Stablecoin and Fiat-Denominated Options

Unlike TradFi equivalents, cryptocurrency options markets are far smaller than the spot markets of their underlying assets, with sparse underlying offerings and illiquid markets. The difficulty in trading crypto-currency options is compounded by the disparate base currencies used – few venues offer direct exposure to BTC or ETH options denominated clearly in fiat currencies like the EUR or USD. Instead, options exposure is collateralised by and quoted in stablecoins or even the underlying itself, complicating calculations of greeks and understanding of market exposure.

However, such options are treated and priced as if they were equivalent to fiat currency-denominated options, ignoring two key factors which mean that such options are must be treated slightly differently: the impact of interest offered on fiat collateral deposits and the risk of depeg if an option is denominated in a stablecoin (while tracking and settling to a fiat-denominated price index).

Posting collateral in USD offers the advantage of earning interest in environments where exchanges or custodians provide yield on deposited funds. This interest-earning potential can reduce the effective holding cost of long positions, particularly in leveraged trading scenarios, making USD-collateralized options more cost-efficient. For short positions, the interest on USD collateral can offset financing costs, enabling traders to allocate capital more effectively. In contrast, posting collateral in USDC generally lacks intrinsic interest-earning mechanisms unless placed in yield-generating platforms, leading to higher net costs for maintaining positions and impacting comparative pricing strategies.

Denominating and settling an options contract that tracks a fiat-denominated settlement index (such as BTCUSD) in stablecoins introduces unique risks. Stablecoin-specific risks, particularly the potential for USDC to depeg from its 1:1 parity with the U.S. dollar, create uncertainty in profit and loss (PnL) calculations. Such de-peg risks affect both short sellers and buyers of options settled on BTCUSD, a risk which is often compensated by requiring overcollateralisation in stablecoin collateral, making stablecoins a less capital efficient choice.

The correlation between stablecoin peg volatility and market volatility necessitates adjustments in pricing models, resulting in systematic mispricing of options premia if the FX exchange risk of the stablecoin is not taken into account. This report aims to provide a detailed understanding of some of these added risks, and trading implications, examining how options’ pricing are affected when margined, quoted, and settled in USD, USDC, or a futures index using different mathematical tools.

Interest on Collateral 

While offering a wide range of products, most implementations of stablecoin-denominated markets do not offer interest payments on the collateral posted as margin. This disproportionately affects short positions, as long positions must only post collateral when trading with leverage. While some exchanges allow the use of yield-bearing tokens as collateral, reducing the carrying costs of options similar to the fiat-currency options market, regulatory frameworks such as MiCA explicitly prohibit interest-earning stablecoins.

When an exchange pays interest on the collateral, such as is the case on many fiat-collateralised options contracts, it changes the economics of holding a short options position. Typically, when collateral is locked up, the investor faces an opportunity cost: this is the return they could have earned if that money were invested at the risk-free rate. Paying interest on the collateral offsets some or all of this opportunity cost, reducing the effective cost of holding the position.

From a pricing perspective, this reduction in opportunity cost impacts the premia. All else held equal, a short seller that is required to post collateral would prefer to sell an option that offers interest payments on the collateral posted at the risk free rate over one that does not. As a result, the premium they demand for the option that pays interest may be lower because the expected cost of maintaining the collateralized position is lower, and therefore more attractive than a short position that did not pay interest on the option. The same applies for buyers of future-style options, as they are also required to post collateral. All else held equal, an options buyer should be willing to pay a premium for positions that pay interest on collateral relative to positions that do not offer collateral.

In addition, collateral held in USD can often earn a straightforward interest rate that reflects the broader market for US dollar-denominated assets. However, for USDC-settled options or other stablecoins, the interest rate on collateral may be tied to the yields available in decentralized finance (DeFi) markets or other blockchain-based mechanisms. These rates may differ from traditional markets and could introduce new considerations for pricing.

Lastly, the choice of collateral can, in order to account for added de-peg risks, affect the notional margin amount required. We often see a haircut applied to stablecoin collateral, where its value is discounted. This practice reduces the effective collateral value, requiring users to post more stablecoins to meet margin requirements. While this approach mitigates risk for the platform, it also makes stablecoins less capital-efficient for users seeking to maximize their borrowing power. 

Fixing the Mispricing on USDC-Settled Options

Quanto Options Framework

Many centralised exchanges offer options contracts that settle in stablecoins, but are settled against an index of BTC valued against the dollar. By settling to a currency other than the base currency of the underlying asset, such options contracts are technically “quanto” (or quantity-adjusted) options, and must be priced accordingly.

A quanto is defined as an option contract in which the underlying is denominated in one currency (such as the Nikkei index denominated in JPY), but the option itself is settled in another currency (such as USD) at some predetermined rate. A commonly quoted example of a quanto product is a cash-settled call option that pays US$1 for each JPY that the Nikkei index trades at above the strike price at expiry.

