i think he is saying that your valuation is assuming zero interest rates therefore the 40 delta forward price is the current spot price.. fwd price with 40D = current spot..
Black-Scholes pricing formula for vanilla option can be, indeed, derived without the use of stochastic calculus and Ito's lemma - that derivation uses pure probabilistic and risk-neutral approach. However, if you can show that you can derive Black-Scholes SDE without the use of Ito's lemma, that would be a feat. There are numerous fields, finance one of them, that are full of "cranks" - people that come from elsewhere and think that they can figure it all out in 20 minutes and make a killing. Yours truly arrived at a hedge fund after completing a PhD in biophysics and thought that in a month I will have it all figured out. A decade and a half have passed, I have changed a few jobs, made hundreds of millions for the various firms, survived 9/11 and muddled through the credit crisis and yet I do not have it all figured out. However, if you think you have, flaunt it while you got it
I'm sensing that someone here is not feeling the love. http://www.youtube.com/watch?v=XBm3E55Lspk&feature=relmfu
Mutluit. Stop posting. You're only digging yourself in deeper. Yes, just lurk until you know what you are doing. Your idea that you can backtest option trading strats on model-based prices derived from recent realized vol is the most idiotic thing I've heard in a long time.
I just wonder why people are so stubborn not to understand this simple method. The HV is just for orientation, you can pull in the desired vola you like, the option pricing engine just processes your input and gives the output. So, what is wrong with it? Nothing! As I said: it is modelling/studying by using a pricing engine, not backtesting using historical crappy options data.
That's what I did, there's nothing more re the BS formula. Research is time consuming, the last time I studied this was 3 years ago, I would need some break to be in the stuff again.
The following table uses gradually rising vola from 20% to 30% in 10 days. Compare these results with that of constant vola...