Falkenblog

Several innovations make this work, all focused on radical simplicity. This lowers costs and reduces direct and indirect costs. The most important innovations are the following:

This contract is designed for those who want to stay off the grid, and so its pseudonymous oracle can maintain its anonymity and avoid censorship. Its main costs are fixed, as once the contract, front-end, and automated scripts for updating prices are created, maintenance is trivial. The oracle is kept honest via the repeated game it is playing, and the ability and incentive for users to burn their PNL rather than submit to a fraudulent PNL at settlement. A centralized oracle is much easier to incentivize because it is all-in on the brand value of its oracle contract, as a cheat should eliminate future users.

the only way to cheat involves colluding with an oracle that posts fraudulent prices, so the contract focuses on minimizing a cheat payoff while concentrating the cheat cost on the oracle. An oracle's reputation is black or white, as its history of reported prices is easy to monitor, and no rational person would ever use an oracle that cheated once.All of an oracle's brand value is in the contract due to its pseudonymous nature, so there is less incentive to sell-out to seize or protect some traditional brand value (e.g., Steem). While explaining the incentive structure requires more space than I have here, the crucial issues are that players have the ability and the will to decimate a cheat.

This site is not encrypted--http as opposed to https--but as this contract is denominated in szabo, and the website and contract do not ask for no user information such as emails, etc, users can interact via MetaMask or MyCrypto.com without worry. Users can also download the front-end from GitHub and run a local version with all the same functionality (it's open source). It is fully functional.

While short-term asset returns are unpredictable, volatility is highly predictable theoretically and practically. The VIX index is a forward-looking estimate of volatility based on index option prices. Though introduced in 1992 it has been calculated back to 1986, because when released they wanted people to understand how it behaved.



Given the conditional volatility varies significantly over time it is very useful to generate a VIX proxy for cases where one does not have VIX prices. This includes pre-1986 US, countries that do not have VIX indices, and when trying to estimate the end-of-day VIX. This latter problem is subtle but important because historical closing VIX prices are taken from the 4:15 ET in the US while the market closes at 4:00, and so using VIX prices for daily strategies can generate a subtle bias when used in daily trading strategies.



As a liquid market price, the VIX is a good benchmark for any equity volatility model. The most common academic way to estimate volatility is some variant of a Garch(1,1) model, which is like an ARMA model of variance:


The problem is that you need to estimate the parameters {w, α, β} using a maximum likelihood function, which is non-trivial in spreadsheets. Further, there is little intuition as to what these parameters should be. We know that α plus β should be less than 1, and that the unconditional variance is w/(1-α-β). That still leaves the model highly sensitive to slight deviations, in that if you misestimate them you often get absurd extrapolations.

For daily data, a simple exponentially weighted moving average (EWMA) version of Garch(1,1) works pretty well, with w=0, α=0.05, and β=0.95. This generates a decent R² with the day and month-ahead variance.

Alas, this has two problems. First, there is a predictable bias in the EWMA because it ignores mean reversion in volatility. Garch models address this via the intercept term, but as mentioned it is tricky to estimate and creates non-intuitive and highly sensitive parameters. We can see this bias by sorting the data by VIX into deciles, and take the average EWMA, where the relative difference in the VIX and the EWMA increases the lower the EWMA. As this bias is fairly linear, we can correct for this via the function

Secondly, there's the correlation between returns and VIX movements that are asymmetric: positive index returns decrease implied volatility while negative movements increase implied volatility. Further, the strength of the relationship is asymmetric, in that down moves are twice as strong as up moves.Here are the contemporaneous changes in the VIX and SPY using daily returns since 2003. I sorted by SPX return into 20 buckets and took the average SPX and VIX percent changes.

An EWMA would generate a symmetric U-pattern between asset returns and volatility as 0.01² = (-0.01)², a huge mismatch with real daily VIX changes.

There are a couple of good reasons for this asymmetric volatility response to price changes. As recessions imply systematic economic problems, there's always a chance that negative news is not just a disappointment, but reveals a flaw in your deepest assumptions (e.g., did you know you don't need 20% down to buy a house anymore?).This does not happen in commodities because for many of these markets higher prices are correlated with bad news, such as oil shocks or inflation increases. Another problem is that many large-cap companies are built primarily of exponential growth assumptions. Companies like Tesla and Amazon need sustained abnormal growth rates to justify their valuations, so any decline could mean an inflection point back to normal growth, lowering their value by 90%. Again, this has no relevance for commodities.

One can capture this by the following function

For example, if the return was +1%, yesterday's vol is multiplied by 0.975, while if it was down 1%, the adjustment factor is 1.05. While the empirical relation of returns on volatility is not just asymmetric but non-linear (the absolute returns have a diminishing marginal impact), putting in a squared term creates problems as they extrapolate poorly, and so this piecewise linear approximation is applied to make the model more robust.

Vol Estimators sorted by VIX

Daily Correlation with VIX Changes

2004-2019

Regression R² for predicting forward day-ahead and 21-day ahead variance