In traditional finance, such products offer exposure to an asset that is denominated in a foreign currency without taking on the corresponding exchange risk when measuring their portfolio against a domestic currency. While not exactly the original use-case, the quanto-option framework can be used to more accurately value a BTC/USD option that settles in a stablecoin such as USDC, which can be thought of as a quanto option with BTC as the asset, USD as the foreign currency, and USDC as the domestic currency.

Intuition for why the change is needed

Having essentially fixed the exchange rate at the writing of the contract, and eliminating exposure to the FX risk over the lifetime of the option, the buyer of the quanto option passes on the risk of hedging the exposure to the seller of the option.

In our stablecoin denominated case, the option is on BTC / USD, but settled in USDC. This means that the options seller must hedge their exposure to both BTC and USDC against the dollar. Firstly, by selling this option, the seller is short BTC against USD. This is the same as in the vanilla option case – and means that the seller must trade BTC against USD to hedge the delta on the option they have sold.

Secondly, however, the seller is also short USDC against USD. While accepting payment of the premium at trade entry in USDC poses no risk as the USD / USDC rate is known at the time of conversion, delivering the payout in USDC at expiry in the case that the option is in the money exposes the seller of the option to the risk of USDC rallying against the dollar. This additional risk to the seller must be priced into the premium of the option.

Hence in addition to the volatility of BTC against the USD (which is ultimately what the buyer is taking a bet on) the volatility of the exchange rate USDC/USD must also be considered. This risk is stronger when the value of BTC and USDC is highly correlated: 

• If BTC and USDC are positively correlated against the dollar, then the seller is required to pay out on the call option at exactly the same time that the currency they must deliver that payout in (USDC) is more expensive. As a result, the quanto option is more expensive for the buyer.

• If BTC and USDC were instead negatively correlated (which we have observed historically on several occasions), then the quanto option would become cheaper – this is because the USDC value is cheaper to deliver in the case where the seller must pay out.

Adjustment Factors

Adapting the regular Black-Scholes price to go from a standard call option to a quanto option is relatively straightforward, taking the form of an “adjusted” risk-free rate that changes the risk-neutral forward price:

where rdomand rfor are the risk-free rates on USDC and BTCUSD respectively. These appear as they do in the usual Black-Scholes formulation. The adjusted rate essentially modifies the forward implied exchange rate by a correction term that captures the additional gains/losses for having fixed the exchange rate. This term is a function of the volatility of the underlying asset (BTCUSD), the exchange rate (USDCUSD), and the correlation between them. After evaluating this, it can be used as the drift term in the regular Black-Scholes formula.:

The same adjustment is used when calculating N(d_1) and N(d_2) in the Black-Scholes formula for a call option. The result is that the “mean” of the risk-neutral distribution is higher when the correlation between BTC and USDC is positive, resulting in a more expensive option price as we’d expect from the reasoning given in the previous section.

While there exist many protocols that offer a yield on USDC deposits, these are not without their risks (at least technical implementation risk, if not market risk). We make the simplifying assumption that the USDC risk free rate is close to the risk-free rate offered on the US dollar. Forward-looking estimates for the volatility can be implied by market-traded options prices, but without an active market for USD / USDC options we resort to estimating these quantities from historical spot price data.

In addition, we also make the simplifying assumption that the risk-free rate offered on BTC is 0. While a yield can be implied by the market price of futures contracts above that of spot, we omit this calculation from our comparison as it has a similar impact on both the vanilla and quanto call option price.

What’s the Difference?

To illustrate the inherent difference between a USD settled option and a USDC settled option, we will estimate each of these adjustment factors and compute the difference in price between that implied by the naive Black-Scholes formula and that calculated using the quantity-adjusted correction.

Estimating the USDC/USD Volatility

A USDC is not exactly a treasury-backed U.S. dollar, and its value is not the same as one dollar. There are at least two factors that mean that one USDC token should be worth slightly less than $1 – although we frequently see demand for onchain dollars result in USDC trading slightly higher than $1, possibly due to the added utility of onchain dollars being cheaper and faster to transfer cross-border.

Firstly, a real greenback pays interest (or in DeFi terms, a “yield”) via access to U.S. Treasury bonds. While some protocols do allow for yield generation on USDC, no matter how small the risk inherent to generating that yield is, it will always be at least slightly more risky than depositing the dollar with the U.S. government and earning the “risk-free” rate.

Secondly, USDC has an inherent de-peg risk. The cryptocurrency market judges these factors to be small, routinely pricing USDC at or even above par, the risk is not unfounded, as USDC briefly depegged to nearly $0.80 during the U.S. Banking Crisis of March 2023.

