How does a delta signify the probability of expiring in the money
Just for clarification, delta and probability of expiring in the money are not the same thing. What the guy meant was that delta is usually a close enough approximation to the probability. One way to think about it is to look at the probabilities and deltas of In the Money, Out of the Money, and At the Money options. In these cases, the delta and probabilities are about the same. In fact if you look at an options chain with delta and probabilities, you can see that they are all about the same. In other words, there is a linear relationship between delta and probability. Here are a couple links to other answers around the web: Hope this answer helps!
"When you buy a put on a stock, you buy the right to sell the stock at fixed price, F, that his usually different from the market price, M. You paid a price, P, for the put.  Your potential profit, going forward, is represented by the DIFFERENCE you get to collect between your fixed price F, and that market price M, plus the price you paid for the put, or F-(M+P). (This assumes that F>(M+P). P is fixed, but the smaller M gets, the larger the term F-(M+P), and therefore the higher your potential profit from owning the put. So when M ""tanks,"" the put goes higher.  The $395 put is already in the money. If it were settled today, the value would be $395-$376 or $19. This, minus the cost of the put itself, represents your profit. The $365 put is ""out of the money."" The stock has to fall $11 more before the put is exercised. But if the stock went down 8 points today, that is less than the $19 difference at the start of the day. Because there is time between now and October, there is a chance for the stock to go down further, thereby going into the money. The current value of the put is represented by this ""chance."" Obviously, the chances of the stock going down $11 more (from today) is greater than the chance of it going down $19 more. On the other hand, the closer it gets to the expiration date, the less an out of the money put is worth. It's a race between the stock's fall, and the time to expiration." Line one shows your 1M, a return with a given rate, and year end withdrawal starting at 25,000.  So Line 2 starts with that balance, applies the rate again, and shows the higher withdrawal, by 3%/yr.  In Column one, I show the cumulative effect of the 3% inflation, and the last number in this column is the final balance (903K) but divided by the cumulative inflation.  To summarize - if you simply get the return of inflation, and start by spending just that amount, you'll find that after 20 years, you have half your real value.  The 1.029 is a trial and error method, as I don't know how a finance calculator would handle such a payment flow. I can load the sheet somewhere if you'd like.  Note: This is not exactly what the OP was looking for. If the concept is useful, I'll let it stand. If not, downvotes are welcome and I'll delete. It really centers on the probability of your position falling to $0 and your level of comfort if that were to happen.  There are a plethora of situations that could cause an option contract to become worthless.  The application of leverage to a position also increases the risk. Zero risk would be an FDIC insured savings account, high risk would be buying options on margin, and there's a very wide grey area in between.  I agree that the whole process of assigning a risk level is dubious at best.  As you say, it seems using past data could help assign a risk level, look to beta values if you believe in that.  The problem here is the main disclaimer in use is that past performance cannot be relied upon for future gains. As an aside, if the US government files bankruptcy you'll have a whole host of more immediate problems than the value of your t-bills.  At that point dollars would have been a risky investment. If they short the contract, that means, in 5 months, they will owe if the price goes up (receive if the price goes down) the difference between the price they sold the future at, and the 3-month Eurodollar interbank rate, times the value of the contract, times 5. If they're long, they receive if the price goes up (owe if the price goes down), but otherwise unchanged. Cash settlement means they don't actually need to make/receive a three month loan to settle the future, if they held it to expiration - they just pay or receive the difference.  This way, there's no credit risk beyond the clearinghouse. The final settlement price of an expiring three-month Eurodollar futures (GE) contract is equal to 100 minus the three-month Eurodollar interbank time deposit rate. "Below I will try to explain two most common Binomial Option Pricing Models (BOPM) used. First of all, BOPM splits time to expiry into N equal sub-periods and assumes that in each period the underlying security price may rise or fall by a known proportion, so the value of an option in any sub-period is a function of its possible values in the following sub period. Therefore the current value of an option is found by working backwards from expiry date through sub-periods to current time. There is not enough information in the question from your textbook so we may assume that what you are asked to do is to find a value of a call option using just a Single Period BOPM. Here are two ways of doing this: First of all let's summarize your information: Current Share Price (Vs) = $70 Strike or exercise price (X) = $60 Risk-free rate (r) = 5.5% or 0.055 Time to maturity (t) = 12 months Downward movement in share price for the period (d) = $65 / $70 = 0.928571429 Upward movement in share price for the period (u) = 1/d = 1/0.928571429 = 1.076923077 ""u"" can be translated to $ multiplying by Vs => 1.076923077 * $70 = $75.38 which is the maximum probable share price in 12 months time. If you need more clarification here - the minimum and maximum future share prices are calculated from stocks past volatility which is a measure of risk. But because your textbook question does not seem to be asking this - you probably don't have to bother too much about it yet. Intrinsic Value: Just in case someone reading this is unclear - the Value of an option on maturity is the difference between the exercise (strike) price and the value of a share at the time of the option maturity. This is also called an intrinsic value.  