Block Scholes x Derive How to Analyse the Volatility Smile to Understand Market Positioning

Structured products are pre-packaged financial products that use options to offer enhanced yields on investments by tailoring a strategy to the investor’s market view. The use of options allows for this customisation as investors are able to sell options that they think are unlikely to expire in-the-money in order to collect a premium. 

Derive offers an implementation of structured products onchain that is integrated with the rest of its derivatives ecosystem. Similar products have been offered before, but none have boasted the seamless integration of execution within a wider options trading platform. Derive implements these products using vaults – users deposit assets to a smart contract, the smart contract executes a predetermined options strategy, and attempts to earn a yield on those assets.

When the options strategy is successful, the yield on the assets is often more lucrative than the native yield offered on the asset. If the options strategy is unsuccessful, then the vault may return a loss to the deposited assets. Executing these strategies through a decentralised exchange is attractive in comparison to offchain expressions of these views as fully-collateralised onchain settlement poses far less credit risk – instead relying on the execution of smart contracts.

In this report we will explore the main strategies offered by the Derive platform, show how to decompose them into recognisable options strategies, and discuss how to use the volatility smile to make informed decisions on how to maximise yield by considering market expectations.

Derive Products 

When depositing into one of the Vaults, investors can choose whether to take a neutral-to-bullish view on either ETH or BTC, with varying levels of risk profile appetite:

• Bull: Investors tapping into this structured product are bullish on the underlying asset (either ETH or BTC). The strategy buys a call spread with the native yield earned on their collateralised asset, with the maximum loss limited to the premium paid.
• Harvest and Safe Harvest: This strategy offers the investor exposure to the case where underlying prices move sideways or slightly upward by selling a covered call. The “Safe Harvest” version offers more protection to stronger upward movements by selling a covered call spread. 
• ‍Maxi: This vault offers exposure to a more bullish outlook on the underlying asset by selling a put spread collateralised with the underlying asset. Investors collect a premium by selling this exposure, and risk a limited shortfall in the case that the price of the underlying asset falls.

While offering investors exposure to movements in the underlying asset of either BTC or ETH, Derive vaults allow for the deposit of native yield bearing assets such as ETH LRTs, staked BTC or Ethena sUSDe. As a result, depositing into the vaults allows the investor to stack the vanilla yield of a covered call strategy with ETH staking yield, staking/re-staking protocols, as well as with points on Derive.

For example, the Maxi vault allows investors to deposit weETH, earning a yield from staking ETH staking, EigenLayer restaking, EtherFi points, DRV points, and enhancing it with a (market-dependent) options yield collected from selling call spreads on ETH.

Options Strategies and Implied Volatility

The yields offered by each of the vaults are enhanced by trading one of several common options strategies: covered calls, call spreads, or put spreads. Each of these strategies involves buying or selling vanilla options positions in combination with holding the underlying asset (or a staking derivative). As a result, the yield earned by these strategies is dependent on the performance of the strategy and the cost (or premium earned) when entering the position.

The price of a vanilla option (like a regular call or put) is dependent on a few things, including time to expiry, strike, and interest rates. However, while all of these things are known quantities and common knowledge among traders, the free variable that encodes the market’s view on the price of the option is implied volatility.

Higher volatility expectations result in higher options prices, all else held equal. Intuitively (but not exactly!) this can be thought of as larger potential price swings in the underlying asset increasing the likelihood of the option moving further in-the-money. This uncertainty makes options on volatile assets more expensive, as they reflect a greater potential for reward.

However, volatility is the one factor in options pricing that we cannot observe ahead of time. Instead, traders usually begin by observing option prices in the market and “reverse engineering” the volatility levels that would lead to options being fairly priced at those levels – hence implied volatility is the volatility implied by the current prices of options in the market. What this gives us is a method to fairly compare the prices of options without needing to account for the impact of high or low strikes, time until expiry, or interest rates.

Interpreting the Smile to Make Decisions

When plotted for options with different strikes at the same tenor, implied volatility exhibits a smile shape, with higher values for more OTM calls and puts. Evaluating the shape of the smile can help traders to make informed decisions – when can we expect possible higher yields due to higher implied volatility levels?

The premium or cost of an option is higher when implied volatility levels for its strike and tenor pair are high. This means that the trader writing the option gets a higher compensation for going against the market view and selling an option that is in high demand. When implied volatility is lower for the option that the investor is buying, it implies that a lower premium is demanded for the option. Therefore, the volatility surface represents a snapshot of the market’s expectations, and it can serve as a tool for identifying which strategies are well-compensated at any given moment.