As a result, the effective  USDC / USD exchange rate has volatility that must be estimated. Since the depeg in March 2023, that volatility has been relatively small compared to the early days of USDC trading. However, in order to more fully estimate the inherent risk of volatility, we estimate the volatility of the exchange rate using daily returns data from 2020 onward – including the depeg date.

The resulting estimate puts the annualised USDC / USD exchange rate volatility at 4.71%. Not huge, given that equity indices frequently trade with volatility of 12-15%, but not small either given the claim of a “stable”coin.

Estimating BTCUSD Volatility and its Correlation to USDC USD

We can estimate the volatility of both BTC and USDC measured against the dollar by calculating their realised volatility. This is a measure that is used to calculate the historical or delivered analogue to the forward-looking volatility implied by the market price of options. While we have liquid options markets available for BTC, few if any offer options on USDC against the dollar.

BTC’s volatility level is to be expected from any trader who has experienced whipsawing price action. While it has trended down over time, it remains a high-volatility asset that is far higher than other FX favourites. It is also far higher than the USDC volatility at all times – even during the depeg in March 2023. However, plotting both series on separate axes reveals a positive correlation.

Interestingly, movements in the USDC peg to the dollar are frequently correlated with volatility in BTC spot markets, although to a relatively weak degree. This can be seen in the chart below, which estimates the correlation of their returns over a rolling window of 30 days. The oscillating value indicates that, while large movements in both currencies tend to occur at the same time as in each other, the direction of those movements are not necessarily the same.

The correlation between the returns of both assets over the full post-2020 period is 8.7% – this is the value that we will use to model the price of our quantity-adjusted option.

Pricing Differences for a Call Option

To measure the impact of the mispricing, we will compute the naive Black Scholes and quantity-adjusted Black Scholes price of a european call option on BTC, expiring in one year, struck at $110K, with spot at $100K. The risk free rate offered on USDC is assumed to be 4.5,  and we assume a volatility of 55% for BTC, 4.7% for USDC, and a correlation of 8.7% between the two assets.

Applying the regular Black-Scholes pricing formula would yield in a quote of 19,879.13 USDC for this contract, while correctly adjusting for the risk of correlation between USDC volatility and BTC volatility would result in a more expensive 19,964.06 USDC – 0.43% more expensive. 

However, this value is dependent on our assumed value of the correlation between BTC and USDC returns at 8.7%. In reality, we have seen this value range between -25% and 25%, with the depeg of USDC correlating with a similar crash in BTC, indicating that the correlation of USDC with the underlying of the option conditional on a depeg is likely even higher. To illustrate the sensitivity of the adjustment to the price on this assumption, we plot the relationship below.

With an assumption of a 25% correlation between BTC and USDC when measured against the dollar, the call option can trade up to 1.25% higher than a naively priced vanilla call option. We also note that the relationship is linear, with a 1% change in correlation resulting in a 0.05% increase in the mispricing (for the $110K strike, one-year BTC option we described), and that a negative correlation would result in a mispricing in the other direction – the quanto option trades at a discount when the correlation between BTC and USDC is negative.

Conclusion

USD-denominated options that pay interest on collateral deposits are more cost-efficient due to interest earnings, reducing holding costs for short positions. In comparison, sellers of contracts that do not offer interest on collateral (such as many the implementation of stablecoin-margined contracts on incumbent centralised exchanges) are less attractive to the seller and therefore demand a higher premium.

In addition to the reduced capital efficiency, options settled in stablecoins introduce additional exchange rate volatility to the seller of an option that is exacerbated during times of market stress. This risk impacts pricing models, necessitating adjustments to avoid mispricing stablecoin-denominated options.

Stablecoin-settled BTC-USD options must be priced accurately using a quantity-adjusted (“quanto”) options framework, requiring adjustments for exchange rate risks. As sellers face dual exposures – short both BTC/USD and USDC/USD – the correlation of their short options position with the value of the payout currency must be taken into account. Positive BTC-USDC correlation increases option costs, while negative correlation reduces them.

Historical data estimates USDC/USD volatility at 4.71%, while BTC remains far more volatile. A weak positive correlation (~8.7%) between BTC and USDC returns increases the option’s price when using a corrected quantity-adjusted Black-Scholes model. For instance, a 1-year BTC call struck at $110K shows a 0.43% mispricing over a naive Black-Scholes approach, which grows linearly with higher correlation.

While unlocking access to sophisticated options exposure to a new generation of crypto-investors, stablecoin-denominated options must be handled with care as a result of the lack of interest paid on collateral and the market-floating rate of the stablecoin against the dollar. Fiat-currency denominated contracts are more familiar to investors and offer a less-convoluted exposure profile to crypto-assets that does not need to account for additional FX risk in its pricing.