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APPENDIX

Additional Resources

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Applied Use Cases

This section will cover an overview of an entire user flow using mint, exercise, and withdrawal of a PodOption.

Example 1 - Selling Puts

Imagine Rob is very bullish on ETH. He frequently buys more ETH to increase his portfolio, and he usually thinks about an entry price that he feels is good to buy more ETH given the moment of the market. Instead of going to an order book or Matcha and placing a limit order, he prefers to sell Put options for the strike price equal to the entry price he has in his strategy. In that way, it is a win-win situation for him:

a) If the spot price hits the strike price and his position is exercised, he ended up buying the underlying asset (ETH) for the price he was willing to purchase AND earned a premium for that.

We say in this situation that the option was in the money (ITM)

b) On the other hand, if the spot price does not hit the strike price, Rob will have earned the premium, and he can try selling another option again at a new strike price if he wants. Additionally, our options accept aTokens as collateral, so it is possible to earn interest in addition to the premium.

We say in that case that the option was out of the money (OTM)

Visualization for time-to-price evolution. Considering the seller's point of view.

Scenario

Here, we will follow a user flow of a seller (Rob) of a PodPut. He will:

Lock strike asset as collateral to mint options and hold his position with shares of the contract.

Rob will then get the new-minted options and sell them on our AMM for a premium (For details on how the calculation for the premium works, check out the how our price works section).

In this scenario, we will assume that the spot price became lower than the strike price, and some options were partially exercised.

After the expiration, Rob will be able to withdraw his collateral based on the number of shares he has.

The collateral will be returned partially in the strike asset and partly in the underlying asset.

Let's add some numbers as an example to illustrate better:

Input Name

Description

underlying asset

WETH

strike asset

aUSDC (a collateral asset in case of Puts)

option type

Put

exercise type

European

strike price

$400

spot price

$500

expiration

31 Dec 2020

current day

21 Nov 2020

Minting options

So, let's say that Rob has 1200 aUSDC and is willing to buy a max of 3 units of ETH at the strike price. The following steps will occur:

Rob calls the mint function with two parameters: amountOfOptions and owner.

amountOfOptionswill be equal to 3 and ownerwill be Rob's address.

Rob needs to call approve() on the strike asset aUSDC contract allowing the PodPut contract to spend his 1200 aUSDC.

The contract will calculate the amountToTransfer that will be equal to amountOfOptions * strikePrice that will equal 1200 aUSDC in our case.

The contract will also store the number of shares Rob has from the PodPut contract using the following equation:

ownerShares = amountToTransfer * totalShares / (strikeReserves + underlyingReserves * strikePrice)

Let's assume that in our case, the contract has 4000 totalSharesand astrikeReserves of 4050 aUSDC.

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Therefore, Rob has 1200 * 4000 / 4050 shares. Resulting in 1185.185 shares.

The contract will then call thetransferFrom function from the strike asset contract usingamountToTransfer as a parameter.

strikeReserves and underlyingReserves represent the PodPut contract balance of strike and underlying.

Exercise

Fast forward to Dec 31, 2020. Babi, who has bought two options in the secondary market, has 24h to exercise her options before the exerciseWindow ends. The spot price is currently at $300

Babi calls the exercise function, passing the amountOfOptions she wants to exercise.

She needs to call approve() on the underlying asset WETH contract, allowing the PodPut contract to spend her underlying asset and give her back an amount of the strike asset.

The amount of underlying tokens the PodPut will use to call thetransferFrom function will be 1:1. So, in our case, if she wants to exercise two options, two units of underlying asset will be transferred to PodPut, increasing theunderlyingReserves.

Babi will receive back amountOfOptions * strikePrice units of thestrike asset. In this case, 2*400 = 800 aUSDC units.

If the spot price was, let's say $300, and she paid $20 in her options. Her returns will be (strike price - spot price) * amountOfOptions - premium

Withdraw

Now 24h passed, and Rob is enabled to withdraw his collateral. Remember that Rob had 0.007407 shares? Let's see how many strike and underlying he will receive back. We will assume that PodPut had no new sellers, and aUSDC strike balance increased a little, earned some interest during that time. So right now, our balances are:

strikeReserves = 4500 aUSDC (4050 we had initially, plus 1200 from Rob, less the amount the PodPut used to pay Babi back during her exercise, plus some interest earned during this time)

underlyingReserves = 2 WETH

totalShares = 5185,185

To calculate how many strikeToReceive and underlyingToReceive the contract will receive, we do the following calculations:

strikeToReceive = ownerShares * strikeReserves / totalShares

underlyingToReceive = ownerShares * underlyingReserves / totalShares

In this situation, Rob will receive back 1185,185 * 4500 / 5185,185 = 1028,571 strike asset. In addition to that, he will receive also 1185,185 * 2 / 5185,185 = 0,45714 underlying asset

Example 2 - Unminting Puts

Let's suppose that Rob from the previous example believes that it's not worth holding the position of selling a put option to buy ETH for the strike price he has previously set. This could happen for many reasons:

1.

