Additional Details

Note: Throughout we use base and power to describe the underlying base and power assets, e.g. osmo and squosmo.

The Crab is a strategy vault containing:

• A 100% allocation to base Asset

• A 50% allocation to short power (the strategy mints and sells power)

Since power has a 2x delta to base, this combination has an equally balanced long and short base exposure. The maximum payoff is achieved if base moves sideways (like a crab), and decreases with the square of base returns.

Deriving the crab payoff

The price of power can be expressed as

$P_{power} = N_t P_{base}^2 \exp{(\sigma^2 T)}/10000$

where $P_{base}$ is the base price, $N_t$ is normalization factor (the accumulated funding for the contract since inception), $sigma^2$ is the annualized variance of base returns, and $T$ is the contract funding period in years (17.5/365).

The return between $t$ and $t+\Delta t$ is

$r_{power} = \frac{N_{t+\Delta t} (P + \Delta P)^2}{NF_t P^2}-1$

$= \frac{N_{t+\Delta t}}{NF_t} \left(1+ 2 \frac{\Delta P}{P} + \left(\frac{\Delta P}{P}\right)^2 \right)-1$

$= \frac{N_{t+\Delta t}}{NF_t} (1+2r+r^2)-1$

where $r$ is the BASE/USD return.

$r_{power} \approx r^2 + 2r - f \frac{\Delta t}{T}$

Where $f$ is the funding rate applied per funding period. Crab strategy is short power with hedged delta, so

$r_{crab} \approx -r^2 + f \frac{\Delta t}{T}$

Understanding Crab from a technical perspective

Short Volatility

The Crab Strategy is short power volatility. More specifically, the strategy is profitable if the price of base moves less than what is implied by power volatility. More specifically, it must move less than funding.

For example, let's say power annualized implied volatility (variance) is 115.63%, or approximately 6.05% per day (standard deviation). Implied volatility is the market's forecast of a likely movement in base price, which impacts the price of squeeth via the funding rate. The funding rate is daily implied volatility squared, which in this case is .39%.

For Crab to be profitable, the price of base must go up or down less than funding (.39% of base price).

When to Deposit

The Crab strategy sells power. Therefore, users want to deposit when implied volatility is "higher" and get out of the vault when implied volatility is "lower." implied volatility impacts the profitability of a Crab depositor's position.