TLDR :

We are excited to announce that we are launching new vaults upon WETH-ARB and WETH-USDC pools on Camelot v3 AMM.

In this article, we firstly introduce our new vaults, and provide a detailed explanation of the profitability metrics adopted by Orange Finance and shed light on our rationale behind the introduction of these two new vaults.

For the profitablity part, to give a background information, we begin with covering some basic aspects of options, followed by the effectiveness of the IV-RV spread in a delta-hedged portfolio using the Black-Scholes model. Finally, we present an in-depth analysis while applying this model to Camelot.

According to our metrics, we can conclude that both pairs being launched this time are expected to be highly profitable.

Introducing WETH-ARB and WETH-USDC vaults

Our goal is to achieve Real Yield through Liquidity Provision, with a focus on the PnL of the Portfolio itself. To achieve this goal, our vault is managing liquidity on top of v3 AMM pools by setting price range, rebalancing, and implementing hedging strategy.

Setting price range : For determining the range of liquidity provision, we are exploring optimal liquidity provision using models that have received certain evaluations in Time-Series-Analysis, such as Average Historical Volatility, GARCH, EGARCH, and GJR-GARCH.

Rebalancing : There are two range settings. One is range settings for liquidity provision, the other is range settings to execute stop loss. To reduce unnecessary stop loss or rebalances, two-layered range settings aim to stabilize the vault’s performance.

Delta Hedging strategyDelta hedging on Orange Finance is powered by Aave, a lending protocol. A portion of deposited USDC.e is collateralized on Aave, and ETH is borrowed from them. As the ETH position is borrowed, even if the ETH price decreases, the vault can hedge a portion of losses compared to an unhedged position.

Adding to the current WETH-USDC.e vault on Camelot, Orange Finance have newly deployed Vaults for WETH-ARB and WETH-USDC pairs on Camelot with an analysis of their profitability explained below sections.

Camelot WETH-ARB vault Overview

• Pool: WETH-ARB v3 AMM pool on Camelot

• Chain: Arbitrum

• Deposit Asset: WETH

• Max. Cap: 10WETH

• Eligibility: The vault will be limited to the Alpha Orange Crew only.

• Strategy: Delta Neutral Strategy

As the pool TVL is small, we set this pool with a small cap.

Camelot WETH-USDC vault

• Pool: WETH-USDC v3 AMM pool on Camelot

• Chain: Arbitrum

• Deposit Asset: USDC

• Max. Cap: 100,000 USDC

• Eligibility: Alpha Orange Crew, Degen Crew, Honey Crew, and Camelot Crew.

• Strategy: Delta Neutral Strategy

This is the pool for WETH and USDC, which is issued by Circle. To learn further details about difference between USDC and USDC.e, please check this article.

LP on CL is like option strategy

In this article, we explain how we select pairs and maintain high profitability. As mentioned in previous articles, providing liquidity to Camelot v3 or Uniswap v3 can be understood as adopting a covered call strategy, which is one of the option strategies.

Note: Liquidity provision inherently behaves like a certain type of Perpetual Option. In other words, there are issues such as the absence of an expiration date, making it difficult to define theta, and the general inapplicability of the Black-Scholes model. Thus, it's important to note that all the metrics we've defined so far are approximate expressions.

When deploying Vaults in each pool, we calculate the Implied Volatility and Realized Volatility from the actual price data of the pair and compare them to deploy strategies in more profitable pools. In the sections that follow, we offer a comprehensive breakdown comparing Implied Volatility with Realized Volatility.

Fundamentals of Options Trading

To explain the validity of Delta-Hedged Portfolios and IV-RV Spread Strategies, we use the Black-Scholes model in the next section. Before discussing Perpetual options using platforms like Uniswap v3, let's talk about traditional options trading in finance to deepen the understanding of basics.

Implied Volatility (IV) is a forecast of the future volatility of the underlying asset. Specifically, it is derived by reverse-calculating the actual option prices traded in the market using the Black-Scholes model. In other words, it's important to note that the order is not that volatility is determined first and then the market price; rather, it's the other way around. The market price is determined first, and then the volatility is decided afterward.

Furthermore, the Black-Scholes model is an equation used to derive the option price. It takes five parameters as input: the risk-free interest rate, the current price of the underlying asset, the remaining time until expiration (from the current point to maturity), the strike price, and the volatility until maturity.

Note:* It's important to be aware that in many cases, the movement of the underlying asset may not follow the log-normal distribution assumed by the model, which contradicts the assumptions of the Black-Scholes model.*

Effectiveness of IV-RV Spread in Delta-Hedged Portfolios

In a previous article, we explained how to construct delta-hedged positions using Uniswap v3 as an example. In this article, we aim to deepen our understanding by using the Black-Scholes-Merton model. From this point on, we will be using highly complex mathematics involving quantitative finance and probability theory. Readers who are not familiar with these topics may skip this section.

To summarize the content below, the PnL (Profit and Loss) of a delta-hedged portfolio can be derived from the difference between Realized Volatility and Implied Volatility.

Now, let's construct a portfolio to hedge a short position in options. This portfolio, evaluated as X(t) at each time (t), invests in a money market account with a constant interest rate (r) and a risky asset modeled by geometric Brownian motion. In simpler terms, this portfolio involves depositing USDC into Aave to earn an interest rate (r) and holding the risky asset ETH.