Wants to use the collateral for other purposes instead of having it locked in

2.

He believes he can find a more profitable operation within another set of options.

Scenario

Here, we will follow a user flow of an owner/seller (Rob) of a PodPut. He will:

Decide how many options he wants to unmint to leave his position by reducing the contract's number of shares.

To unmint, the options will need to be burned. Consequently, Rob will need to have the options in the wallet he used to mint the options to do so.

In case Rob already sold his options in our AMM for a premium, he will have to buy the number of the options he wants to unmint from the same series to leave the position.

It is important to have in mind that if Rob has to buy back the options to call the unmint function, there is no guarantee the option will be the same as the premium he received for selling the option from the same series.

Let's add some numbers as an example to illustrate better:

Input Name

Description

owner

Rob

owner shares

1185.185

user-minted options

3

amount of options to withdraw

1

strike asset aUSDC (collateral)

1200

total shares

5185.185

strike asset

aUSDC

underlying asset

WETH

strike price

$400

expiration

31 Dec 2020

current day

15 Dec 2020

exercise type

European

So, let's say that Rob wants to leave his position on 1 put option he had previously minted in the Example 1, getting back the collateral at the strike price of 400 aUSDC. The following steps will occur:

Rob calls the unmint function with two parameters: the amount of options to unmint and owner.

amount of options to unmint will be equal to 1 and owner will be Rob's address.

Rob needs to call unmint() on the option contract

The contract will calculate the ownerShares of Rob to have the number of the protocol's shares the user will unmint.

ownerShares_w =(amountOfOptionsToWithdraw âˆ— ownerShares_i-1)/ userMintedOptions

So: amountOfOptionstoWithdraw will be equal to 1 and ownerShares_i-1 is equal to 1185.185 and the userMintedOptions will be equal to 3. Therefore, ownerShares_w will be equal to 395.06.

We will assume that PodPut had no new sellers, and aUSDC strike balance increased a little, earned some interest during that time. Furthermore, no options were exercised yet as we did not reach the expiration date. So right now, our balances are:

strikeReserves = 5300 aUSDC (4050 we had initially, plus 1200 from Rob, plus some interest earned during this time)

totalShares = 5185.185 shares

To calculate how many strikeToSend the contract will send, we do the following calculations:

strikeToSend=(ownerShares_wâˆ—OSBn)/totalShares_iâˆ’1

In this situation, Rob will receive:

395.06 * 5300 / 5185.185 = 403.807 strike asset which in this case is aUSDC.

By the end of this process, the new balances will be the following:

Variable

Formula

Value

totalShares_i

totalShares_i = totalShares_iâˆ’1 âˆ’ ownerShares_w

= 5185.185 - 395.06 = 4,790.125 shares

ownerShares_i (Rob)

ownerShares_i = ownerShares_iâˆ’1 âˆ’ ownerShares_w

=1185.185 - 395.06 = 790.125 shares

strikeReserves (sRi)

sRi = sRi-1 - strikeToSend

= 5300 - 403.807 = 4,896.193

Example 3 - Buying Puts

Let's take Babi from the 1st example and drill down what steps she had to go through to buy two put options from Rob.

Babi is bearish on ETH and wants to reduce her exposition to the asset by buying a put option with a strike price that is lower than the current spot price of $500 but that still limits her potential loss according to her feeling about the asset. In case the price of ETH falls below $500, she will be able to exercise her option and sell her asset for a higher price than the spot price, being able to profit on that. Let's take the following example:

Spot price of ETH at expiration: 300 USDC

Strike price: 500 USDC

In this case, the option is in the money (ITM).

She knows the pricing of options needs to take into consideration important variables such as implied volatility and the time to maturity, so she goes to the AMM as she knows she will pay a premium that correctly translates the value of the option at the time she gets to buy the option. (For details on how the calculation for the premium works, check out Pricing).

The pricing of the put option was of 20 USDC each.

Considering the conditions above, Babi would be able to sell the asset for 500 USDC, which is higher than the ETH market offers. Taking into consideration that she paid 20 USDC for 2 put options from Pods' AMM, Babi made a profit of: 2 * (500 - 300) - 2 * 20 = 360 USDC.

