Converting Eurodollar Option Inputs for Implied Volatility

Summary

The document addresses why a standard Black–Scholes implied volatility calculation may fail to reproduce a calculator’s result for Eurodollar options. Its accepted answer says the quoted volatility is based on the implied rate, so the futures price and strike should be converted to rate terms by subtracting each from 100. It also emphasizes that the option premium and underlying must use consistent units; a premium quoted in hundredths of a point should not be entered as whole points.

A second answer recommends Black’s futures option model, commonly called Black–76, for rate options because rates can be negative, and advises reversing call and put treatment when translating from price terms to rate terms. These are practical modeling and quote-convention adjustments rather than a full replication procedure. The discussion gives no worked calculation or verification against the exchange calculator, so users still need to confirm the contract’s conventions, units, and model specification.

Key ideas

• Eurodollar option volatility may be expressed in rate terms rather than futures-price terms.
• Convert futures price and strike into implied-rate values by subtracting them from 100.
• Keep the option premium and underlying in consistent units when solving for implied volatility.
• Black–76 is suggested for rate options because rates can move below zero, and the call and put mapping may reverse in rate terms.

Tags

# Black Scholes on Eurodollar Options


# Black Scholes on Eurodollar Options












I am trying to replicate the Black Scholes results of CME option calculator for options on Eurodollar Options. (link)

I am trying to replicate the implied volatility result by unaltering the spot and strike values. But I am not able to match the numbers. What is the approach that is to be followed to replicate the results of the CME calculator

I have tried to use only black scholes implied volatility calculators to check the result.

## Answer by dm63 (score 1, accepted)

https://quant.stackexchange.com/a/42932

At least 2 problems here I think. 1) the CME vols are of the implied rate, not the price. Therefore express underlying price and strike in yield terms by taking 100-price and 100-strike. 2) the units of option price need to be the same as the underlying. For example , option whose strike is 2.50 has price 0.03, not 3. Try those adjustments.

## Answer by yungpadewon (score 0)

https://quant.stackexchange.com/a/51040

A bit late to chime in here, but you cannot use the Black-Scholes model to extract IV's / price rate options, since rates can technically go negative, you're better off using the black model (aka black76). Also adjust the underlying and strikes into rates (100-fp, 100-k), and treat calls as puts and vis versa...

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.