Adjustable-rate mortgage securities (ARMS)
Mortgage-backed securities where the underlying asset is a pool of Adjustable rate mortgages.
An option that can be exercised on any day until its expiration date. In most cases, an American option is more valuable to the buyer and hence costlier than a European option.
Amortizing interest rate swap
Swap in which the principal or notional amount declines over time.
Arbitrage Pricing Theory (APT)
An alternative model to the capital asset pricing model developed by Stephen Ross and based purely on arbitrage arguments. The APT implies that there are multiple risk factors that need to be taken into account when calculating risk-adjusted performance or alpha.
An option whose payoff depends upon the average price of the underlying asset. As a result of this averaging feature, Asian options have a lower volatility and hence cheaper relative to their European counterparts.
A digital option that pays the value of the underlying security if the option expires in the money.
An autocallable is a strucured product that automatically gets exercised before the scheduled maturity date, if certain predetermined market conditions are realized. For example, a triggering event may be the underlying index breaching a predetermined level. Autocallable is one of the most widely traded OTC structured products.
Autoregression is a time series model used in statistical analysis, which uses past observations as input to predict future values.
An AR(p) model is an autoregressive model where specific lagged values of yt are used as predictor variables. The value of p is called the order. AR1 is the first order process, meaning that future value depends upon immediately preceding value. Similarly, AR2 is the second order process, meaning that future value depends upon the previous two values.
The AR(p) model is defined as:
yt = δ + θ1yt-1 +θ2yt-2 + … + θpyt-1 + εt
yt-1, yt-2…yt-p are the past series values
εt is white noise (randomness)
and δ is constant
An option that whose payoff depends on whether the price of the underlying asset crosses a predetermined barrier. There are two kinds of barrier options – Knock in and Knock out. Knock in options get activated only when the barrier is breached wheras knock out options get deactivated when the barrier is breached.
An option whose payoff is dependent on multiple underlying assets.
Holder of a Bermudan option has a right to exercise the option on multiple prespecified observation dates.
Best-of option is a basket option whose payoff at maturity is based on the best performer among all the underlying assets.
The price volatility of a financial instrument relative to the price volatility of a market or index. A high-beta instrument is riskier than a low-beta instrument.
Beating the gun
In the context of general equities, gaining an advantageous price in a trade through a quick response to market developments.
An option which pays a fixed amount/asset if the option expires in the money and nothing otherwise. Note the discontinuos nature of the payoff.
A method which assumes that the probability over time of price or interest rate follows a binomial distribution. At any time step, the price or rate can move to two possible values (one higher and one lower).
Black Box Trading
A black box trading or algorithmic trading or automated trading is a computerized trading system that utilizes pre-programmed logic to generate buy and sell orders. Black box system is named as such since the user need not see or need not know the mathematical calculations or the logic used in the trading strategy while placing an order.
Black-Derman-Toy (BDT) Model
A one-factor log-normal interest rate model where the single source of randomness is the short-term rate. The inputs into the model are the observed term structure of spot interest rates and their volatility term structure.
A closed form solution developed assuming constant volatility for European style options.
A debt instrument through which corporates and government raise money.
The right to sell a bond back to the issuer (put) or to redeem a bond from its current owner (call) at a specific price and on a specific date.
A butterfly spread is a limited risk, neutral options trading strategy. Butterfly spread uses four options contracts with the same expiration but with three different strike prices. It can be constructed using either puts or calls.
Buy 1 ITM call (Lower Strike)
Sell 2 ATM calls
Buy 1 OTM call (Higher Strike)
Suppose XYZ stock is trading at $50 and the contract lot size is 100. A trader enters a long call butterfly by purchasing a call at strike $40 for $1100, writing two ATM calls at $50 for $400 each and purchasing another call at $60 for $100. The net debit taken to enter these positions is $400.
At expiration, if the XYZ stock is still trading at $50. The ATM calls and OTM call expire worthless while the call at the strike of $40 still has an intrinsic value of $1000. Subtracting the initial debit of $400, the resulting profit is $600, which is also his maximum profit.
When the stock is trading below $40, all the options expires worthless and loss occurs which is the initial debt taken. When the stock is trading above $60, any profit from the two long calls will be neutralized by the loss from the two short calls. In both situations, the butterfly trader suffers loss which is the initial debit of $400 taken to enter the trade. This is the maximum possible loss that one can incur in the strategy.
A strategy that involves buying and selling options or futures with the same (strike) price but different maturities.
An option that gives its holder the right to buy a certain quantity of a stock or commodity for a specified price at a specified time.
An option that gives its holder the right to enter into an interest rate swap in which the buyer of the option pays the fixed rate and receives the floating rate.
