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."
"There are a few different ""kinds"" of implied volatility. They are all based on the IVs obtained from the option pricing model you use. (1) Basically, given a few different values (current stock price, time until expiration, right of option, exercise style, strike of the option, interest rates, dividends, etc), you can obtain the IV for a given option price. If you look at the bid of an option, you can calculate the IV for that bid. If you look at the ask, there's a different IV for the ask. You can then look at the mid price, then you have a different IV, and so on and so on. And that's for each strike, in each expiration cycle! So you have a ton of different IVs. (2) In many option trading platforms, you'll see another kind of IV: the IV for each specific expiration cycle. That's calculated based on some of the IVs I mentioned on topic (1). Some kind of aggregation (more on this later). (3) Finally, people often talk about ""the IV of stock XYZ"". That's, again, an aggregation calculated from many of the IVs mentioned on topic (1). Now, your question seems to be: which IVs, from which options, from which months, with which weight, are part of the expiration cycle IV or for the IV of the stock itself? It really depends on the trading platform you are talking about. But very frequently, people will use a calculation similar to how the CBOE calculates the VIX. Basically, the VIX is just like the IV described on topic (3) above, but specifically for SPX, the S&P 500 index. The very detailed procedure and formulas to calculate the VIX (ie, IV of SPX) is described here: http://cfe.cboe.com/education/vixprimer/about.aspx If you apply the same (or a similar) methodology to other stocks, you'll get what you could call ""the IV of stock XYZ""." "The question ""do they?"" is a fair one, but the answer, ""we can only observe the past, and that's what they did,"" may not be so satisfying to you.  It's safe to say that any longer term view of any market will show far less volatility than a short one. It only takes a glance at the return of the 2000's  2009 27.11   2008 -37.22  2007      5.46  2006  15.74 2005  4.79   2004 10.82   2003  28.72  2002    -22.27  2001 -11.98 2000     -9.11 (for the S&P) to see that in an awful decade containing -37% and -22% that the full decade was ""only"" down 9% in total or just less than 1% per year compounded. I'm not predicting any particular returns forward, just noting this is how the math works.  DCA performs well through such a decade, better than in a rising one. You are offered the opportunity to buy into a market selling below the long term trend.  Added note in response to Enno's answer below - On rereading the linked article, I see where the author cites Zvi Bodie who clearly made a logical error. He concludes that since a 20 month S&P put costs triple what a 2.3 mo put costs, that there's more risk the market falls over the longer period, not less. American options can be sold or exercised at any time. If a 2 year option were cheaper than a 2 month option, no one would buy the shorter term. It's pretty simple that the Options Pricing Models take time into account and their value, put or call, increases along with the time till expiration.  On a lighter note, when I take the S&P data for 1871-2012 (I know, no S&P back then, but it's Schiller's data) I get average 40 year returns of 44X, similar to the author's conclusion, $1K growing to $44K. But, the Standard deviation is 28. So the high end of +1 STDEV is $72K, not the author's $166K. Although, the low end 44-28=16 comes close to his $14K figure. $16K is a 7.18% long term return which today doesn't look bad. When the article was written, the author was looking at a 6% short term risk free rate." Yahoo Finance's Historical Prices section allows you to look up  daily historical quotes for any given stock symbol, you don't have to hit a library for this information. Your can choose a desired time frame for your query, and the dataset will include High/Low/Close/Volume numbers. You can then download a CSV version of this report and perform additional analysis in a spreadsheet of your choice. Below is Twitter report from IPO through yesterday: http://finance.yahoo.com/q/hp?s=TWTR&a=10&b=7&c=2013&d=08&e=23&f=2014&g=d I understand the question, I think. The tough thing is that trades over the next brief time are random, or appear so. So, just as when a stock is $10.00 bid / $10.05 ask, if you place an order below the ask, a tick down in price may get you a fill, or if the next trades are flat to higher, you might see the close at $10.50, and no fill as it never went down to your limit.  This process is no different for options than for stocks.  