# More Than Just A Decentralized Oracle: Bringing Crypto-Options on par with the S&P 500

## We designed the world’s first arbitrage-free options pricing model for cryptocurrencies and brought crypto-options on par with the options available on traditional derivatives.

Cryptocurrency trading on the spot markets is now comparable to the traditional stock markets when it comes to the level of sophistication offered. In fact, with the emergence of DEXs such as Uniswap and PancakeSwap, one can argue that cryptocurrency spot market trading has overtaken the regular equities markets.

However, this cannot be said of the crypto-derivatives trading front.

## TL;DR

- Crypto-Options’ pricing models used today are not efficient
- Simply due to lack of adequate data, several strikes are found missing in an options chain
- Umbrella Network’s Options’ Pricing Model brings, for the first time, crypto-options on par with sophisticated systems such as the S&P 500
- This is achieved by collecting all strikes, adding non-arbitrage constraints, and
*then*calculating the greeks that are more accurate - The end result is more accurate risk management for retail and institutions alike when it comes to crypto-options AND the availability of several more strikes in the same options chain!

Crypto-options platforms, amazing in their own right, lag woefully behind when compared to the TradFi (traditional finance) systems.

Why is it so? Why have crypto-options not walked in lockstep with the spot markets when taking on TradFi?

**The short answer is DATA, or rather, the absence of fresh and comprehensive call and put data.**

As the world’s largest decentralized oracle by transaction volume, we at Umbrella Network found ourselves flush with that missing piece of the puzzle — and we did exactly what you’re thinking.

We designed the world’s first arbitrage-free options pricing model for cryptocurrencies and brought crypto-options on par with the options available on traditional derivatives.

If you’re wondering why arbitrage is something to be eliminated, what was lacking in crypto-options, and how Umbrella Network’s new arbitrage-free options pricing model improves your trades, you’re in luck. This piece is for you.

We’ll break down what we’ve built, why, and how it can be used by any existing or upcoming crypto-options trading platforms to offer strike prices that were previously unavailable in the crypto-markets (due to alleged volatilities) AND, how, for the first time ever, brought crypto-options trading on par with that of the TradFi systems such as the S&P 500.

# But first, a short primer on options trading

Let’s say Alice has 1 BTC and wishes to sell it for ETH, she goes to an exchange and sells her BTC and receives the ETH. This is spot trading and is fairly simple to understand.

Options, on the other hand, are a little more complicated, and a regular options trade goes like this:

Let’s say that Alice *believes that *the price of BTC shall increase within 30 days. In this case, she *buys a call option*.

Every options contract includes the following details:

- The underlying asset
- Price of the underlying asset
- The date she wants to sell it on

She then pays a **premium** (a calculated value based on the underlying asset’s price and the time value) so that she *has the option to buy bitcoin* on 31st December 2021 at the pre-determined strike price. If the spot price is above the strike price at the expiration of the contract, she makes a profit on the difference.

**Impact of Spot Price on Options Contract Price**

Every options contract has a **strike price** which is the price at which the contract shall be executed on the given date. The higher the current price is, compared to the strike price, the more expensive the call option contract shall be. On the other hand, a higher spot price begets a cheaper put options contract price — for a given strike price.

**Impact of Expiration Date on Options Contract Price**

The longer the time to expiration (maturity of the contract), the higher would be the value of the contract (for both, a call or a put option)

**But there’s more to Derivatives**

Complex formulae and charts are used to derive what are known as greeks — delta, theta, vega, etc to quantify the value of the contracts when the price of the underlying asset changes. *These are used in risk management and form the bedrock of Wall Street*.

For example, delta measures the change in price of contract when the price of the underlying asset changes. This helps a trader (at least theoretically) to assess the value of their options contracts as the price of the underlying asset changes.

Similarly, the other *greeks* track other sensitivities and help a trader manage their risks.

# The Conundrum of Call spread Arbitrage

Imagine if Alice offers to buy 1 BTC at 30,000 at the end of the month (buying a call option) and then sell 1 BTC at 40,000 at the end of the same month (selling a call option). This means that at the end of the month (on contract expiry), Alice would earn a profit of up to $10,000. (See the blue line in the chart below)

If she buys a call with a strike of $40,000 and sells a call option with a strike price of $50,000, she’ll be able to make a profit of up to $10,000 (See the red line in the chart below)

This is called a call spread and is fairly straightforward.