A bond that gives the issuer the right to buy back the bond at a predetermined price at specified future dates. The embedded call option reduces the price of the bond.
Interest-rate option that guarantees that the rate on a floating-rate loan will not exceed a certain predetermined level. Normally a Cap is a multi period agreement where the floating rate in any period is determined by the equation Rate = Max(CAP, floating rate loan).
An interim cap component in a multiperiod interest-rate cap agreement.
A digital option that pays some fixed amount of cash at expiry if the option expires in the money and zero otherwise.
A path dependent option that can be perceived as a prepurchased series of ‘At the money’ future start options. The strike prices for these options being set on predetermined observation dates. Consider a three year cliquet with reset dates each year. The first would payoff at the end of the first year and has the same payoff as a normal ATM option. The second year’s payoff has the same payoff as a two year option, but with strike equal to the stock price at the end of the first year and similarily for the third year.
Collateralized Bond Obligation (CBO)
Investment-grade bonds backed by a collection of junk bonds with different levels of risk, called tiers, that are determined by the quality of junk bond involved. CBOs backed by highly risky junk bonds receive higher interest rates than other CBOs.
Collateralized Debt Obligation (CDO)
A general inclusive term which covers Collateralized Bond Obligations, Collateralized Loan Obligations, and Collateralized Mortgage Obligations.
Cornering the Market
Purchasing a security or commodity in such volume as to achieve control over its price. An illegal practice.
Brothers Nelson Bunker Hunt and William Herbert Hunt attempted to corner the world silver markets in the late 1970s and early 1980s, at one stage holding the rights to more than half of the world’s deliverable silver. During the Hunts’ accumulation of the precious metal, silver prices rose from $11 an ounce in September 1979 to nearly $50 an ounce in January 1980. Silver prices ultimately collapsed to below $11 an ounce two months later, much of the fall occurring on a single day now known as Silver Thursday, due to changes made to exchange rules regarding the purchase of commodities on margin.
On July 17, 2010, Armajaro Asset Management purchased 240,100 tonnes of cocoa. The buyout caused cocoa prices to rise to their highest level since 1977. The purchase was valued at £658 million and accounted for 7 per cent of annual global cocoa production. The transaction, the largest single cocoa trade in 14 years, was carried out by Armajaro Holdings, a hedge fund co-founded and managed by Anthony Ward. Ward was dubbed “Chocfinger” by fellow traders for his exploits. The nickname is a reference to both the Bond villain Goldfinger and a British confection.
An option that gives its buyer the right to buy or sell an option at a prespecified price at a prespecified date.
Constant Maturity Swap
Interest rate swap where one of payment leg is a constant maturity rate. This constant maturity rate is the yield on an instrument with a longer life than the length of the reset period, so the parties to a constant maturity swap have exposure to changes in a longer-term market rate.
Credit Default Swap
A swap where one party (buying protection) pays a fixed periodic fee, generally a percentage of the notional amount in return of a contingent payment by the counterparty (selling protection) if a prespecified credit event occurs.
A currency swap, sometimes referred to as a cross-currency swap, involves the exchange of interest—and sometimes of principal—in one currency for the same in another currency. Interest payments are exchanged at fixed dates through the life of the contract.
Consider an example, suppose a US company A wants to start a business in France for which it gets $10 million in the form of a loan from the US market and exchanges this amount with a French company B. Now company A has Euro currency for doing business in France and company B has US currency and they can bear the advantage of foreign exchange earnings.
For bonds or notes, the coupon rate divided by the market price of the bond.
A dark pool is a privately organized financial forum or exchange for trading securities. Dark pools allow institutional investors to trade without exposure until after the trade has been executed and reported. Dark pools are a type of alternative trading system that give certain investors the opportunity to place large orders and make trades without publicly revealing their intentions.
The rate of change of the price of a derivative security relative to the price of the underlying asset.
Delta Neutral Strategy
Delta neutral strategies refer to a portfolio of related financial securities, where portfolio value remains unchanged due to small changes in the value of the underlying security. As such the underlying securities such that positive and negative delta components of options offset, making portfolio’s value being relatively insensitive to changes in the value of the underlying security.
Assume you have a stock position that you believe will increase in price in the long term. You are worried, however, that prices could decline in the short term, so you decide to set up a delta neutral position.
Assume that you own 200 shares of Company X, which is trading at $100 per share. Since the underlying stock’s delta is 1, your current position has a delta of positive 200 (the delta multiplied by the number of shares).
To obtain a delta-neutral position, you need to enter into a position that has a total delta of -200. Assume then you find at-the-money put options on Company X that are trading with a delta of -0.5.