Note that American Option can be exercised prior to it's maturity in this case the intrinsic value it simply the diference between strike price and the underlying share price at the time of an exercise. But the Value of an option at period 0 (also called option price) is a price you would normally pay in order to buy it. So, say, with a strike of $60 and Share Price of $70 the intrinsic value is $10, whereas if Share Price was $50 the intrinsic value would be $0. The option price or the value of a call option in both cases would be fixed.  So we also need to find intrinsic option values when price falls to the lowest probable and rises to the maximum probable (Vcd and Vcu respectively) (Vcd) = $65-$60 = $5 (remember if Strike was $70 then Vcd would be $0 because nobody would exercise an option that is out of the money) (Vcu) = $75.38-$60 = $15.38 1. Setting up a hedge ratio:  h = Vs*(u-d)/(Vcu-Vcd) h = 70*(1.076923077-0.928571429)/(15.38-5) = 1 That means we have to write (sell) 1 option for each share purchased in order to hedge the risks. You can make a simple calculation to check this, but I'm not going to go into too much detail here as the equestion is not about hedging. Because this position is risk-free in equilibrium it should pay a risk-free rate (5.5%). Then, the formula to price an option (Vc) using the hedging approach is: (Vs-hVc)(e^(rt))=(Vsu-hVcu) Where (Vc) is the value of the call option, (h) is the hedge ratio, (Vs) - Current Share Price, (Vsu) - highest probable share price, (r) - risk-free rate, (t) - time in years, (Vcu) - value of a call option on maturity at the highest probable share price. Therefore solving for (Vc): (70-1*Vc)(e^(0.055*(12/12))) = (75.38-1*15.38) => (70-Vc)*1.056540615 = 60 => 70-Vc = 60/1.056540615 => Vc = 70 - (60/1.056540615)  Which is similar to the formula given in your textbook, so I must assume that using 1+r would be simply a very close approximation of the formula above. Then it is easy to find that Vc = 13.2108911402 ~ $13.21 2. Risk-neutral valuation: Another way to calculate (Vc) is using a risk-neutral approach. We first introduce a variable (p) which is a risk-neutral probability of an increase in share price. p = (e^(r*t)-d)/(u-d) so in your case: p = (1.056540615-0.928571429)/(1.076923077-0.928571429) = 0.862607107 Therefore using (p) the (Vc) would be equal: Vc = [pVcu+(1-p)Vcd]/(e^(rt)) => Vc = [(0.862607107*15.38)+(0.137392893*5)]/1.056540615 => Vc = 13.2071229185 ~ $13.21 As you can see it is very close to the hedging approach. I hope this answers your questions. Also bear in mind that there is much more to the option pricing than this. The most important topics to cover are: Multi-period BOPM Accounting for Dividends Black-Scholes-Merton Option Pricing Model" [] As you can see from the graphs above, as absolute distance from ATM (At The Money) increases, the ratio represented by Delta begins to approach 0:1 or 1:1. Meaning, as Delta approaches 1 the option price moves up 1 dollar for every 1 dollar the stock price moves up. As Delta approaches 0 the option price does not move as the stock price moves. As the absolute distance from ATM increases Gamma approaches zero (0). Meaning, as the price of the option increases or decrease the change in delta is at its highest as the option price is nearest the money. As the price of the option moves away from the money, in either direction, it changes less drastically. Interestingly, Delta is the first derivative of the value of the option price with respect to the underlying asset price. And Gamma is the first derivative of Delta. Definition of Delta Definition of Gamma Here is what I could find on the net: http://education.wallstreetsurvivor.com/options-symbol-changes-coming-february-12th-2010 So it sounds like it does not affect how you invest in options but only how you look them up.  I remember using a Bloomberg terminal and it wasn't clear what the expiry date of the option you were looking at was.  It looks like the new quote system addresses this. HTH. "It's a form of debt issued by the United States Treasury. As the name implies, a 10-year note is held for 10 years (after which you get the face value in cash), and it pays interest twice per year. It's being used in the calculator to stand for a readily available, medium-term, nearly risk-free investment, as a means of ""discounting"" the value that the company gains. The explanation for why the discounting is done can be found on the page you linked. As a Canadian you could use the yield of comparable Canadian treasury securities as quoted by Bank of Canada (which seem to have had the bottom fall out since the new year), although I don't suppose American notes would be hard for a Canadian investor to come by, so if you wanted to be conservative you could use the US figure as long as it's higher." "Suppose the stock is $41 at expiry. The graph says I will lose money. I think I paid $37.20 for (net debit) at this price. I would make money, not lose. What am I missing? The `net debit' doesn't have anything to do with your P/L graph. Your graph is also showing your profit and loss for NOW and only one expiration. Your trade has two expirations, and I don't know which one that graph is showing. That is the ""mystery"" behind that graph. Regardless, your PUTs are mitigating your loss as you would expect, if you didn't have the put you would simply lose more money at that particular price range. If you don't like that particular range then you will have to consider a different contract. it was originally a simple covered call, I added a put to protect from stock going lower.. Your strike prices are all over the place and NBIX has a contract at every whole number.... there is nothing simple about this trade. You typically won't find an ""always profitable"" combination of options. Also, changes in volatility can distort your projects greatly." "First lets understand what convexity means: Convexity -  convexity refers to non-linearities in a financial model. In other   words, if the price of an underlying variable changes, the price of an   output does not change linearly, but depends on the second derivative   (or, loosely speaking, higher-order terms) of the modeling function.   