# Theoretical value of a financial option

I am using the following function to get option pricing but it does not give me the right answer (\$10.50). Where is my problem:

FinancialDerivative[{"American", "Call"}, {"StrikePrice" -> 705.00,
"Expiration" -> 4}, {"InterestRate" -> 0.64, "Volatility" -> 27.69,
"CurrentPrice" -> 716.00}]


You can verify the inputs yourself: • Just two observations: "Expiration" is measured in years, "Volatility" in percent, i.e. 0.2769 in your case. – b.gates.you.know.what May 9 '16 at 12:24
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I don't get the exact same answer as the calculator I found here or here or here.

Sadly, I can't get any of them to agree with each other when we ask for "American" pricing, so there seems to be some variability in their calculators.

But I can get the exact same value from Mathematica if I use the "European" pricing, which uses the Black-Scholes model, if I make a few key changes to your inputs. Both the interest rates and the volatility are percentages, so multiply the numbers you input by 0.01. And the "Expiration" should be given in years (4/365) or by using DatePlus[DateList[], 4]. So this,

FinancialDerivative[{"European",
"Call"}, {"StrikePrice" -> 705.00,
"Expiration" -> 4./365}, {"InterestRate" -> 0.0064,
"Volatility" -> .2769, "CurrentPrice" -> 716.00}]
(* 14.8954 *)


matches exactly what you find online.