When I want to trade options, I make sure the strike has decent volume, and enter a market order. Edit - I reworded a bit to clarify. The Black–Scholes is a model, not a rigid equation. Say I discover an option that's underpriced, but it trades under right until it expires. It's not like there's a reversion to the mean that will occur. There are some very sophisticated traders who use these tools to trade in some very high volumes, for them, it may produce results. For the small trader you need to know why you want to buy a stock or its option and not worry about the last $0.25 of its price. "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" "Number 2 cannot occur. You can buy the call back and sell the stock, but the broker won't force that #2 choice. To trade options, you must have a margin account. No matter how high the stock goes, once ""in the money"" the option isn't going to rise faster, so your margin % is not an issue.  And your example is a bit troublesome to me. Why would a $120 strike call spike to $22 with only a month left? You've made the full $20 on the stock rise and given up any gain after that. That's all. The call owner may exercise at any time. Edit: @jaydles is right, there are circumstances where an option price can increase faster than the stock price. Options pricing generally follows the Black-Scholes model. Since the OP gave us the current stock price, option strike price, and time to expiration, and we know the risk free rate is <1%, you can use the calculator to change volatility. The number two scenario won't occur, however, because a covered call has no risk to the broker, they won't force you to buy the option back, and the option buyer has no motive to exercise it as the entire option value is time premium." Use the Black-Scholes formula. If you know the current price, an options strike price, time until expiration, and risk-free interest rate, then knowing the market price of the option will tell you what the market's estimation of the volatility is. This does rely on a few assumptions, such as Gaussian random walk, but those are reasonable assumptions for most stocks. You can also get a list of past stock prices, put them in Excel, and ask Excel to calculate the standard deviation with stdev.s(), but that gives you the past volatility. The market's estimate of future volatility is more relevant. as no advantage from exerting American call option early,we can use Black schole formula to evaluate the option.However, American put option is more likely to be exercised early which mean Black schole does not apply for this style of option I frequently do this on NADEX, selling out-of-the-money binary  calls. NADEX is highly illiquid, and the bid/ask is almost always from  the market maker. Out-of-the-money binary calls lose value quickly  (NADEX daily options exist for only ~21 hours). If I place an  above-ask order, it either gets filled quickly (within a few minutes)  due to a spike in the underlying, or not at all. I compensate by  changing my price hourly.  As Joe notes, one of Black-Scholes inputs is volatility, but price  determines (implied) volatility, so this is circular. In other words, you can  treat the bid/ask prices as bid/ask volatilities. This isn't as  far-fetched as it seems:  http://www.cmegroup.com/trading/fx/volatility-quoting-fx-options.html Robert is right saying that options' prices are affected by implied volatility but is wrong saying that you have to look at the VIX index. For two reasons:  1) the VIX index is for S&P500 options only. If you are trading other options, it is less useful. 2) if you are trading an option that is not at the money, your implied volatility may be very different (and follow a different dynamics) that the VIX index.  So please look at the right implied volatility.  In terms of strategy, I don't think that not doing anything is a good strategy. I accept any point of view but you should consider that option traders should be able to adjust positions depending on market view.  So you are long 1 call, suppose strike 10. Suppose the underlying price at the time of entry was 10 (so the call was at the money). Now it's 9.  1) you still have a bullish view: buy 1 call strike 9 and sell 2 calls strike 10. This way you have a bull call spread with much higher probability of leading to profit. You are limiting your profit potential but you are also reducing the costs and managing the greeks in a proper way (and in line with your expectations).  2) you become bearish: you can sell 1 call strike 9. This way you end up with a bear call spread. Again, you are limiting your profit potential but you are also reducing the costs and managing the greeks in a proper way (and in line with your expectations). 3) you become neutral: buy 1 call strike 8 and sell 2 calls strike 9. This way you end up with a call butterfly. You are almost delta neutral and you can wait until your view becomes clear enough to become directional. At that point you can modify the butterfly to make it directional.  These are just some opportunities you have. There is no reason for you to wait. Options are eroding contracts and you must be fast and adjust the position before time starts eroding your capital at risk.  It's true that buying a call doesn't make you loose more than the premium you paid, but it's better to reduce this premium further with some adjustment. Isn't it?  Hope that helps. :) "Note that the series you are showing is the historical spot index (what you would pay to be long the index today), not the history of the futures quotes. It's like looking at the current price of a stock or commodity (like oil) versus the futures price.  