# Financial Derivative european call option

When estimating financial derivatives like a european call option there is a parameter named: dividend paid per time unit. What does this mean, I have not been able to find any more information about dividend per time unit, and what it means.

Could someone give me an example of how this work, does it mean dividend par share or?

Example:

0.50 in dividend payed twice, once in two months, and once in 5 months. current price 40 strike 40 vol 30% annual interest 9% annual time to maturity is six months.

If i discount and sum the dividend and subtract it from the share price I get 40 - 0.9741 as new share price. This give the option price 3.67. Which is the same result as my text book. However if I use dividend as in the function I am not able to get the correct answer?

Here is the code:

 Input: FinancialDerivative[{"European", "Call"}, {"StrikePrice" -> 40,
"Expiration" -> 0.5},  {"InterestRate" -> 0.09,
"Volatility" -> 0.3, "CurrentPrice" -> 39.0259}]
Output: 3.67126


This is how new share price is calculated and output is correct according to tekstbook. 40 - ((0.5 E^(-0.09*2/12)) + (0.5 E^(-0.09*5/12))) However, the function provides an option for dividend in its output but I am not able to use it to get same result:

FinancialDerivative[{"European", "Call"}, {"StrikePrice" -> 40,
"Expiration" -> 0.5},  {"InterestRate" -> 0.09,
"Volatility" -> 0.3, "CurrentPrice" -> 40,
"Dividend" -> 0.9741531786619422}]

Output 0.0437682


Clearly it is because dividend put in is in the wrong format, however thats why I wonder how dividend payed per time unit means and how to get the correct price using Dividend in function. I have to say, I have looked through two well known option pricing books and no were does it say per time unit so It would have been nice if they could provide a bit more info in the documentation.

• You've said: "However if I use dividend as in the function I am not able to get the correct answer?" What have you tried in Mathematica? Can you post some code to clarify it? – dr.blochwave May 17 '14 at 22:00
• Dear Alexander, perhaps you were looking for quant.stackexchange.com? – Verbeia May 17 '14 at 22:41