Hi everyone, I am an Assistant Professor of Finance at the University of Colorado Colorado Springs.
I am trying to price a USDT option. Any comments and advice are welcome!
It is my first time posting here. I would also like to make friends!
Here's the details of the problem:
I wish to structure a call option that gives me the right, but not the obligation, to buy USD from my Counterparty at a fixed strike price of 1 USDT per 1 USD. The notional value of this option is USD 100 million. The objective is to hedge against potential USD appreciation beyond the 1 USDT per USD level.
(B) Key Terms
Option type: USD call (i.e., right to sell USDT for USD, or equivalently, buy USD at a fixed rate)
Strike price: 1 USDT per 1 USD
Notional amount: USD 100,000,000
Underlying: USD/USDT exchange rate
Expiry Tenor: 10 days
Settlement: Cash
(C) Initial Proposal for Pricing Approach
To price this option, I suggest using the Black-Scholes option pricing model (or an appropriate model for digital assets, given the USDT component and any idiosyncrasies in the USD/USDT market), considering:
- Spot rate: Current USD/USDT exchange rate (assumed close to 1)
- Strike: 1
- Notional: USD 100 million
- Time to expiry: 10 days
- Volatility: Implied or historical volatility of USD/USDT
- Risk-free rate: U.S. Treasury or relevant USDT lending rate
- Dividend yield: N/A
Given the unique features of USDT as a stablecoin and potential counterparty risk in OTC structure, I expect some adjustments for liquidity, potential de-pegging scenarios, or credit considerations.
I propose the option premium should be computed using the above methodology, with particular attention paid to: - Any historical deviations of USDT from its 1:1 USD peg
- Market liquidity for such a large notional
- Settlement risks inherent to this asset pair
I would be grateful if you could review the above details and proposal, identify any areas that require refinement, and provide a formal quote or your comments on the suitability and limitations of this pricing approach.
Please let me know if you require further details or specific market data inputs.
If we think in FX terms:
Base currency = USD
Quote currency = USDT
Strike price = 1.0000 USD/USDT
Option type (in FX convention): This is USD call / USDT put.
Settlement: Cash-settled in USDT (or USD) based on market USD/USDT at expiry.
The pay off at expiry T is:
Payoff=max(K-S_T,0)×Notional in USD
Where:
K = 1.0000
S_T= USD/USDT at expiry
Notional = 100,000,000 USD
If USD appreciates (USDT weakens), S_T<K in USDT terms, the option is in-the-money.
Black–Scholes can be applied, but we can have some caveats:
Volatility: USD/USDT exhibits extremely low volatility under normal conditions (<0.5% annualized), but fat tails are present during depeg events. Use a jump-diffusion or mixed distribution to reflect rare but large moves.
Interest rates: r_1(USD risk-free) and r_2(USDT “risk-free”) differ: r_2 should reflect stablecoin lending/borrowing yields on major exchanges Use r_1-r_2 in the drift term.
Liquidity: $100M notional is very large for spot USDT markets — may exceed visible depth and move the price on execution. Add a liquidity premium to implied vol.
Counterparty risk: If OTC, include a CVA/DVA adjustment. This could be material given the tenor and the size.
Depeg Risk: This is the real risk you’re hedging. It is not normally priced in standard BS models, so vol must reflect tail risk. Historical episodes (e.g., May 2022, Nov 2022) should be modeled as jump scenarios.
A more robust structure would be:
C=e^(-r_q T) S_0 N(d_1 )-e^(-r_b T) KN(d_2)
P=e^(-r_b T) KN(〖-d〗_2 )-e^(-r_q T) S_0 N(-d_1)
Where:
r_b= base currency rate (USD)
r_q= quote currency rate (USDT)
S_0= current USD/USDT spot
K= strike
σ= implied vol
T= time to expiry (in years)
Then adjust σ to incorporate jump risk:
Fit historical return distribution of USDT/USD
Incorporate stress scenarios (e.g., 1–3% depeg events over 10 days)
Combine normal vol (~0.2–0.5% annualized) with a jump component.
Finally, apply:
Liquidity premium: Higher bid–ask or direct spread widening.
Credit valuation adjustment (CVA) for counterparty default risk.
To actually produce a premium, you’d need:
Spot rate S_0 — currently ~1.0000
USD risk-free rate for 10 days (SOFR or Treasury bill yield)
USDT yield — could be from on-chain lending, CeFi, or repo markets
Implied volatility — from any available USD/USDT option market (rare) or proxy stablecoin vols
Historical jump data — from past depeg episodes to calibrate σ_jump
Bid/ask depth — to estimate liquidity cost for $100M notional
Suitability: For small notional, short tenor, no major stress expected, BS model works fine.
Limitations:
Ignores path dependency and liquidity shocks.
Doesn’t capture jump-to-default-like moves in stablecoins.
$100M notional is far above normal market depth; in practice, liquidity risk dominates pricing.
In reality, a dealer pricing this trade will:
Use BS model for base price
Inflate vol for jump/depeg risk
Add margin for balance sheet usage & counterparty risk
Likely quote a substantially higher premium than BS model suggests
Take realistic market inputs for USD/USDT (spot = 1.0000, 10-day vol ~0.30%, jump probability from history ~5% over 10 days) and show both the pure BS price and the jump-risk-adjusted price for $100M notional. That will illustrate why the OTC premium could be much higher than the “theoretical” one.
Here’s what the numbers look like with reasonable market assumptions:
Scenario Model Assumptions Premium per USD Total Premium (USD)
Pure BS price Vol = 0.30% annualized, no jumps 0.000326 $32,618
Jump-risk adjustment +5% chance of 2% depeg (USD appreciates) +0.001000 $132,618
Interpretation
Without depeg risk, the 10-day option is extremely cheap in theory because normal USD/USDT volatility is tiny.
With depeg jump risk, the premium jumps ~4× — and this is still conservative. Dealers might price in higher jump probability or larger move, which would push the premium up further.
For $100M notional, even tiny vol changes have big dollar impact.