What exactly is a “derivative”?
The basic idea behind a derivative is very simple actually.  It is a contract where the final value depends on (is derived from) the value of something else.  Stock, for instance, is not a derivative because the contract itself is actually ownership of part of a company.  Whereas car insurance is a derivative because the payout depends on the value of something else namely your (and other peoples') cars. The problem with such a simple definition is that it covers such a broad class.  It covers simple contracts like Futures where the end value just depends on the price of something on a future date.  But it extends to contracts complicated enough that people in finance call them Exotics. Derivatives are broadly used for two things reducing risk (sometimes called insurance) and speculation.  A farmer can use derivatives to make sure she gets paid a certain amount for her corn.  A banker can group a bunch of loans together and sell slices to reduce the pain of a particular loan failing.  At the same time people can use the same instruments to speculate on the price of (for example) that corn or those loans and the main advantage is that they don't have to buy the corn or loans directly.  Any farmer will tell you corn can be very expensive to store. Derivatives generally cause problems both individually and sometimes world wide when people don't properly understand the risks involved.  The most famous example being Mortgage-backed Securities and the recent Great Recession.  You can start understand the instruments and their risks by this wonderful Wikipedia article and later perhaps a used collection of CFA books which cover derivatives in great detail. Edit: Michael Grünewald mentioned Hull's text on derivatives a wonderful middle ground between Wikipedia and the CFA books that I can't believe I didn't think about myself. A derivative is a financial instrument of a special kind, the kind “whose price depends on, or is derived from, another asset”.  This definition is from John Hull, Options, Futures and Other Derivatives – a book definitely worth to own if you are curious about this, you can easily find old copies for a few dollars. The first point is that a derivative is a financial instrument, like credits, or insurances, the second point is that its price depends closely from the price of something else, the mentioned asset. In most cases derivatives can be understood as financial insurances against some risk bound to the asset. In the sequel I give a small list of derivatives and highlight the assets and the risk they can be bound to.  And first, let me point out that the definition is (marginally) wrong because some derivatives depend on things which are not assets, nor do they have a price, like temperature, sunlight, or even your own life in the case of mortgages.  But before going in this list, let me go through the remaining points of your question. What is the basic idea and concept behind a derivative? As already noted, in most cases, a derivative can be understood as a financial insurance compensating from a risk of some sort.  In a classical insurance contract, one party of the contract is an insurance company, but in the broader case of a derivative, that counterparty can be pretty anything: an insurance, a bank, a government, a large company, and most probably market makers. How is it really used, and how does this deviate from the first point? Briefly, how does is it affecting people, and how is it causing problems? An important point with derivatives is that it can be arbitrarily complicated to compute their prices.  Actually what is hidden in the attempt of giving a definition for derivatives, is that they are products whose price Y is a measurable function of one or several random variables X_1, X_2, … X_n on which we can use the theory of arbitrage pricing to get hints on the actual price Y of the asset – this is what the depends on means in technical terms.  In the most favorable case, we obtain an easy formula linking Y to the X_is which tells us what is the price of our financial instrument. But in practice, it can be very difficult, if at all possible, to determine a price for derivatives. This has two implications: Persons possessing sophisticated techniques to compute the price of derivatives have a strategic advantage on derivatives market, in comparison to less advanced actors on the market. Organisation owning assets they cannot price cannot compute their bilan anymore, so that they cannot know for sure their financial situation. They are somehow playing roulette. But wait, if derivatives are insurances they should help to mitigate some financial risk, which precisely means that they should help their owners to more accurately see their financial situation! How is this not a contradiction? Some persons with sophisticated techniques to compute the price of derivatives are actually selling complicated derivatives to less knowledgeable persons.  For instance, many communes in France and Germany have contracted credits whose reimbursements have a fixed interest part, like in a classical credit, and a variable interest part whose rate is computed against a complicated formula involving the value of the Swiss frank at each quarter starting from the inception of the credit.  (So, for a 25 years running credit of theis type, the price Y of the credit at its inception depends on 100 Xs, which are the uncertain prices for the Swiss frank each quarter of the 25 next years.)  