In case the option is OTM, which means that the spot price of ETH was higher than the strike price, there would be no reason for Babi to exercise her put option as she would be selling the asset for a lower price than what the market is currently offering. In this case, she would have lost only the amount of the premium paid for the options bought in Pods' AMM.

Visualization for time-to-price evolution from the point of view of the buyer of puts.

Example 4 - Selling Calls

Imagine Gabriel is long and bullish on ETH. Gabriel has a lot of ETH exposure in his portfolio, and one of the things he could do to increase his passive income on his current assets is to sell call options on ETH. By doing so, Gabriel agrees that he will get a premium for selling the options (and therefore generative a yield on the idle assets) and take the risk of being exercised (sell ETH at the strike price if the buyer chooses to exercise).

a) If the spot price surpasses the strike price and his position is exercised, he ended up selling the underlying asset (ETH) for a lower price than what the asset is worth in the market.

We say in this situation that the option was in the money (ITM)

b) On the other hand, if the spot price does not surpass the strike price, Gabriel will have earned the premium.

We say in that case that the option was out of the money (OTM)

Visualization for time-to-price evolution from the point of view of calls sellers,

Scenario

Here, we are going to follow a user flow of a seller (Gabriel) of a PodCall He will:

Lock underlying asset (ETH) as collateral to min option and hold his position with the contract shares.

Gabriel will then get the minted options and sell them on our AMM for a premium (For details on how the calculation for the premium works, check out the how our price works section).

In this scenario, we will assume that the spot price became higher than the strike price, and some options were partially exercised.

After the exerciseWindow, Gabriel will be able to withdraw his collateral based on the amount of shares he has.

The collateral will be returned partially in the strike asset, and partially in the underlying asset.

Let's add some numbers as an example to illustrate better:

input name

Description

underlying asset

WETH (a collateral asset in case of Calls)

strike asset

USDC

option type

Call

exercise type

European

strike price

$700

spot price

$500

expiration

31 Dec 2020

current day

21 Nov 2020

Minting Options

So let's say that Gabriel has 4 ETH and believes that selling each of them at the strike price of 700 aUSDC is fair. The following steps will occur:

Gabriel alls mint function with two parameters: amountOfOptions and owner.

amountOfOptions will be equal to 4 and owner will be Gabriel's address.

Gabriel needs to call approve( ) on the underlying asset ETH contract allowing the PodCall contract to spend his 4 ETH.

The contract will calculate the amountToTransfer that will be equal to optionsAmount of the underlyingAsset that will equal to 4 ETH in our case.

The contract will also store the number of shares Gabriel has from the PodCall contract using the following equation:

ownerShares = (amountToTransfer * totalShares_i-1) / (underlyingReserves_i + (strikeReserves_i / strikePrice))

Let's assume that in our case the contract has 500 totalShares and an underlyingReserve of 580

Therefore, Gabriel has 4 * 500 / 580 shares. Resulting in 3.448 shares.

The contract will then call the transferFrom function from the underlying asset contract using amountToTransfer as a parameter.

strikeReserves and underlyingReserve represent the PodCall contract balance of strike and underlying.

Exercise

Fast forward to Dec 31, 2020. Gui, who has bought three options in the secondary market, has 24h to exercise his options before the exerciseWindow ends. The spot price is currently at $900.

Gui calls the exercise function, passing the amountOfOptions he wants to exercise.

He needs to call approve() on the strike asset USDC contract, allowing the PodCall contract to spend his strike asset and give him back and amount of the underlying asset (ETH).

The amount of underlying tokens the PodCall will use to call the transferFrom function will be 1:1. So, in our case, if he wants to exercise three options, three units of the strike asset will be transferred to PodCall, increasing the strikeReserves.

Gui will receive back the amountOfOptions units of the underlying asset. In this case, 3 ETH units.

If the spot price was let's say $1000 and he paid $20 in her options. Her returns will be (spot price-strike price) * amountOfOptions - premium

Withdraw

Now 24h passed, and Gabriel can withdraw his collateral. Remember that Gabriel had 0.1428 shares? Let's see how many strikes and underlying he will receive back. We will assume that during that time, PodCall had no new sellers. So right now, our balances are:

strikeReserves = 2100 aUSDC (3 call options with the strike price of $700 were exercised)

underlyingReserve= 581 WETH (500 ETH we had initially plus 4 from Gabriel minus the 3 PodCall used to pay Gui during his exercise).

totalShares = 503.448 shares

To calculate how many strikeToSend and underlyingToSend the contract will receive, we do the following calculations:

strikeToSend = ownerShares * strikeReserves / totalShares

underlyingToSend = ownerShares * underlyingReserve / totalShares

In this situation, Gabriel will receive back:

strikeToSend = 3.448 * 2100 / 503.448 = 14.382 USDC

underlyingToSend = 3.448 * 581 / 503.448 = 3.979 ETH

Example 5 - Unminting Calls

Let's suppose that Gabriel from the previous example believes that it's not worth holding the position of selling a call option to sell ETH for the strike price he has previously set. This could happen for many reasons:

1.

