# 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.

• Maybe it would be useful to show your code / what you did so far. – LocalVolatility Dec 5 '18 at 14:28
• I have been trying to use online black scholes implied volatility calculators. But with the parameters shown in the image. I end up with an implied volatility of 5.85%. The doubt that I have is if there is a modification required for the input Strike and Spot? – Bhaskar Gudimetla Dec 5 '18 at 15:11

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.

• Should the type of option also be reversed, meaning call should be treated as put and put should be treated as calls. Altering the strike and spot as you said would make the call option move from out of the money to in the money and therefore the delta should be in the 0.5 to 1 range. But the CME results show otherwise – Bhaskar Gudimetla Dec 6 '18 at 4:41
• Yes , switch call to put and vice versa – dm63 Dec 7 '18 at 11:10

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...