Some of these communes can be quite small, with 5.000 inhabitants, and needless to say, do not have the required expertise to analyse the risks bound to such instruments, which in that special case led the court call the credit a swindling and to cancel the credit.  But what chain of events leads a 5.000 inhabitants city in France to own a credit whose reimbursements depends on the Swiss frank?  After the credit crunch in 2007 and the fall of Lehman Brothers in 2008, it has begun to be very hard to organise funding, which basically means to conclude credits running long in time on large amounts of money.  So, the municipality needs a 25 years credit of 10.000.000 EUROS and goes to its communal bank.  The communal bank has hundreds or thousands of municipalities looking for credits and needs itself a financing.  So the communal bank goes to one of the five largest financial institutions in the world, which insists on selling a huge credit whose reimbursements have a variable part depending on hundred of values the Swiss frank will have in the 25 next years. Since the the big bank has better computation techniques than the small bank it makes a big profit.  Since the small bank has no idea, how to compute the correct price of the credit it bought, it cuts this in pieces and sell it in the same form to the various communes it works with.  If we were to attribute this kind of intentions to the largest five banks, we could ask about the possibility that they designed the credit to take advantage of the primitive evaluation methods of the small bank. We could also ask if they organised a cartel to force communal banks to buy their bermudean snowballs. And we could also ask, if they are so influent that they eventually can manipulate the Swiss frank to secure an even higher profit.  But I will not go into this.  To the best of my understanding, the subprime crisis is a play along the same plot, with different actors, but I know this latter subject only by what I could read in French newspapers. So much for the “How is it causing problems?” part. What is some of the terminology in relation to derivatives (and   there meanings of course)? Answering this question is basically the purpose of the 7 first chapters of the book by Hull, along with deriving some important mathematical principles.  And I will not copy these seven chapters here! How would someone get started dealing in derivatives (I'm playing a     realistic stock market simulation, so it doesn't matter if your     answer to this costs me money)? If you ask the question, I understand that you are not a professional, so that your are actually trying to become the one that has money and zero knowledge in the play I outlined above. I would recommand not doing this.  That said, if you have a good mathematical background and can program well, once you are confindent with the books of Hull and Joshi, you can have fun implementing various market models and implementing trading strategies. Once you are confident with this, you can also read the articles on quantitative finance on arXiv.org. And once you are done with this, you can decide for yourself if you want to play the same market as the guys writing these articles. (And yes, even for the simplest options, they have better models than you have and will systematically outperform you in the long run, even if some random successes will give you the feeling that you do well and could do better.) (indeed, I've made it a personal goal to somehow lose every last cent of my money) You know your weapons! :) Two parties agree today on a price for one to deliver a commodity to the other at some future instant.  This is a classical future contract, it can be modified in every imaginable way, usually by embedding options.  For instance one party could have the option to choose between different delivery points or delivery days. Two parties write today a contract allowing the one party to buy at some future time a commodity to the the second party.  The price is written today, as part of the contract.  (There is the corresponding option entitling the owner to sell something.)  Unlike the future contract, only one party can be obliged to do something, the other jas a right but no obligation. If you buy and option, your are buying some sort of insurance against a change of price on some asset. This is the most familiar to anybody.  Credits can come in many different flavours, especially the formula to compute interests, or also embed options.  Common options are early settlement options or restructuration options. While this is not completely inutitive, the credit works like an insurance.  This is most easily understood from the side of the organisation lending the money, that speculates that the ratio of creanciers going bankrupt will be low enough for her to make profit, just like a fire insurance company speculates that the ratio of fire accidents will be low enough for her to make a profit. This is like a mortgage on a financial institution.  