Vol Smile Strategy Analysis

Harvest 

Harvest collects options premium by selling OTM calls that are collateralised by the base assets (ETH LRTs, e.g. weETH and rswETH) that are deposited in the vault at the beginning of the week. If the option expires out-of-the-money, the investor keeps the premium and is exposed to the movements of the underlying asset. If the OTM call option expires in-the-money, the investor misses out on further upside that they would have enjoyed if holding the underlying asset alone, but continues to collect the native yield offered by the collateralised base asset. This encodes the view that a significant price increase is unlikely, but that exposure to the underlying asset is desirable.

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Selling the OTM call results in a higher yield to the investor in the vault when the price of the option is highest. Using the volatility smile we can identify when this occurs – by noting that a higher implied volatility leads to a higher option price. This can happen in two ways: when outright volatility levels are high across all strikes, as shown below on the left, and when the implied volatility of OTM call options is high relative to the rest of the smile. 

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To highlight how the volatility smile can be used to identify attractive entry points, we can illustrate how a strategic entry point would have performed historically under this choice. As noted above, we aim to choose an entry point where implied volatility for OTM options was high, and therefore selling a call option would have generated a relatively higher premium. 

One such case is when implied volatility for 7D tenor, 10 delta call options spiked on 2021-05-23, as can be seen in the chart above. The following position is equivalent to those targeted by the Harvest strategy:

• ETH spot: $2296
• Strike for short call: $3.3K,
• Price for option: $26.89.

Consider the case that an investor deposited 1 weETH to the vault. This currently generates a native yield of 3.29% APY (with an equivalent weekly percentage yield is 0.06%). The Vault would proceed to sell 1 of the ETH calls described above, allowing the investor to collect the premium which is automatically converted to additional weETH. One week later, spot settled at $2279, meaning that the option expired OTM, implying that the investor did not incur any losses. Hence, the yield earned by the strategy is calculated as follows:

1. Premium collected: $26.89, converted at the spot rate of $2296, a 1.17% yield on the initial 1 weETH deposit. 
2. Yields from weETH: 0.06%;
3. Total yield of 1.23%, or 88.8% APY.

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Safe Harvest 

As the Harvest vault effectively gives up exposure to rising prices in the underlying, earnings are capped in the case that the underlying rallies in price significantly. In the case the trader is willing to give up some of the collected premium in order to regain exposure to further potential bullish price action, the Safe Harvest additionally buys OTM calls in order to achieve this desired exposure. Therefore, the vault earns by selling the original OTM call, but gives up some of this premium in order to buy a further out-the-money call. This payoff can be visualised in Figure 3. 

The volatility smile helps us to analyse this product once again. The only difference when compared to the Harvest product is that the investor also buys a further OTM call option. Hence the previous set up of a high outright volatility level applies, with the addition of one extra requirement.

If implied volatility is relatively low for deeper OTM calls, the long OTM call position is less expensive. This is most attractive when the OTM call wing of the smile is flatter – that is when the implied volatility of deep OTM call options is not that high relative to OTM call options with lower strikes.

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This occurred on May 23rd, 2021 – the same date as our example above – when a spot-market crash saw ATM and OTM put options in large demand while calls traded relatively cheap. In fact, the dislocation was so strong that deeper OTM options traded at a lower implied volatility than those nearer to the ATM level.

This meant that the following spread offered a high premium for selling the upside exposure at the lower strike while not demanding as much of a premium for capping the losses by buying a higher strike OTM call:

• ETH spot at entry: $2296
• Strike for 10 delta,  7 day tenor call (sell): $3.3K,
• Strike for 8 delta,  7 day tenor call (buy): $3.5K,
• Price for option:7.58$.

Once again, the week after, spot expired at $2279, meaning that the both call options expired OTM, allowing the investor to collect the net premium without paying out on the short options position. The yield earned by the strategy over this period is calculated as follows:

1. Premium collected: $7.58, a 0.33% yield on an initial investment of 1 weETH at the initial rate of $2296.
2. Yields from weETH: 0.06%.
3. Total yield of 0.39%, or 22% APY.

The Vault would have therefore generated a lower yield compared to the harvest in this instance, but protected against the investor losing out on extreme upside in the case where ETH rallied above the strike of the long further OTM call.

BULL

BULL uses the native yield generated by the deposited asset in the previous week to buy an “around-the-money” call-spread strategy with a target return of 2.5x on the invested options premium. This means that it takes a long position in an in-the-money call below the current spot price, and sells an out-the-money call at a strike higher than the current spot price.

The long call position gives long exposure to the underlying asset, while selling the OTM call at the higher strike reduces the cost of the upside exposure – at the expense of giving up upside further than the higher strike.

