---
# System prepended metadata

title: Decentralizing Options - A New Approach

---

# 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.

Option pricings are commonly affected by a few factors and in the option world, people have used several greek letters to denote them. Check them out [here](https://www.optionsplaybook.com/options-introduction/option-greeks/) for a quick intro to what they mean.

Over here, we design a pricing calculator which takes into considering the few greek letters that play a role in the determining of option price. Also ideally, our pricing calculator has to be 'smart' and has to be able to adjust the option pricing based on some form of implied volatility

#### <u>Strike price vs Current price</u>
The value of the option changes with its strike price. If the option is ITM, the option will be more valuable and we can expect the premium to be higher. Conversely, for options that are OTM, they will be less valuable and cheaper to be purchased. The logic behind this is that the underwriter of the option will incur a higher risk for options that are in profit. They will only be encouraged to underwrite a riskier option in exchange for a higher fee. 

Our pricing calculator consist of two formulae in order to mimic this behaviour. For simplicity, the formulae assumes that the option is a call option. Put option will simply be the reverse.

<u>When strike price is greater than current price</u>
$P_{norm\ diff} = (strikePrice - currentPrice)/currentPrice$

$P_{premium} =Y_{intercept} * e^{-P_{norm\ diff} * k}$        $where\ k=decay\ constant$

<u>When strike price is lesser than current price</u>
$P_{norm\ diff} = (currentPrice - strikePrice)/currentPrice$

$P_{premium} =Y_{intercept} * e^{P_{norm\ diff} * k}$        $where\ k=growth\ constant$

For now $Y_{intercept}$ can be ignored and we will talked about it in the next section.

From the above formulae, when the option is OTM (strike price greater than current price), the premium will decay exponentially. This represents the loss in value of the option the 'more' OTM an option. 


On the other hand, the 'more' ITM the option is, the premium will increase exponentially as the underwriter will incur for risk for the options that they are underwriting.

This is vaguely similar to `delta` as the option value moves in accordance to the strike price and the `gamma` is depicted by the exponential growth or decay of the price.

![](https://i.imgur.com/xjMqDYs.png)
<span style='font-size:0.8em; font-style: italic;'>
Premium price paid in the form of underlying token where the amount purchased is set to be 1.
Premium Price decays exponentially when strike price is greater 2000 and growths exponentially when strike price is lesser than 2000. In the actual implementation, the min premium price is clipped. This ensure that the option buyers will always have to pay for a reasonable amount of premium  
</span>

#### <u>Time to Expiry</u>
Another important factor that affects the value of the option is the time to expiry. Option value decreases with time and this is where we properly introduce  $Y_{intercept}$ and see how can be used to capture this property

$Y_{intercept}=	(\sqrt{t})/(\sqrt{t_{per\ day}}) * \nu$        

$where\ t=time\ in\ seconds$
            $t_{per\ day} = seconds\ in \ a\ day$
            $\nu = percentage\ factor\ (more\ on\ this\ later)$

The division by $\sqrt{t_{per\ day}}$ is just a constant factor to normalized $\sqrt{t}$ and has no impact on our analysis.

$\sqrt{t}$ will mean that when time in seconds increases, the $Y_{intercept}$ increases in a square root fashion. This will be analogous to `theta` of the option.

![](https://i.imgur.com/DiP0HWM.png)
<span style='font-size:0.8em; font-style: italic;'>
$Y_{intercept}$ which determines the final premium increases with expiry.
</span>

Putting it together with the premium price formula, $Y_{intercept}$ gives the premium price curve a 'starting' point. This is when the option is ATM. And the higher the time to expiry, the higher the value of the 'starting' point will be. The premium price will grow or decay accordingly with respect to the strike price.

![](https://i.imgur.com/trKgRgW.png)
<span style='font-size:0.8em; font-style: italic;'>
The premium paid for a longer expiry will be greater compared to that of a short expiry
</span>

#### <u>Market demand</u>
Another commonly used option term is implied volatility of the underlying asset. Typically, a higher implied volatility will result in a higher premium price. However, implied volatility is tricky to measure and we introduce `percentageFactor` instead which will have the ability to change with with market demand. Recall that we briefly introduced `percentageFactor` as $\nu$ [above]($\sqrt{t}$)

`percentageFactor` decreases the longer the option has not been sold and increases with each option purchase. Intuitively, the longer the option has not been sold, the demand for the option is low and so the premium price will need to be adjusted to be lower to attract potential buyers. Conversely, when there is a option purchase, this signifies an increase demand in the market and the premium will become more expensive.

<u>Percentage Factor with time since last purchased</u>
$\nu_{decayed}=\nu_{current}\ e^{-b_{diff}k_{decay}}$

$where \ b_{diff}=block\ diff\ since\ last\ purchase$
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;$k_{decay}=decay\ constant$


<u>Percentage Factor increase with option purchase</u>
$\nu_{latest}=\nu_{decayed}\ *\ k_{increase}\ *\ amount$

The `percentageFactor` will decay exponentially with each passing block and will increase at a linearly with the amount with an option purchase

![](https://i.imgur.com/hZikWFm.png)
<span style='font-size:0.8em; font-style: italic;'>
Percentage factor which is an indicator to the market demand falls the longer the option has not been bought. This value is clipped to a preset minimum in the actual implementation
</span>

## 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 `percentageFactor` 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!