# Vault System

Every product offered by Knox Finance has its own vault -- a smart contract responsible for holding collateral and writing options contracts.
Vaults are distinguished by their collateral asset (wETH, wBTC, DAI, etc) and delta (bullish or bearish).
They are accompanied by three other design components:
• Queues act as liquidity buffers for vaults, holding user funds until they can be deposited
• Pricers determine the strike price for options and auction pricing parameters
• Auctions sell options using a Dutch auction format

### Epochs

Together with the other design components, vaults work on 7-day schedules called epochs. They start and end every Friday at 8AM UTC.

#### Epoch Timeline

• 24 hours before the start of a new epoch, on Thursday at 8AM UTC*, the strike price for that epoch's auction is determined and the auction is initialized.
• The epoch starts on Friday at 8AM UTC*.
• The auction starts on Friday at 4PM UTC and lasts 30 minutes.
• The auction ends on Friday at 4:30PM UTC* and options are written. Note, the auction may end earlier if all available option contracts have been sold within the alotted time.
• Options expire at the end of the epoch, i.e. on Friday at 8AM UTC.
* Process is driven via cron-job, times are approximate.

### Selection Methodology

#### Option Delta

As mentioned earlier, each vault has an option delta. The textbook definition of delta is the amount an option price is expected to move based on a $1 change in the underlying. If a call option has a$0.1 delta, the price of the option will increase or decrease $0.1 for every$1 change in the underlying. Calls have a range of delta values between 0-1, puts have a range between -1-0. As the option approaches expiration the delta for ITM options will approach 1 for calls and -1 for puts, while the delta for OTM options will approach 0. For calls an exercised option represents "stock" purchased by the option buyer, likewise puts represent "stock" sold by the option buyer. For both calls and puts an OTM option after expiration has no intrinsic value. Keep in mind that the option delta is relative to the position of the strike price compared to the spot price of the underlying. In other words, an option further ITM will always have a higher delta than an option further OTM.
Another way of thinking about delta is that it is a proxy for an options probability of expiring ITM. Consider the following example, we have two wETH calls, and the spot price is $2000: 1. 1. Strike -$2200, Maturity - 1 week
2. 2.
Strike - \$2500, Maturity - 1 week
Since option 1 is closer ITM than option 2, it will have a higher delta due to the fact that as time decays the first option has a higher likelihood of expiring ITM. Similarly, if the wETH spot price increases, the delta for both options will also increase, but the delta of option 1 will remain higher than that of option 2.

#### Delta Strike Selection

Under the delta strike formula, we determine a strike price
$K_{delta}$
at a specific option delta as a function of implied volatility
$\sigma$
. In other words, if we know
$\sigma$
, we can obtain
$K_{delta}$
, provided that the spot price, time to expiration, and option delta are constants. We can therefore create vaults with varying levels of relative risk and return.

### Option Pricing

Knox Finance will offer a certain quantity of options to be sold at a pre-specified time, and pre-determined strike. Our vaults enable price discovery to occur on-chain via a Linear Gradual Dutch Auction (LGDA). During the allotted time period, options will be written at a price specified by a linear curve. The implied volatility of the option will start at a maximum value (
$\sigma_{\max}$
) and it will be gradually decremented according to the remaining time in the auction to a minimum reserve implied volatility (
$\sigma_{\min}$
). A bidder will have the chance to secure this price for a given lot size, depending on how much capital has been utilized prior to their bid.