Investors are assumed to hold Δ(t) units of the risky asset at each time (t). The remaining value of the portfolio X(t) - Δ(t) is invested in a money market account.

Therefore, the investor's profit in an infinitesimal amount of time can be considered as the profit from holding the risky asset Δ(t)dS(t) and the interest income from the money market r(X(t) - Δ(t)S(t))dt. Modeling this, we get:

Here, (α- r) is what is commonly referred to as the risk premium.

Up to this point, we have constructed the risky asset S(t) and the portfolio X(t). For ease of handling going forward, we will use the discounted stock price e^(-rt) S(t) and the discounted portfolio value e^(-rt) X(t).

Applying the Ito-Doeblin formula to the above equation, the differential of the discounted stock price is :

And the differential of the discounted portfolio value is as follows:

Further, let's also calculate the differential of the discounted option :

With all the preparations done, we can now proceed to construct the portfolio for hedging the short option position. The portfolio X(t) for hedging the short option position is constructed to match c(t,s(t)) at time t. That is, at X(0), investments are made in the risky asset and the money market account.

Therefore, the goal is to satisfy the equation:

To verify this equation, we need to ensure that the following holds:

and X(0) = c(0, S(0)).

Integrating the above equation, we get:

If X(0) = c(0, S(0)), then each term cancels out, and we obtain the desired equation.

Further, by comparing the equation for the discounted portfolio and the discounted option, we can derive the following equation:

For the above equation to hold, Δ(t) = c_x(t, S(t)), (t) in [0, T) is required, which is precisely the option's delta. Proceeding further with these calculations, we get:

Finally, we obtain the above equation.Based on this, we can decompose the P&L in a small time interval Δ(t) using Taylor's expansion. However, we make the following four assumptions here:

1. The option is delta-hedged.

2. The sensitivity to interest rates, Rho, can be ignored.

3. The implied volatility is constant.

4. Higher-order Greeks beyond Gamma can also be ignored.

Then, we can approximate:

Using the Black-Scholes model, we have:

Organizing the Greeks symbols for theta, gamma, and delta, and using the above assumptions, the delta term disappears. Further, if we ignore the interest rate ( r ), we get:

Substituting this into the earlier P&L equation, we get:

The terms inside the brackets represent the Realized Variance in the first term and the Implied Variance in the second term. Variance is the square of volatility. From this, we can define the P&L of a delta-hedged option portfolio as the difference between Realized Variance and Implied Variance. As referenced in the previous article, when providing liquidity to Uniswap v3, Gamma becomes negative. This implies that you can profit when the Implied Volatility exceeds the Realized Volatility in Uniswap v3. This highlights the importance of focusing on the spread between Implied and Realized Volatility.

Note:* the Implied Volatility discussed here is only an approximation derived from Uniswap v3.*

Measurement Method of IV-RV in Uniswap v3:

While there are various methods for calculating the Implied Volatility of pairs in Uniswap v3, we will adopt the IV model used by Guillaume Lambert in his articles and Panoptic's whitepapers. Specifically, Implied Volatility can be expressed using the following formula:

As for Realized Volatility, it is annualized by summing up the squares of the logarithmic returns and multiplying by 365. In the world of stocks, it is common to annualize by multiplying by 252, which includes holidays. However, since crypto trading is possible 24/7, 365 days a year, we adopt 365 for the calculation.

Results in Camelot:

Based on the content discussed above, Orange Finance has created profitability metrics for each pool using the IV-RV spread. We will continue to use this as a basis for the future development of each Vault. Below, we are sharing a simplified version of some of these metrics with our readers. Specifically, we are revealing the Profitability Index for the WETH-USDC.e Pair that we have deployed so far. It has produced numbers far exceeding 0.73 and 0.5, substantiating its high profitability.

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The graph takes dates on the vertical axis and IV (Implied Volatility) and RV (Realized Volatility) on the horizontal axis. It also includes a graph of their spread.

From mid-July to mid-August, the WETH-USDC.e Vault boasted high returns, largely influenced by a positive IV-RV Spread. On the other hand, the Vault suffered losses on days like August 17th and August 30th when RV surged sharply. In recent days, the IV-RV Spread has narrowed, causing a slight decline in the rate of return.

Note:* Of course, these factors are also influenced by the range of liquidity provided, so they cannot be discussed definitively.*

The WETH-USDC and WETH-ARB pools that we are launching this time have been decided upon because a certain level of profitability has been confirmed in hedge-able pool pairs.

Additionally, as you can see above, the ARB-USDC pool also has high level of profitability. We are also currently advancing development for the ARB-USDC.e pool with an aim for deployment.

Conclusion:

In this article, we have explained the profitability metrics adopted by Orange Finance in launching new WETH-ARB and WETH-USDC Vaults on Camelot. Going forward, we will continue to refine the IV-RV spread index discussed above, as we explore higher yield strategies in liquidity provision. Finally, according to our metrics, we conclude that all the pairs we are launching this time are expected to be highly profitable.

About Orange Finance

Orange Finance is an Automatic Liquidity-Management protocol tailored for concentrated-liquidity type DEXes on Arbitrum. Its core objective is to enhance the capital efficiency of v3 AMM by managing price ranges through statistical modeling and employing delta hedging strategies to offset losses due to asset price fluctuations.