Two parties agree that one will recive an upfront today and give a compensation to the second one if some third party defaults. Here this is an explicit insurance against the unfortuante event, where a creancier goes bankrupt. One finds here more or less standard options on electricity. But electricity have delicious particularities as it can practically not be stored, and fallout is also (usually) avoided. As for classical options, these are insurances against price moves. A swap is like two complementary credits on the same amount of money, so that it ends up in the two parties not actually exchanging the credit nominal and only paying interest one to the other — which makes only sense if these interests are computed with different formulas. Typical example are fixed rate vs. EURIBOR on some given maturity, which we interpret as an insurance against fluctuations of the EURIBOR, or a fixed rate vs. the exchange ratio between two currencies, which we interpret as an insurance against the two currencies decorrelating. Swaps are the richest and the most generic category of financial derivatives.  The off-the-counter market features very imaginative, very customised insurance products. The most basic form is the insurance against drought, but you can image different dangers, and once you have it you can put it in options, in a swap, etc.  For instance, a restaurant with a terrasse could enter in a weather insurance, paying each year a fixed amount of money and becoming in return an amount of money based on the amount of rainy day in a year. Actually, this list is virtually without limits! A derivative in finance is simply any asset whose value is based on the value of another asset or based on the value of a group of assets. A derivative contract is a type of contract (usually a 'standardized contract') with specific payout instruction based on the price changes of a different asset. The basic idea is that it becomes easier to make a claim to an asset or property (and profit from this claim), without needing to physically transfer it (or even the title to said asset), and use much less capital to do so (reduce risk). They become problematic when multiple people may have claims to the real asset, or when the value of the derivatives changes very quickly or are hard to calculate. There are also liquidity problems the further you get from the real asset. This is not a problem for all kinds of derivatives contracts. And you must recognize that derivatives are used colloquially in a way that has nothing to do with reality to cause fear in people/investors that are not financially savvy. Many derivatives also have dubious or no economic purposes such that regulators don't allow them to be traded since they can't see how it is different from gambling. This is seen in financial markets that are less liberalized or cultures with puritanical backgrounds. Typically the trick is to convince regulators that the derivative or financial product helps with reducing risk and hedging and it will get approved. I've mentioned some terminology, but this depends specifically on what kind of derivatives contract you become interested in. Swaps, Credit Default Swaps, Futures, Options, Options on Futures, Leveraged Exchange Traded Funds, Inverse Leveraged Exchange Traded Funds, warrants, and more all have their own terminology. How to trade them in a simulation? It all depends on which financial product you really become interested in. There are a few unsavory factors that have led to the creation of new derivatives:
"I think that any ETF is ""open source"" -- the company issues a prospectus and publishes the basket of stocks that make up the index. The stuff that is proprietary are trading strategies and securities or deriviatives that aren't traded on the open market. Swaps, venture funds, hedge funds and other, more ""exotic"" derivatives are the things that are closed. What do you mean by ""open source"" in this context?" It's a debt derivative.  Credit default swaps are contracts drawn up on a specific issue of a bond (in the case of single-name), or on a basket/index of a class of bonds (in the case of credit default index swaps/CDX).  When it comes to derivatives you would have to look at the underlying instrument.  For example, options on AAPL common stock are equity derivatives.  Forwards on corn or wheat are commodity derivatives.  Interest rate swaps where the floating leg is pegged to LIBOR are debt/rates derivatives. "Derivatives derive their value from underlying assets.  This is expressed by the obligation of at least one counterparty to trade with the other counterparty in the future.  These can take on as many combinations as one can dream up as it is a matter of contract. For futures, where two parties are obligated to trade at a specific price at a specific date in the future (one buyer, one seller), if you ""short"" a future, you have entered into a contract to sell the underlying at the time specified.  If the price of the future moves against you (goes up), you will have to sell at a loss.  The bigger the move, the greater the loss.  You go ahead and pay this as well as a little extra to be sure that you satisfy what you owe due to the future.  This satisfaction is called margin. If there weren't margin, people could take huge losses on their derivative bets, not pay, and disrupt the markets.  Making sure that the money that will trade is already there makes the markets run smoothly. It's the same for shorting stocks where you borrow the stock, sell it, and wait.  