You could purchase 4 of these put options, which would have a total delta of (400 x -0.5), or -200. With this combined position of 200 Company X shares and 4 long at-the-money put options on Company X, your overall position is delta neutral.
A financial instrument whose payout is based or derived from some underlying asset. For example, an option is a derivative instrument based on the underlying asset.
A model in which the model variable for a time step is dependent solely on the model varaible calculated in the previous step.
An option whose payout is either a fixed amount or nothing depending on whether the option expires in the money or not.
A coefficient which is multiplied to the future cash flow to account for the time value of money. A cash flow to be received in future is equivalent to receiving its present value today.
Double Barrier Options
An option with two barriers – one specifying the upper limit for the price of the underlying asset and the other specifying the lower limit for the underlying asset.
An option which gets activated only when when the price of the underlying asset hits the low barrier.
An option which gets deactivated if the price of the underlying asset hits the low barrier.
A option strategy involving going long on an OTM call and an OTM put option.
An option that can be exercised only on its expiration date.
A capital guaranteed structure generally offering the investor the sum invested at maturity and potential upside linked to the performance of the worst-performing asset of the basket of underlying assets. It is one of the Mountain range structured products.
Date when the effect of the announced corporate action on the price is assumed to have taken place.
The price set for buying an asset (call) or selling an asset (put). The strike price.
Any nonstandard option.
Factor investing utilizes multiple factors, including macroeconomic as well as fundamental and statistical, are used to analyze and explain asset prices and build an investment strategy. Factors that have been identified by investors include: growth vs. value; market capitalization; credit rating; and stock price volatility – among several others.
A distribution where the probability of extreme events is higher than the proposed distribution.
The May 6, 2010, flash crash, also known as the crash of 2:45 or simply the flash crash, was a United States trillion-dollar stock market crash, which started at 2:32 p.m. EDT and lasted for approximately 36 minutes.
A type of HFT trading wherein an exchange will “flash” information about buy and sell orders from market participants to HFT firms for a few fractions of a second before the information is made available to the public. Flash trading is controversial because HFT firms can use this information edge to trade ahead of pending orders, which can be construed as front running.
U.S. Senator Charles Schumer had urged the Securities and Exchange Commission in July 2009 to ban flash trading, saying that it created a two-tiered system where a privileged group received preferential treatment, while retail and institutional investors were put at an unfair disadvantage and deprived of a fair price for their transactions.
Fixed Lookback Option
Strike price is fixed at purchase. The underlying is priced at its highest or lowest level, depending whether it is a call or put, during the life of the option rather than expiring at market.
Floating Lookback Option
Strike price is fixed at maturity. For a call, the price is fixed at the lowest price during the life of the option; for a put it is fixed at the highest price.
Interest-rate option that guarantees that the rate on a floating-rate loan will not fall below a certain level. Normally a multiperiod agreement.
One of the interim period floors in a multiple period floor agreement.
Future rates of a bond calculated from the available yield curve of traded zero coupon bonds.
Forward Start Option
An option that becomes activated after a future date.
GameStop, an American video game retailer, had been struggling, especially during the pandemic, so its share price was low. Wall Street saw this as an opportunity—they bet on the decline of the company’s stock.
However, in an attempt to stick it to the man (and make some money in the process) small investors who belong to the subreddit r/WallStreetBets, got together and bought so much of GameStop shares, its price went through the roof. They were motivated first by a view that the fundamentals were better than the price would suggest, but more importantly by the view that as a group they could force other investors—namely, hedge funds who’d made bets that the price of the stock would go down—to buy shares at these higher prices. The rest is history.
The rate of change of delta for a derivative security relative to the price of the underlying asset.
An option in which the strike price determines the size of the payoff, but a different constant determines whether or not the payoff is made.
Payoff call = S-X2 if S>X1 else 0
Payoff put = X2-S if S1 else 0
X1 is called Gap and X2 is called Strike.
Heath-Jarrow-Morton (HJM) Model
A multifactor interest rate model that requires two inputs: the initial yield curve and a volatility structure for the forward.
A financial transaction that reduces or offsets the risk on an existing open fiancial position.
High Low Option
An option that pays the difference between the high and the low of the underlying asset during the life of the option.
Ho Lee Model
A single factor interest rate model that makes a simplying assumption of constant volatility of term structure.
Value of the volatility embedded in the option price.
A collection of financial assets. A portfolio.
Loans of $1 billion or more. Or, loans that exceed the statutory size limit eligible for purchase or securitization by the federal agencies.
The Kelly Criterion is a mathematical formula that helps investors and gamblers calculate what percentage of their money they should allocate to each investment or bet.