As shown in the payoff diagram below, the call-spread strategy achieves better performance than just buying call options as long as the price of the underlying expires below the short call strike. While this misses out on possible returns for big upward movements, the entry point becomes cheaper than the case of a simple call option.

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The call-spread strategy involves buying a call at strike K1 and selling a call at strike K2, with the sale of the second option alleviating some of the costs associated with the first option. Therefore, the position is cheapest when the value of the long position is lowest relative to the value of the short position. 

The volatility smile can help us identify when this occurs – by noting that a higher implied volatility leads to a higher option price. We can identify when the long call option (that has a strike price lower than the ATM) is cheapest by looking for when the outright implied volatility level is lowest.

Similarly, we can identify when the short call allows us to collect the largest relative yield when the implied volatility of the OTM call wing is highest relative to the rest of the smile.

One such case occurred on Nov 5, 2023, as seen on the chart below of ETH 1 week ATM volatility.

At the same time as a relatively low level of volatility across the smile, this example date also recorded a high relative level of implied volatility for OTM calls, leading to a higher compensation earned from selling the OTM call. We call this a volatility smile that is “skewed towards calls” as the distinct smile shape smirks upward to the right, reflecting a higher demand for upside exposure in options.

The yield earned in this example was larger as the call spread later expired ITM and the vault was able to buy more units of the call spread as the entry point was cheaper. By depositing 1000 sUSDe to the vault, an investor can expect to earn $1.93 over 1 week at the current rate from the native yield on sUSDe. If that earned yield was used to purchase the following call spread in the following week:

• ETH spot at entry: $1581.46,
• Strike for 7-day tenor ITM option: $1775
• Strike for 7-day tenor OTM option: $1975
• Price for 1 call spread: $81.28

The investor would have gained exposure to 0.0237 units of the call spread. At expiry, the spot price was recorded at $2054.54, meaning that both options expire in the money. The payoff collected per unit of the call spread was $200, meaning that the 0.193% earned on the initial 1000 sUSDe deposited was boosted to the following yield:

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1. Returns from the call spread: $200*0.0237
2. Total weekly yield of 0.474% (on 1000 sUSDe) or 27.88% APY.

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Maxi

Maxi allows the investor to express a bullish view on the underlying asset while collecting the native yield offered by LBTC, a staking derivative of BTC, particularly one that is willing to risk spot prices falling in order to earn a higher yield in the case that the underlying rallies. The strategy sells an OTM put and takes a long position in a put struck further OTM, and collects the net premium.

If the put spread expires in the money, the investor will have to payout on the option contract. In order to do this, part of the collateral will need to be sold, incurring a loss. However, the ideal case for the investor is that spot prices rally, their deposited assets appreciate in value and they retain the collected premium. The net payoff can be visualised in Figure 4, where we highlight the different possible scenarios. 

This strategy is similarly structured to the Safe Harvest strategy discussed above – instead of selling a call spread, the vault sells a put spread. This consists of a short position in a put struck at K2 and a long position in a put struck at K1. This position is most expensive (and yields the highest option premium to the seller) when outright implied volatility levels are highest and the put wing of the volatility smile is flattest relative to the ATM level. When the smile is flatter, the long position in the OTM put struck at K1 is cheaper relative to the short position in the OTM put struck at K2, and the net premium collected by the put spread seller is highest.

For this last example we therefore wanted an entry point where implied volatility levels were relatively high, and the put-wing was relatively flat. This could be seen on 2021-01-15, where 1-week tenor implied volatility levels were above 130% and smiles were much more positively skewed, indicating a higher volatility premium assigned to calls than puts.

In this scenario, selling the below put spread:

• BTC spot: $39417.44
• Strike for 7-day tenor 11 delta options: $31000
• Strike for 7-day tenor 9 delta OTM option: $29700
• Premium from put spread sale: $92.44.

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would have generated an enhanced yield as the put spread eventually expired OTM. If an investor had deposited 1 LBTC into the Maxi Vault, then the vault would have generated a net premium of $92.44 from the put spread, or a 0.23% yield on the 1 LTBC, which translates to a 12.7% APY. 

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You can’t always win the bet, but you can make it cheaper

While an investor cannot determine the payout of any options strategy ahead of time, they can ensure that they are well compensated for taking on risk. They can do this by using the volatility smile to understand which outcomes the market believes are more likely (and therefore more expensive) and consider them against their own market view. Derive’s structured product vaults allow an investor to earn an enhanced yield on their assets by taking on options exposure – the volatility smile allows them to determine the exposure for which they will be best compensated.