The prompt futures quote will be different that the spot quote. If you graphed the history of the prompt future you might notice the discontinuity more. How do you determine when to roll from one contract to the other? Many data providers will give you a time series for the ""prompt"" contract history, which will automatically roll to the next expiring contract for you.  Some even provide 2nd prompt, etc. time series.  If that is not available, you'd have to query multiple futures contracts and interleave them based on the expiry rules, which should be publicly available. Also is there not a price difference from the contract which is expiring and the one that is being rolled forward to? Yes, since the time to delivery is extended by ~30 days when you roll to the next contract. but yet there are no sudden price discontinuities in the charts. Well, there are, but it could be indistinguishable from the normal volatility of the time series." The mathematics make it easier to understand why this is the case. Using very bad shorthand, d1 and d2 are inputs into N(), and N() can be expressed as the probability of the expected value or the most probable value which in this case is the discounted expected stock price at expiration. d1 has two σs which is volatility in the numerator and one in the denominator.  Cancelling leaves one on top.  Calculating when it's infinity gives an N() of 1 for S and 0 for K, so the call is worth S and the put PV(K).  At 0 for σ, it's the opposite. More concise is that any mathematical moment be it variance which mostly influences volatility, mean which determines drift, or kurtosis which mostly influences skew are all uncertanties thus costs, so the higher they are, the higher the price of an option. Economically speaking, uncertainties are costs.  Since costs raise prices, and volatility is an uncertainty, volatility raises prices. It should be noted that BS assumes that prices are lognormally distributed.  They are not.  The closest distribution, currently, is the logVariance Gamma distribution. "According to the book of Hull, american and european calls on non-dividend paying stocks should have the same value. American puts, however, should be equals to, or more valuable than, european puts. The reason for this is the time value of money. In a put, you get the option to sell a stock at a given strike price. If you exercise this option at t=0, you receive the strike price at t=0 and can invest it at the risk-free rate. Lets imagine the rf rate is 10% and the strike price is 10$. this means at t=1, you would get 11.0517$. If, on the other hand, you did'nt exercise the option early, at t=1 you would simply receive the strike price (10$). Basically, the strike price, which is your payoff for a put option, doesn't earn interest. Another way to look at this is that an option is composed of two elements: The ""insurance"" element and the time value of the option. The insurance element is what you pay in order to have the option to buy a stock at a certain price. For put options, it is equals to the payout= max(K-S, 0) where K=Strike Price and St= Stock price.  The time value of the option can be thought of as a risk-premium. It's difference between the value of the option and the insurance element. If the benefits of exercising a put option early (i.e- earning the risk free rate on the proceeds) outweighs the time value of the put option, it should be exercised early. Yet another way to look at this is by looking at the upper bounds of put options. For a european put, today's value of the option can never be worth more than the present value of the strike price discounted at the risk-free rate. If this rule isn't respected, there would be an arbitrage opportunity by simply investing at the risk-free rate. For an american put, since it can be exercised at any time, the maximum value it can take today is simply equals to the strike price. Therefore, since the PV of the strike price is smaller than the strike price, the american put can have a bigger value. Bear in mind this is for a non-dividend paying stock. As previously mentioned, if a stock pays a dividend it might also be optimal to exercise just before these are paid." Just a few observations within the Black-Scholes framework: Next, you can now use the Black-Scholes framework (stock price is a Geometric Brownian Motion, no transaction costs, single interest rate, etc. etc.) and numerical methods (such as a PDE solver) to price American style options numerically, but not with a simple closed form formula (though there are closed-form approximations). In short, yes. Implied volatility will capture any expected upcoming material announcements. There is also supply/demand impact bundled in which may inflate an option price, and by extension increase implied volatility. OTM and ITM options are particularly predisposed to this phenomenon -- which is of course at odds with the traditional BS model assumptions -- the result is referred to as the volatility smile. Implied volatility is quoted as an annualised measure but isn't necessarily an annual value -- it will correspond to the option time period.