If she buys the (30,40) call spread (blue line) and sells the (40,50) call spread (red line), she would get what we call a *butterfly*.

The value (price) of the butterfly has to be positive as it always has a non-negative payout. In an inefficient market, the value (price) of the butterfly can be negative.

This means that we can buy the butterfly for a negative value which basically means we earn money for holding it. On top of that, we also get paid up to $10,000 at the expiration of the contract.

This is an example of arbitrage and it is unacceptable in efficient or informed markets such as the S&P 500.

This is the conundrum of crypto-options’ call spread arbitrage.

The presence of risk-free money-making opportunities depicts the presence of an immature and inefficient market and for crypto-options to find greater adoption, this risk-free arbitrage needs to be eliminated.

# What Causes The Call Spread Arbitrage in Crypto-Options?

Unlike the more efficient/developed markets (such as the S&P 500), the crypto markets are inefficient and also more volatile. What this means is that there are certain prices at which buyers and sellers would be available on one exchange but not on the other.

Compound this peculiarity with the existence of hundreds of trading portals and the result is what gets attributed as *choppy prices*.

Since the options are basically contracts based on an underlying asset (a cryptocurrency in this case), they are also subject to wild swings and choppy availability. This causes two major problems that do not exist in the TradFi world:

**Intervening strike**prices are absent altogether- The
**emergence of arbitrage**opportunities

The impact of this choppiness can be best demonstrated by plotting the *Implied Volatility curve*.

To calculate trends and to make theoretical predictions of the price of a crypto-options contract, we create a 3D surface of Implied Volatility by plotting it as a function of the strike price and the time to maturity of the contract.

(*The volatility surface is a three-dimensional plot where the x-axis is the time to maturity, the z-axis is the strike price, and the y-axis is the implied volatility — Investopedia*)

On the S&P 500, the IV curve looks like this -

But, the bitcoin Implied Volatility Surface looks like this -

The presence of this undulating surface depicts risk-free arbitrage opportunities.

These risk-free arbitrage opportunities also lead to other undesirable effects such as:

- Absence of several call strike prices
- Absence of several put strike prices
- Presence of incorrect call strike prices
- Presence of incorrect put strike prices

# How Does Umbrella Network’s Options Pricing Model Fix this Arbitrage Problem?

Option valuation models are based on an arbitrage strategy — hedging the option against the underlying asset and rebalancing continuously until expiration — that is only possible in a frictionless market.

Umbrella Network, based on the strength of processing hundreds of data pairs across platforms, is practically sourcing the entire call-put ecosystem.

Now that we have all of the prices (thank you, call-put parity), we apply algorithmic non-arbitrage constraints that practically *remove all outliers*.

We call this process

smoothening(think of it as ironing out the kinks) which ensures thatall arbitrage at the price levelof the options contract, is removed.Then, we extrapolate the value of the options contract for all strikes,

after removing the arbitrage(making extrapolations tighter for accuracy).

These new values of the options contract for the strikes are then used to calculate the Implied Volatility (using the newly determined strike prices’ grid).

Finally, the greeks are calculated using the more accurate Implied Volatility. These greeks are, in turn, more accurate than the greeks provided by the existing crypto-options trading platforms.

The greeks calculated with Umbrella Network’s options pricing model are more attuned to the sensitivities of the market and align better with the Implied Volatility curve, instead of going haywire (as is the case with current solutions of the day)

*This also enables us to calculate strike prices that usually do not exist in the trading market. adding granularity to the strike levels and, for the first time ever, brings crypto-options strike prices’ calculations on par with the granularity in strike prices of the historically stable S&P 500 strike prices.*

# How Does This Improve Your Trades?

First and foremost, this level of detailing and calculations *eliminates the impact of temporary outliers* (which are evident from the rough volatility surface of IV without the Umbrella Network). Therefore the IV and the greeks provided by the Umbrella Network are more accurate and carry a lesser risk.

