Black Scholes Model

[srinu2singaraju]

Hi David,

In the Hull practice questions No: 13.05 b

Dividend yield was given as 2%. We have calculated the PUT option price thru Black- Scholes model:

In the given calculation first, we discounted the spot price to 49.75 from 50 (S*EXP(-q*T)) and subsequently we have used the same formula for d1.( Here we have not deducted the dividend yield from the risk free rate and reduced the SPOT)

I have the following doubt:
In your recordings it was mentioned as if there is any dividend yield we have to less the dividend yield %ge from the risk free rate.
Also it was mentioned LN (S/K) in the numerator NOT the present value of S
(Here we have reduced the dividend yield from the risk-free rate and not reduced the SPOT)

Which is correct?

Thanks in advance

Regards,
Srinivas

 

[David Harper CFA FRM]

Hi Srinivas,

It's a good observation but I think there is not a difference. In the answer to 13.05, I used d1* rather than d1:
see http://forum.bionicturtle.com/viewthread/1650/
... and for convenience I pulled the underlying XLS: http://sheet.zoho.com/public/btzoho/hull-13-05b-1

so, the correct method--in the convenient but maybe unrealistic case where dividend can be expressed as constant pecent of spot (q%)-- is to BOTH reduce the stock price in the "outer " Black-Scholes; i.e., S*EXP(-qT)
and ALSO to reduce the stock price for the "inside" d1; i.e., use d1* rather than d1

please note the potential confusion may arise because, given (q) and d1/d2, we have either:
LN(S0/K) + (r -q) ...; i.e., we subtract (q) in d1 numerator

or its equivalent given by:
LN(S*EXP(-qT)/K) + rT

...because:
LN(S*EXP(-qT)/K) + rT = LN(S) + LN(EXP(-qT) - LN(K) + rT = LN(S) + (-qT) - LN(K) + rT = LN(S/K) + (r-q)T
please see cell C21 in the XLS where i show this "alternative" but equivalent d1

Hope that helps, David