options as well as OKEX options. For options which have the same option expiration, we sometimes see different levels of implied volatilities, so which one should we use? For example, we have sometimes observed that longer expiration options on CME demonstrate significantly higher implied volatilities than Deribit options (~10 vol points or more), granted there are differences in the settlement process, exercise procedures and type of market participants involved, but yet, we do not observe the same level of discrepancy for the short-dated options where the implied volatilities are essentially the same on both exchanges. An even more fundamental question is: what option expirations should I look at since they result in different levels of implied volatilities? A simple approach is to use the option expiration that matches closely the tenor of the lending transaction, but is that a reasonable approach? Another fundamental question to the options approach is: what strikes should we consider in calculating the implied volatilities? Should we use a strike that is way out-of-the-money since that is the primary risk in a bitcoin lending transaction where the posted collateral may not be sufficient to cover the losses due to excessive volatility in the movement of bitcoin prices? Or should we use at-the-money options which have more liquidity and market participants, so it may be a much more reasonable consensus estimate to market-based implied volatilities? Or should we use a weighted approach, and if so, what weights should we use?
The use of historical data to compute volatilities present similar problematic issues. For example, how much data should we use to calculate historical volatilities? If we use the length of data that matches closely the length of the bitcoin lending transaction, are we underestimating the volatility since significant movement outside of that window may occur in the future? Do we even trust that historical data is going to be representative of future price movements? Should we weigh recent data more heavily as compared to data from a longer time ago? Even if we can agree on all of the above, what percentiles should we use, and what probability distribution should I use to model bitcoin prices? In our previous documents, we have advocated using the 99th percentiles and a Student’s t-distribution to model the distribution of bitcoin prices; is that reasonable? Even more fundamentally, which data source should we use and from what exchange? How does the selection of time-stamp to determine daily prices affect the calculation? Also, should we consider futures prices as well since the derivatives market in bitcoin is expanding rapidly? If we also use futures prices, how do we resolve the issue where there might be discrepancy between the cash prices and the futures prices?
Even if we can agree definitively on the approach to compute historical or implied volatility accurately for our purpose, which one should I trust? In our weekly options report, we have seen that implied volatilities from options can be significantly higher than realized volatilities, sometimes on the order of 50%-80%. Hence, the choice of either volatility will have a significant impact on the collateral calculation. The use of historical data obviously assumes that the past will be representative of the future (which is typically not a reasonable assumption!), but the use of options information may also be somewhat problematic given the motives and strategies adopted by options traders for bitcoin options in a nascent market such as this may not be representative of the whole market and the “truth”.
Given how sensitive the collateral calculation process is to the various issues discussed above, our methodology results in a significant range of initial collateral percentages, going from about 10% at the minimum to 30% at the maximum. In order to select a number to use which is appropriate to safeguard the interest of our clients, we have determined a range of 20%-25% to be appropriate for initial collateral, granted there is a degree of judgment call that is involved in the process. We will continue to refine the process as we go forward, especially if the options markets develop more to reflect sufficient trading depth.