Secondly, for the first time, the crypto-markets would have *access to arbitrage-free pricing for erstwhile non-existent strike prices*. A DeFi crypto-options trading platform could build an entire market around arbitrage-free prices by simply sourcing all data from Umbrella Network’s decentralized oracles.

Finally, the benefits of Umbrella Network’s pricing of options can be reaped by retail users as well. One could visit another crypto-market and compare the options prices there, with the arbitrage-free prices on Umbrella Network’s feeds. If the trade seems favorable, they can be entered into.

Once bought, the calculated greeks would provide the pinpoint sensitivity, more frequently, and via better heuristics, because, Umbrella Network processes a higher transaction volume than every other decentralized oracle out there.

To get a better understanding, let’s look at the price of an ETH call option from a chain on the Hegic platform (red) and compare it to the price that the Umbrella Network’s options price modeling suggests (blue)

As can be seen above, even closer to the strike price (where the two lines are the closest), there is a substantial difference between the arbitrage-free price (blue) and the red line.

As we move further away from the strike price closest to the price of the underlying asset (ETH) we see that the difference between the theoretical price and the available price becomes bigger.

Thus, the arbitrage-free price offered by Umbrella Network’s options pricing model emerges as the clear winner when it comes to entering into an options contract that is both — in the money or out of the money.

On the contrary side, the put options contract pricing of the same chain also presents an interesting picture

Even here, the entry price for the put option, for strike prices in the money and out of the money, is substantially lesser than that offered by one of the best platforms out there.

(*It is to be noted here that we are not implying that the arbitrage opportunity is pocketed by the current crop of options trading platforms. These arbitrage opportunities are almost always pocketed by sophisticated bots programmed to find and target these opportunities — at the cost of the retail trader.*)

# Filling in the gaps in an options chain

To understand this better, we plotted a graph below for a BTCUSD option chain expiring on 2021–04–30 (as of 2021-Apr-15, 8 am UTC)

The x-axis represents the strike price and the y-axis represents the price in bitcoin.

The orange line shows the mid-prices of the available options at that point in time.

The gaps between any two orange lines depict the absence of intervening strike prices due to the volatile nature of cryptocurrency prices exacerbated by the existing options pricing models on Deribit.

Also plotted on the graph is the impact of Umbrella Network’s options pricing model with the removal of arbitrage via our smoothening processes. The continuous blue line — never seen before in crypto-options, is the first time ever where strike prices without gaps are available.

## Without getting too technical, it is worth noting that if the gaps between BTC options are so vast, what would be the case of lesser liquid options?

Answer — Even larger gaps!

This is why our options pricing model, based on holistic smoothening provides not just:

- Greater variety in strike prices for all cryptocurrencies
- An arbitrage-free call strike price
- An arbitrage-free put strike price

But also, better risk management.

The call and put strike prices, calculated by Umbrella Network’s options pricing model are used to calculate the greeks (useful for tracking price sensitivities) that are more attuned to a holistic curve and not dependent on the undulating topography that had come to be accepted as the ‘*cost of trading crypto-options*’.

# Conclusion

Umbrella Network’s options pricing model was made possible due to our decentralized oracles that are faster, cheaper, more comprehensive, and are more frequently updated than any other oracle service out there. Because we’re able to source data faster and cheaper, we’re able to make available crypto-options prices that are fresh and because the entire oracle service is decentralized, the data feeds are also secure.

The architecture that we’ve built, not just source the entire trading grid, but also crunch the numbers and derive the price sentiments that are more holistic and practically evolve the entire crypto-options ecosystem.

The entire setup is highly scalable and if you’re looking to get our data feeds directly into your smart contracts, you can either find them here or simply write to us to request it.

# About Umbrella Network

Umbrella Network is a scalable, cost-efficient, and community-owned oracle for the DeFi and blockchain community. Its Layer 2 technology uses the latest advances in Merkle tree technology to write multiple data points on a single on-chain transaction, so it allows for batching data to smart contracts accurately, securely, and inexpensively. Umbrella believes a community-owned oracle is not only possible but essential to creating a truly decentralized financial system.

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