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Re: Black-Scholes theoretical value

Posted by Luigi Ballabio on May 10, 2007; 8:10am
URL: http://quantlib.414.s1.nabble.com/Black-Scholes-theoretical-value-tp823p824.html

On Wed, 2007-05-09 at 16:44 -0400, Jack Jones wrote:

> I'd like to calculate the Black-Scholes theoretical value of an
> option.
>
> Here is the relevant setup (questions at bottom):
>
> //==========================
>
> // Underlying price
> shared_ptr<SimpleQuote>
>     underlyingPrice(new SimpleQuote(stockPrice));
>
> // Dividend term structure
> shared_ptr<YieldTermStructure>
>     dividendTS(new FlatForward(expiryDate,
>                    dividend,
>                    Actual360()));

This is not correct. The first argument to FlatForward should be the
evaluation date, or rather the date for which the discount equals 1.
This might be today's date, or a couple of days later if settlement days
should be considered. The same applies to the interest-rate and
volatility term structures. The rest of the setup is correct.

> I have two questions:
>
> 1. what does the "price" argument to option.impliedVolatility()
>    represent?

Given an option, and once you have fixed dividend yield and risk-free
rate, you can find the price for a given volatility, or the other way
around. impliedVolatility(price) is the latter calculation; given a
target price, it returns the value of the volatility which causes the
option to have such a price.


> 2. now that I have this object infrastructure built up, what is the
>    actual method call to get the theoretical value of the option?

option.NPV()

Later,
        Luigi


----------------------------------------

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-- Mark Twain



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