You have to leave the money with the broker as well as deposit a little extra to be sure you can make good if the market moves to a large degree against you." You first compute your Ordinary Income (which includes Dividends, since they are taxed as OI), then you apply the standard tax bracket function to it, which is a piecewise linear function f() such that TAX = f(INCOME). It can be found at About.com. You can transform this into NET_INCOME = g(INCOME) = INCOME - TAX = INCOME - f(INCOME). Presumably g() is what you want to graph. I've actually graphed it before:  Not too interesting, even on a LogLog scale. More interesting is the marginal tax rate, which is the derivative of f(), or the negative of the derivative of g():  ST (straight tax) shows what the marginal tax rate would look like if f() was just f(x)=kx or f(x)=kx+c, i.e. a straight/flat tax. The net tax rate (f(x)/x) actually gets more interesting if you also include [federal subsidies/deductions](Src: http://fbheron.org/wp-content/uploads/2014/03/fedassistance_ft.jpg) as a negative tax:  Capital Gains are taxed separately and have (almost) nothing to do with this function. Corporate tax is not payed by you (although the burden of the tax [technical term] may fall upon you). Sorry I couldn't simplify; taxes are just complicated. "As Dheer pointed out, Wikipedia has a good definition of what a negotiable instrument is.  A security is an instrument or certificate that signifies an ownership interest in something tangible. 1 share of IBM represents some small fraction of a company. You always have the ability to choose a price you are willing to pay -- which may or may not be the price that you get. A derivative is a level of abstraction linked by a contract to a security... if you purchase a ""Put"" contract on IBM stock, you have a contractural right to sell IBM shares at a specific price on a specific date. When you ""own"" a derivative, you own a contract -- not the actual security." "Translation : Funds managers that use traditionnal methods to select stocks will have less success than those who use artificial intelligence and computer programs to select stocks.  Meaning : The use of computer programs and artificial intelligence is THE way to go for hedge fund managers in the future because they give better results.  ""No man is better than a machine, but no machine is better than a man with a machine."" Alternative article : Hedge-fund firms, Wall Street Journal. A little humour : ""Whatever is well conceived is clearly said, And the words to say it flow with ease."" wrote Nicolas Boileau in 1674." "A derivative contract can be an option, and you can take a short (sell) position , much the same way you would in a stock. When BUYING options you risk only the money you put in. However when selling naked(you don't have the securities or cash to cover all potential losses) options, you are borrowing. Brokers force you to maintain a required amount of cash called, a maintenance requirement. When selling naked calls - theoretically you are able to lose an INFINITE amount of money, so in order to sell this type of options you have to maintain a certain level of cash in your account. If you fail to maintain this level you will enter into whats often referred to as a ""margin-call"". And yes they will call your phone and tell you :). Your broker has the right to liquidate your positions in order to meet requirements. PS: From experience my broker has never liquidated any of my holdings, but then again I've never been in a margin call for longer then a few days and never with a severe amount. The margin requirement for investors is regulated and brokers follow these regulations." EDIT: After reading one of the comments on the original question, I realized that there is a much more intuitive way to think about this. If you look at it as a standard PV calculation and hold each of the cashflows constant. Really what's happening is that because of inflation the discount rate isn't the full value of the interest rate. Really the discount rate is only the portion of the interest rate above the inflation rate. Hence in the standard perpetuity PV equation PV = A / r r becomes the interest rate less the inflation rate which gives you PV = A / (i - g). That seems like a much better way to get to the answer than all the machinations I was originally trying. Original Answer: I think I finally figured this out. The general term for this type of system in which the payments increase over time is a gradient series annuity. In this specific example since the payment is increasing by a percentage each period (not a constant rate) this would be considered a geometric gradient series. According to this link the formula for the present value of a geometric gradient series of payments is: Where P is the present value of this series of cashflows.   A_1 is the initial payment for period 1 (i.e. the amount you want to withdraw adjusted for inflation).   g is the gradient or growth rate of the periodic payment (in this case this is the inflation rate)   i is the interest rate   n is the number of payments This is almost exactly what I was looking for in my original question. The only problem is this is for a fixed amount of time (i.e. n periods). In order to figure out the formula for a perpetuity we need to find the limit of the right side of this equation as the number of periods (n) approaches infinity. Luckily in this equation n is already well isolated to a single term: (1 + g)^n/(1 + i)^-n}. And since we know that the interest rate, i, has to be greater than the inflation rate, g, the limit of that factor is 0. So after replacing that term with 0 our equation simplifies to the following: Note: I don't do this stuff for a living and honestly don't have a fantastic finance IQ. It's been a while since I've done any calculus or even this much algebra so I may have made an error in the math.