Geometrically, the model is no longer flat but curved, and the degree   of curvature is called the convexity. Okay so for us idiots this means: if the price of ABC (we will call P) is determined by X and Y. Then if X decreases by 5 then the value of P might not necessarily decrease by 5 but instead is also dependent on Y (wtf$%#! is Y?, who cares, its not important for us to know, we can understand what convexity is without knowing the math behind it). So if we chart this the line would look like a curve. (clearly this is an over simplification of the math involved but it gives us an idea) So now in terms of options, convexity is also known as gamma, it will probably be easier to talk about gamma instead of using a confusing word like convexity(gamma is the convexity of options). So lets define Gamma: Gamma - The rate of change for delta with respect to the underlying asset's price. So the gamma of an option indicates how the delta of an option will change relative to a 1 point move in the underlying asset. In other words, the Gamma shows the option delta's sensitivity to market price changes. or Gamma shows how volatile an option is relative to movements in the underlying asset. So the answer is: If we are long gamma (convexity of an option) it simply means we are betting on higher volatility in the underlying asset(in your case the VIX). Really that simple? Well kinda, to fully understand how this works you really need to understand the math behind it. But yes being long gamma means being long volatility. An example of being ""long gamma"" is a ""long straddle"" Side Note: I personally do trade the VIX and it can be very volatile, you can make or lose lots of money very quickly trading VIX options. Some resources: What does it mean to be ""long gamma"" in options trading? Convexity(finance) Long Gamma – How to Make a Long Gamma Position Work for You Delta - Investopedia Straddles & Strangles - further reading if your interested. Carry(investment) - even more reading." That looks like a Bloomberg terminal. And like @Jer said, it would appear to be the symbol for the S&P 500 E-mini index future. Although it doesn't look right all on its own, as it should have a modifier indicating the month (or quarter) of expiry. However, since it appears on a Bloomberg terminal in the image, I checked a source for Bloomberg Symbol Lists and found one of two possibilities for ES1. It is most likely the S&P 500 e-mini future: CME E-Mini Futures  E-Mini S&P 500    ES1 INDEX the only alternative was LIFFE 3 Month Euroswiss   ES1 COMDTY I think the former is far more likely, as the latter has the COMDTY commodity tag instead of INDEX as the tag in the image. Also, it isn't the ESI which pertains to Ethibel Sustainability Indices and something with the Eurozone (also Bloomberg Indices). Here we go! Excerpt straight is from a presentation presentation on charting from a business school PDF see pp.12-13, and appears to be a straight excerpt from September 2007 Bloomberg documentation. I didn't know any other way to imbed it besides taking a screen shot then uploading to imgur. Or of course, see pp.12-13 in the referenced PDF I've attached.  See NL7 is right and his B-S reference, a good one.   Time decay happens to occur in a way that 2X the time gives an option 1.414X (the square root of 2) times the value, so half the time means about .707 of the value.  This valuation model should help the trader decide on exactly how far out to go for a given trade. "But what happen if the stock price went high and then go down near expiry date? When you hold a short (sold) call option position that has an underlying price that is increasing, what will happen (in general) is that your net margin requirements will increase day by day.  Thus, you will be required to put up more money as margin to finance your position.  Margin money is simply a ""good faith"" deposit held by your broker.  It is not money that is debited as cash from the accounting ledger of your trading account, but is held by your broker to cover any potential losses that may arise when you finally settle you position.   Conversely, when the underlying share price is decreasing, the net margin requirements will tend to decrease day by day.   (Net margin is the net of ""Initial Margin"" and ""Variation Margin"".) As the expiry date approaches, the ""time value"" component of the option price will be decreasing." An expiration 2 years out will have Sqr(2) (yes the square root of 2!) times the premium of the 1 year expiration. So if the option a year out sell for $1.00, two is only $1.41.  And if the stock trades for $10, but the strike is $12, why aren't you just waiting for expiration to write the next one? "It's talked about quite often among more experienced investors. They were/ are used extensively by hedge funds.  Keep in mind that if your option expires when not ""in the money"" you lose the premium you paid for the purchase of the option. That's where the risk comes in.  I've grown really interested in options over the last couple months. Check out McMillan's Guide to Options. It's generally thought of as the quintessential beginners guide to understanding options.  Good luck!"