Implied or historical volatility to calculate theoretical options price with black scholes?
"Option pricing models used by exchanges to calculate settlement prices (premiums) use a volatility measure usually describes as the current actual volatility.  This is a historic volatility measure based on standard deviation across a given time period - usually 30 to 90 days.   During a trading session, an investor can use the readily available information for a given option to infer the ""implied volatility"".  Presumably you know the option pricing model (Black-Scholes).  It is easy to calculate the other variables used in the pricing model - the time value, the strike price, the spot price, the ""risk free"" interest rate, and anything else I may have forgotten right now.  Plug all of these into the model and solve for volatility.  This give the ""implied volatility"", so named because it has been inferred from the current price (bid or offer). Of course, there is no guarantee that the calculated (implied) volatility will match the volatility used by the exchange in their calculation of fair price at settlement on the day (or on the previous day's settlement).  Comparing the implied volatility from the previous day's settlement price to the implied volatility of the current price (bid or offer) may give you some measure of the fairness of the quoted price (if there is no perceived change in future volatility).  What such a comparison will do is to give you a measure of the degree to which the current market's perception of future volatility has changed over the course of the trading day.   So, specific to your question, you do not want to use an annualised measure.  The best you can do is compare the implied volatility in the current price to the implied volatility of the previous day's settlement price while at the same time making a subjective judgement about how you see volatility changing in the future and how this has been reflected in the current price."
While open interest usually correlates to volume, the mark of liquidity is the bid ask spread. Even when trading options with spreads as large as an ask 2x the bid, a more realistic price that traders are willing to accept lies somewhere in the middle. Any option can easily be exited at intrinsic value: underlying price - exercise price for calls, exercise price - underlying price for puts.  For illiquid options, this will be the best price obtained.  For longer term options, something closer to the theoretical price is still possible. If an underlying is extremely liquid, yet the options aren't quite then options traders will be much more ready to trade at the theoretical price. For exiting illiquid options, small, < 4 contracts, and infrequent, > 30 minute intervals, orders are more likely to be filled closer to the theoretical price; however, if one's sells are the only trades, traders on the other side will take note and accept ever lowering implied volatilities. With knowledge of what traders will accept, it is always more optimal to trade out of options rather than exercise because of the added costs and uncertainty involved with exercising and liquidating. "people are willing to pay higher premiums for options when stocks go down. Obviously the time value and intrinsic value and interests rates of the option doesn't change because of this so the miscalculation remainder is priced into the implied volatility part of the formula.  Basically, anything that suggests the stock price will get volatile (sharp moves in either direction) will increase the implied volatility of the option. For instance, around earnings reports, the IV in both calls and puts in the nearest expiration dates are very high. When stocks go down sharply, the volatility is high because some people are buying puts for protection and others are buying calls because they think there will be a rebound move in the other direction. People (the ""sleep-at-night"" investors, not the derivatives traders ;) )  tend to be calm when stocks are going up, and fearful when they are going down. The psychology is important to understand and observe and profit from, not to quantitatively prove. The first paragraph should be your qualitative answer" http://dailyfinance.com Enter a stock ticker, then click on the Chain link to the left. Then, click on the option tickers to see their charts. EDIT: the site has changed, and there are no more option charts. So why are option charts so tough to find? Options are derivatives of the stock. Option prices are defined by a formula. The inputs are stock pricxe, strike, days to expiration, dividend, risk-free interest rate, and volatility. Volatility is the only thing that cannot be easily looked up. With a Black-Scholes calculator, and some reasonable volatility selections, it's possible to make your own fairly accurate option chart. I don't think it's very enlightening, though. The interesting things are: the stock price movement (as always), and the nature of option pricing behavior in general (understanding how the formula represents crowd behavior). Changes in implied volatility are caused by many things, of course, and it is tough to isolate the effect you are describing, but let's try to generalize for a moment. Implied volatility is generally a measure of how much expect uncertainty there is about the future price of the stock.  Uncertainty generally is higher in periods including earnings announcements because it is significant new information about the company's fortunes can make for significant changes in the price. However, you could easily have the case where the earnings are good and for some reason the market is very certain that the earnings will be good and near a certain level.  In that case the price would rise, but the implied volatility could well be lower because the market believes that there will be no significant new information in the earnings announcement. "As JoeTaxpayer says, there's a lot you can do with just the stock price. Exploring that a bit: Stock prices are a combination of market sentiment and company fundamentals. Options are just a layer on top of that. As such, options are mostly formulaic, which is why you have a hard time finding historical option data -- it's just not that ""interesting"", technically. ""Mostly"" because there are known issues with the assumptions the Black-Scholes formula makes. It's pretty good, and importantly, the market relies on it to determine fair option pricing. Option prices are determined by: Relationship of stock price to strike. Both distance and ""moneyness"". Time to expiration. Dividends. Since dividend payments reduce the intrinsic value of a company, the prospect of dividend payments during the life of a call option depresses the price of the option, as all else equal, without the payments, the stock would be more likely to end up in the money. Reverse the logic for puts. Volatility. Interest rates. But this effect is so tiny, it's safe to ignore. #4, Volatility, is the biggie. Everything else is known. That's why option trading is often considered ""volatility trading"". There are many ways to skin this cat, but the result is that by using quoted historical values for the stock price, and the dividend payments, and if you like, interest rates, you can very closely determine what the price of the option would have been. ""Very closely"" depending on your volatility assumption. You could calculate then-historical volatility for each time period, by figuring the average price swing (in either direction) for say the past year (year before the date in question, so you'd do this each day, walking forward). Read up on it, and try various volatility approaches, and see if your results are within a reasonable range. Re the Black-Scholes formula,  There's a free spreadsheet downloadable from http://optiontradingtips.com. You might find it useful to grab the concept for coding it up yourself. It's VBA, but you can certainly use that info to translate in your language of choice. Or, if you prefer to read Perl, CPAN has a good module, with full source, of course. I find this approach easier than reading a calculus formula, but I'm a better developer than math-geek :)" You may refer to project http://jstock.sourceforge.net. It is open source and released under GPL. It is fetching data from Yahoo! Finance, include delayed current price and historical price. If you're talking about just Theta, the amount of decay due to the passage of time (all else being equal), then theoretically, the time value is a continuous function, so it would decay throughout the day (although by the day of expiry the time value is very, very small).  Which makes sense, since even with 15 minutes to go, there's still a 50/50 shot of an ATM option expiring in-the-money, so there should be some time value associated with that one-sided probability. The further away from ATM the option is, the smaller the time value will be, and will be virtually zero for options that are deep in- or out-of-the-money. If you're talking about total time value, then yes it will definitely change during the day, since the underlying components (volatility, underlying price, etc.) change more or less continuously. The value at expiration does not depend on the price path for a plain vanilla European or American option. At expiration, the value would simply be: max[K - S_T, 0], where: K is the strike price, and S_T is the underlying price at expiration.