---
# System prepended metadata

title: (old) Decentralizing Options - A New Approach

---

# (old) Decentralizing Options - A New Approach

###### tags: option

Option is arguably one of the oldest financial instrument in TradFi. Used correctly, it unlocks new possibilities for traders. However we will not be going through how option works in detail and its various advantages it offers.  [Here](https://www.investopedia.com/terms/o/option.asp) and [here](https://www.investopedia.com/articles/optioninvestor/06/options4advantages.asp) offers more explanation for those of you who are interested.

DeFi summer has brought many of the financial instrument from TradFi land over to DeFi land and naturally option is one of those. However, options in DeFi in my opinion, hasn't quite reach the level of usability that we would have liked.

## How does options look like now in DeFi?
Two commonly used option protocols currently are [Opyn](https://www.opyn.co/) and [Hegic](https://www.hegic.co/).

In Opyn, for each specific strike price and expiry, a seperate vault needs to be created. The options are then minted from the vault and can be sold fungibly in an open market. The price of the option will effectively be the premium paid to the minter. What that also means is that a buyer of the option is unable to purchase an option that he/she desires. Say, a buyer would be interested in purchasing an Eth Call option for 3500usd and expires 20 days later, however no vault that matches that option specification exist. The buyer ultimately would either have to choose the next best option to purchase or to wait until someone with enough liquidity is able to fund a vault that the buyer desires.

Hegic operates on an [American style option](https://www.investopedia.com/terms/a/americanoption.asp). At the time of writing, Hegic supports only ATM (At The Money) options in Ethereum chain and OTM (Out of the Money) & ATM options on Arbitrum. The liquidity of the option comes from a general pool. (i.e. Eth call option has a unique pool of its own and buyers will be able to select (within a range) the expiry date and the strike price of the option the buyer wants to purchase). The premium price is based on a formula which relies upon an IV variable which is manually configurable by the admin. From my understanding, the IV will be set to be lower than that in Deribit which effectively means that the options that are being sold in Hegic will be cheaper. Though such a method gives option buyers the flexiblity of purchasing any kind of options they like, the premium price depends on the manual input of the admin. Also each options that are purchased are non fungible and will prove to be tricky to resell in a secondary market.

## Another approach
In my opinion, both protocols have their strengths and limitations and I humbly state upfront that the proposed option here has no intention in replacing neither Opyn nor Hegic. It merely tries to take another approach to options in the DeFi space in the hope of giving aspiring option buyers more choices and flexibility in expressing their creativity in DeFi.   

Our aim is to: 
1.  Have a premium price strategy that will depend on buyer's interest in purchasing the option
2.  Have a fungible kind of option that enables buyers to resell them in the secondary market
3.  Similar to Hegic, have a single pool that will sell options of varying strike price and expiry


We will primary focus on the #1 and leave #2, #3 for the later [discussions](https://hackmd.io/5uXL-HC3SDe0yWhYC76CTQ).

### Automated Pricing strategy
[The Black Scholes model](https://www.investopedia.com/terms/b/blackscholes.asp) is the common and reliable way of determining the premium price in TradFi however due to its rather complex formula and the limitations of EVM, directly applying the model may not be feasible.  Hence we need to tweak it to make it EVM friendly.

Our approach takes the form of two formulae

<u>When strike price is lesser than current price</u>

$P_d = (currentPrice - strikePrice)/currentPrice$

$P_y = \sqrt t_e * IV$

$PremiumPrice = P_ye^{P_d * k}$

$k = growth\ constant$

<u>When strike price is greater than current price</u>

$P_d = (strikePrice - currentPrice)/currentPrice$

$P_y = \sqrt t_e * IV$

$PremiumPrice = P_ye^{-P_d * k}$

$k = decay\ constant$

<u>which also means that when currentPrice == strikePrice</u>

$PremiumPrice =\sqrt t_e * IV$

$where:$
$t_e = duration \ to \ expiry$

The premium price will be more expensive the lower the strike price is when and will be cheaper when the strike price is higher. In our actual implementation, we will clip the price at the lower and upper bound to give the premium price a more realistic value.

![](https://i.imgur.com/PSp0KIY.png)
<span style='font-size:0.8em; font-style: italic;'>Premium price grows exponentially when strike price is below the current price and decreases exponentially when strike price is above the current price. The price is clipped to be at the maximum of the current price (left end of the chart). And is clipped at a minimum price (percentage of the current price)</span>


The crux to the model will be the determination of IV. IV in our case, is simply a convenient index that attempts to track the market demand of the option. At a lower demand, IV will decrease which results in the premium price to also decrease. Without manually interaction and the use of an oracle, we came out with an equation that looks like 

$IV_{intermediate} = IV_{current} . e^{-kt}$ 

$IV_{new} = IV_{intermediate}P \ * \ amount$

$where:$
$k = decay \ constant$

$t = blockNumber_{now} - blockNumber_{lastUpdated}$

$P = percentage \ increase$

![](https://i.imgur.com/XwqlEDf.png)
<span style='font-size:0.8em; font-style: italic;'>IV decays exponentially at each block when no options are being purchased, signifiying a lowering demand</span>

The TLDR explanation for the IV formula is that the more blocks that has passed when there are no option purchases, the IV will decay which will result in the premium price to be lowered, thereby attracting buyers to pounce on a deal they deem profitable.

Conversely, as more options are being purchased within a short time span, the IV will increase and the premium will be more expensive.


## Rounding up
There we have it, a simple strategy to price the premium of an option according to the supply-demand of the market. The IV serves as the crux that will determine the base price of the premium when the strike price is the same as the current price, and grows or decays exponentially the the strike price decreases/increases in relative to the current price.


In the next one, we will go through how we are able to resell options fungibly in an open market. Be sure to check that out too!