Hi,In Black-Scholes equation, volatility, interest rate and dividend are thought to be S (asset price) and t (time) dependent in general. If I have to plug the just-said parameters into the BS pde, what functional forms should they possess? In other words, I am asking how would people determine their functional forms? By real data and then extrapolation or what? Thanks.Mic

For reasonably short equity options, interest rate movements are not very significant and dividends are predictable. Variation in these parameters becomes more important for longer-dated options, but the effect of uncertainty about volatility is so much greater that it seldom makes sense to fine-tune the other parameters. FX options are the same, except of course you have two interest rates instead of an interest rate and a dividend.For fixed-income options, variation of interest rates is so crucial that you cannot use Black-Scholes in the first place.So the important practical problem is the modeling of volatility variation in equity and FX options. There are many approaches. Most incorporate a mean-reverting componant and a smile. That is volatilty increases as the underlying price moves away from the exercise price in either direction, and volatility can move up and down randomly, but tends to return to its long-term mean value.

I see. However, do you know some good references (books, journal articles) that talk about it? Thanks.Mic