if you have a theoretical option pricing model like this one: http://www.intrepid.com/robertl/option-pricer1/option-pricer.cgi, what should you put in when it asks for volatility (in percentages per annum) should that be the historical volatility over the past 256 days? Is there an easier way of calculating the volatility in percentages per annum other than inputing manually all the data and price changes day by day over the past 256 days and doing calculations yourself? Anybody recommend any websites with free theoretical option pricing models? thanks, I am reading Natenberg's option volatility and pricing and I am trying to understand all of this so if I had some models to go by it would be easier to understand.
I think you've touched on the holy grail of option trading, which volatility should I use when pricing an option ... In a nutshell, I personally believe all option traders need to develop their own volatilty model in order to be successful. I wouldn't price options using actual historical vol since the option price is intended to value the volatility of the underlying in a future period not historical. However, rolling historical implied vols of the same tenor of the option you are pricing can provide a useful indicator when trying to model trends such as mean reversion. Market implied vol derived from the current listed option prices is just another way of viewing the current market price of an option, and shouldn't be used for determining the fair value. Most option traders will develop their own proprietary volatility model which tries to model the skew and kurtosis of an underlyings' price return distribution in a systematic manner. The vol models I've worked with take various parameters for a set of option maturities and allow you to "fit" smooth volatilty curves across the strikes of each maturity. We refer to this as our fair volatility surface and we interpolate a vol from this surface to arrive at the volatilty to use when pricing an option of a specific strike and tenor. We then apply a bid-ask spread in terms of vol points to arrive at the fair value of the option we are pricing. We can use the vol surface for pricing both listed and OTC options. We do still use the market implied vols to calibrate our curve parameters so we can obtain smooth vol curves that are a reasonable fit to the available market prices. If you don't have the resources to build your own volatility model, then I think its still possible to develop a systematic approach by looking at the historical implied vol of the option tenor you are trying to price, and across the whole curve for that tenor, so look at the implied vol of ITM and OTM strikes. Even traders who have some very advanced vol models at their disposal, still refer to historical implied vols when forming a view. However you do it, once you have your own vol model, you can then use this model to price options and compare your fair value prices with the market prices to identify trading opportunities. Option volatility modelling is actually a huge topic, quants at the big houses earn big bucks building volatility models which claim to be more robust and accurate than the competition. Traders rely on them not just for pricing but for the risk parameters also (ie the option greeks) in order to hedge correctly.
The attached link is a useful starting point to get acquainted with the fundamentals of option volatility modelling http://www.ivolatility.com/help/iv_education.html Cheers