Introducing the Gamma Vault

August 19th, 2022

Today we’re excited to announce the Gamma Vault, first of its kind in DeFi. Earlier this month Polynomial launched **Dynamic Option Vaults (DOV)**, the next iteration of our Option Vaults. Unlike DOVs, the Gamma Vault runs a fully on-chain **delta-neutral strategy** combining options and futures powered by **Lyra** and **Synthetix Futures**.

Since the Gamma Vault runs an experimental strategy, the vault will be running in beta mode. While in beta mode, the vault capacity will be limited to only $50k and only certain selected addresses are allowed to deposit. This includes **existing Polynomial Earn users, Cryptotesters NFT holders and top degenscore holders**.

Options are complicated financial instruments and they are often used for speculation and hedging risk. **An option’s price can be influenced by a number of factors, these risk factors are measured using the Greeks**. Delta, Gamma, Vega and Theta are the primary Greeks.

**Delta (Δ)**measures the sensitivity of an option’s price relative to the change in the underlying asset’s price. In other words, if the price of the underlying asset increases by $1, the price of the option will change by*Δ*amount.**Gamma (Γ)**represents the rate of change of Delta relative to the change of the price of the underlying asset. Since Delta frequently changes with underlying asset’s price, Gamma provide insights into what to expect from the future. Near at-the-money options have highest Gamma value.**Vega (v)**measures the sensitivity of an option’s price to volatility. If the underlying asset’s volatility increases by 1%, option’s price will increase by*v*amount.**Theta (Θ)**represents the rate of time decay of an option. If the option’s time to maturity decreases by one day, the option’s price will change by the*Θ*amount.

With this assumption, we can also define Greeks for Perpetual Futures. Unlike options, Perpetual Futures have a constant delta of 1 since price increments of underlying assets are reflected equally in Perpetual Futures. They also have a zero Gamma since the Delta is constant.

**Gamma vault tries to profit from short-term volatility by taking advantage of option’s gamma.** To achieve this the vault buys a near at-the-money call option with highest gamma and shorts perpetual futures equal to the delta of the option. This initial position structure is delta-neutral, which means the position is directionally neutral.

Let’s consider an example where Ethereum is trading at $1820. The vault will purchase a call option of strike price $1800 with a delta of 0.56. To make the position delta-neutral, the vault will short 0.56 Ethereum worth of perpetual futures. Net delta of this position is zero. The position structure can be seen below.

It is evident from the chart that if the market were move to either direction, the vault will profit from it. This is due to the gamma of the option, as the underlying asset changes in price the delta of the option changes but the delta of the futures position stays the same. So what’s the catch? If the market stays idle, the vault starts losing money due to the time decay of the option. Given this, the Gamma Vault works best in highly volatile market.

The above picture shows the same position after staying idle for 2 days. It is clear that, if the market stays neutral for longer time a bigger market move is required to profit from the trade. Due to this nature, the vault will try to close a position in few hours after the trade has become profitable. Also the vault will not keep a position for more than 3 days irrespective of the PnL from that trade.

Let’s reconsider the above example numerically. If Ethereum is trading around $1820, the price of a call option with a strike price of $1800 expiring in 7 days would be $92. This option has a delta of 0.56 and let’s assume 1x leverage for futures position.

Total cost = Option Price + Futures Margin = $92 + 0.56 * $1820 = $1111.2

**Market moves up**

Let’s say after 6 hours, Ethereum is trading around $1910, the same option’s price would be $149. We have a made a profit of $57 from the option’s position, but have made a loss of $50.4 (0.56 * $90) from the futures position. That’s a **total profit of $6.6 per unit size.**

**Market moves down**

If Ethereum is trading around $1730 after 6 hours, the option’s price would be $49. That’s a total loss of $43 from the option position, but we have made a profit of $50.4 (0.56 * $90) from the futures position. That’s a **total profit of $7.4 per unit size.**

**Market stays neutral**

This is where the vault loses money. Let’s say Ethereum is trading around $1810 after 6 hours, this would mean that the option’s price would be $85. That’s a loss of $7 from the option position and we have only made $5.6 profit from the futures position. This would give a **total loss of $1.4 per unit size.**

We have tested the strategy on 1-year data (1 Aug 2021 to 1 Aug 2022) of hourly Ethereum prices extracted from Coingecko API. Volatility data is collected from Deribit through their API services. A fixed fee of 0.35% is applied on each futures trade, similarly an appropriate fee is applied on option trades according to Lyra’s AMM implementation. The following backtest result uses an **initial investment of $50k**.

The backtest yields a **final portfolio value of $69k**, which would imply an **APR of 38%**.

- The strategy works well when the market is highly volatile, as evident from the chart.
- The strategy fails when the market stays neutral for a longer period of time.

Generally Delta neutral is a low-risk strategy, but sometimes we need to adjust the delta too many times which can result in numerous transactions. A large number of transactions can lead to costly fees.

If the market stays neutral, the vault will lose money as explained above in the example.

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