Wants to use the collateral for other purposes instead of having it locked in.

2.

He believes the price of ETH will surpass the strike price making it more profitable to sell the asset for the spot price.

3.

Believes he can find a more profitable operation within another set of options

Scenario

Here, we are going to follow a user flow of an owner/seller (Gabriel) of a PodCall. He will:

Decide how many options he will want to unmint to leave his position by reducing the contract's number of shares.

To unmint, the options will need to be burned so, consequently, Gabriel will need to have the options in the wallet he used to mint the options to do so.

In case Gabriel already sold his options in our AMM for a premium, he will have to buy the number of the options he wants to unmint from the same series to leave the position.

It is important to have in mind that if Gabriel has to buy back the options to call the unmint function, there is no guarantee the option will be the same as the premium he received for selling the option from the same series.

Let's add some numbers as an example to illustrate better:

input name

Description

owner

Gabriel

ownerShares

3.448

userMintedOptions

4

amountOfOptionsToWithdraw

2

underlying asset (collateral)

4

totalShares

503.448

strike asset

USDC

underlying asset

WETH

strike price

$700

expiration

31 Dec 2020

current day

15 Dec 2020

exercise type

European

So, let's say that Gabriel wants to leave his position on 2 call options he had previously minted in the Example 3, getting back the collateral of 2 ETH. The following steps will occur:

Gabriel calls the unmint function with two parameters: amount of options to unmint and owner.

amount of options to unmint will be equal to 2 and owner will be Gabriel's address.

Gabriel needs to call [function] on the strike

The contract will calculate the ownerSharesw of Gabriel to have the number of the protocol's shares the user will unmint.

ownerSharesw =(amountOfOptionsToWithdrawâˆ—ownerShares_iâˆ’1)/ userMintedOptions

So: amountOfOptionstoWithdraw will be equal to 2 and ownerShares_i-1 is equal to 3.448 and the userMintedOptions will be equal to 4. Therefore, ownerShares_w will be equal to 1.724.

We will assume that during that time, PodCall had no new sellers and ETH underlying balance. Furthermore, no options were exercised yet as we did not reach the expiration date. So right now our balances are:

underlyingReserve = 584 ETH (580 we initially had plus 4 from Gabriel).

totalShares = 503.448

To calculate how many underlyingToSend the contract will send, we do the following calculations:

underlyingToSend = 2 ETH

By the end of this process, the new balances will be the following:

Name

Formula

Value

totalShares_i

totalShares_i = totalShares_iâˆ’1 âˆ’ ownerShares_w

= 503.448 - 1.724 = 501.724 shares

ownerShares_i (Gabriel)

ownerShares_i = ownerSharesiâˆ’1 âˆ’ ownerSharesw

= 3.448 - 1.724 = 1.724 shares

underlyingReserve (uRi)

OUBi = OUBi-1 - underlyingToSend

= 584 - 2 = 582 ETH

Example 6 - Buying Calls

Let's take Gui from the 4th example and drill down what steps she had to go through to buy 3 call options from Gabriel.

Gui is bullish on ETH and wants to buy a call option with a strike price that will be lower than the spot price by the time of the option's expiry. If this happens, he will be buying ETH for cheaper than what the market is charging and would be able to profit on that. Let's take the following example:

Spot price of ETH at expiration: 900 USDC

Strike price: 700 USDC

In this case, the option is in the money.

He knows the pricing of options needs to take into consideration important variables such as implied volatility and the time to maturity so she goes to Pods Finance's AMM as she knows she will pay a premium that correctly translates the value of the option at the time she gets to buy the option. (For details on how the calculation for the premium works, check out the how our price works section).

The pricing of the call option was 20 USDC each.

Considering the conditions above, Gui would be able to buy the asset for 700 USDC and then sell the ETH in the market for 900 USDC. Taking into consideration that he paid 20 USDC for 3 call options from Pods' AMM, Gui made a profit of: 3 * (900 - 700) - 3 * 20 = 540 USDC.

In case the option is OTM, which means that the spot price of ETH was below the strike price, there would be no reason for Gui to exercise his call option as he would be buying the asset for a higher price than what the market is currently offering. In this case, he would have lost only the amount of the premium paid for the options bought in Pods' AMM.

Visualization for time-to-price evolution from the calls buyer.

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Last modified 3mo ago