# SPY American option Greeks and Premium

I am trying to replicate Ivolatility.com's option calculator for a client. Here's the example Using standard Black Scholes model, I can replicate the exact calculations if there is no dividend. With dividend, I understand I need to subtract PV of div from current underlying price to get the adjusted underlying price to be used in standard B-S model. My questions are

1) does everything else in calculating d1, greeks and premium remain the same? or do we still need the dividend yield (even after calculating adjusted underlying price) for calculating the above parameters?

2) I understand the price of an American option is max of two european options calculated for different maturities, i.e ex dividend date and actual maturity. Can you please clarify?

Also, is it possible to know which model Ivolatility is using?

• "I understand the price of an American option is max of two european options calculated for different maturities, i.e ex dividend date and actual maturity". That is called Black's Approximation and is only one (inexact) method that has been proposed en.wikipedia.org/wiki/Black%27s_approximation – noob2 May 30 '17 at 14:17

## 1 Answer

From what authority do you understand that the value of an American option is the max of two Europeans? I believe this is a false assumption (but it might give you a lower bound value). E.g. a deep-in-the-money American option might be optimally exercisable before the ex-div date, to capture the time value of money for some interest rates vs. dividends. American option values are typically solved by numerical techniques (such as the binomial method). Ditto European options having complex dividend streams. --BEZ

• I was actually just referring to the Black's approximation method. Should have made it clear. – Vineet Kalra May 30 '17 at 17:05