Auctions are a particularly popular topic in game theory, with dutch auctions in particular being widely studied. Generally, dutch auctions facilitate price discovery, but may not necessarily reach an equilibrium state where all participants reveal their true valuation of the item for sale.
In Algorand, the dutch auctions are ran with an embedded 1-year put option, with a strike price tied to the auction clearing price. This added optionality gives a new dimension to consider for auction participants.
Below we provide a simple reference on how participants should bid in the auction, depending on their valuation view of the token.
Assume your fair valuation for the token is p, which means you expect the token to trade at p at equilibrium post-auction. The highest price you would pay is B - which means if the auction clears at B you would break-even. The annualized volatility for the ALGO token is δ. The risk-free rate (your funding cost) is r. The embedded put option maturity is t (which is 1 year in this case). The strike of the embedded put option is K which is mapped to the clearing price.
Hence, we have:
p + N(-d2) * K * exp(-r * t) — N(-d1) * p >= B
We use the Black-Scholes model to price the put option where:
N is the cumulative distribution function (CDF) of the standard normal distribution.
To solve the above; assume the auction clears at price B (since B here is the highest price you want to bid). For simplicity, we assume strike K of the embedded put option equals 0.9 * B, which is the case if the auction clears >$1 (which the market currently expects). Set X = B / p which is where you want to bid given a fair value assumption. That gives us:
You can solve the above equation to get a target ratio x. As you can see, x would depend on your assumption on risk-free rate (r), and the annualized volatility of ALGOs, δ. For simplicity’s sake we can assume r is the 1-year Fed Funds rate, which is 2.4%. This gives us the below table as a reference to different B/P ratios, which correspond to different assumptions of annualized volatility.
The current 1-year realized volatility for ETH is 90% — 100%. If you assume ALGO volatility will be similar, and you expect the token to trade at p post-auction, you would bid as high as 1.77–1.92 p during the auction to account for the embedded put option. In the above example, we have assumed a staking yield (q) of 0%. If we assume q = 15% and think of staking rewards as continuous stock dividends (as opposed to cash dividends), then the updated table would be:
The first auction happens 6AM EDT on June 19th (today). 25mio tokens will be sold with a price limit of $10.
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