John Kelly, who worked for AT&T’s Bell Laboratory, originally developed the Kelly Criterion to assist AT&T with its long-distance telephone signal noise issues. Soon after, the method was published as “A New Interpretation of Information Rate” in 1956. However, the gambling community got wind of it and realized its potential as an optimal betting system in horse racing. Today, many people use it as a general money management system for gambling as well as investing.
A barrier option that gets activated when a predetermined barrier is hit. Two kinds of Knock-in option are Up-and-In and Down-and-In.
A barrier option that gets deactivated when a predetermined barrier is hit. Two kinds of Knock-in option are Up-and-Out and Down-and-Out.
A path-dependent option whose payout increases stepwise as the underlying trades hits prespecified barrier levels (the ‘rungs’ of the ladder). Each time the underlying asset hits the new barrier, the option payout is locked-in at the higher level.
The practice of buying or selling an instrument based on the difference between the consolidated and direct feeds. A term used to refer to the idea that firms have different capacities to receive and process public market data; some firms – typically those employing HFT technology – make investment decisions to co-locate with exchanges in order to minimize data processing time (or latency) as much as possible because they regard it as necessary to facilitate their strategies.
Least Squares Method
A mathematical method of determining the best fit of a curve to a series of observations by choosing the curve that minimizes the sum of the squares of all deviations from the curve.
An European style option whose payout depends on the performance of the underlying assets that remain after a certain number of worst and/or best performers are removed from the basket on a prespecified date before maturity.
A path dependent option whose payoff depends on either the high or the low of the underlying asset during the life of the option. Two kinds of Lookback options are Fixed Lookback option and Floating Lookback option.
Low volatility anomaly
The low volatility anomaly refers to the finding that stocks exhibiting lower volatility achieve higher returns than can be explained by the efficient market theory.
The tendency of a variable to return to its mean value in the long run.
Monte Carlo Simulations
A derivatives valuation technique in which a number of underlying spot paths are generated. A discounted average of the payoffs for these scenarios is the approximate price of the option.
A multi-factor model employs a set of different factors in its computations in order to analyze and explain market phenomena, as well as equilibrium prices of an asset. A multi-factor model can be used to analyze the returns of individual securities but also of entire portfolios.
A typical example is the famous Fama-French Three-factor model, an asset pricing model introduced back in the early 1990s by future Nobel prize laureate Eugene Fama and fellow researcher Kenneth French.
A unhedged open position in the option.
Open Ended Product
A structured product with no expiry.
The Optimal F system of money management was devised by Ralph Vince, and he’s written several books about this and other money management issues. The idea is that you determine the ideal fraction of your money to allocate per trade based on past performance. If your Optimal F is 18%, then each trade should be 18 percent of your account. F is a factor based on the basis of historical data, and the risk is the biggest percentage loss that you experienced in the past. Using these numbers and the current price, you can find the contracts or shares you need to buy.
An option gives the right but not the obligation to buy or sell the underlying at a prespecified strike price on or before the agreed maturity.
Palladium is range structured product that takes long positions on the best performing stocks and short positions on the worst performing stocks of a basket.
Parisian Barrier Option
A kind of a barrier option in which the barrier is trigger only if the underlying spot meets the barrier condition for a specified time period.
Refers to the tactic of entering small marketable orders—usually for 100 shares—in order to learn about large hidden orders in dark pools or exchanges. While you can think of pinging as being analogous to a ship or submarine sending out sonar signals to detect upcoming obstructions or enemy vessels, in the HFT context, pinging is used to find hidden “prey.” This “electronic front-running” happens because the high-frequency traders have an advantage in terms of speed, and because “the stock market” doesn’t really exist — what exists are many stock exchanges in a trading network.
A full capital guarenteed structured product where the annual coupon payments are linked to the number of assets in the basket meeting a prespecified performance criteria.
An option where the payoff is linked to underlying price at expiry raised to some power.
A collection of financial assets. Also called an instrument set.
An basket option where the payoff is linked to difference between the performance of the portfolio and the a prespecified strike.
An option that gives its holder the right to sell an asset for a prespecified price on or before a prespecified date.
An option that gives its holder the right to enter into an interest rate swap to receives fixed rate and pays floating rate.
A bond that allows the holder to redeem the bond at a predetermined price at specified future dates. The bond contains an embedded put option; that makes the bond costlier than bonds without the put option.
A quanto is a type of derivative in which the underlying is denominated in one currency, but the instrument itself is settled in another currency at some fixed rate.
An abusive market practice whereby a large number of orders to buy or sell a financial instrument are placed and cancelled immediately afterwards.
A single option linked to two or more underlying assets. In order for the option to pay off, all the underlying assets must move in the intended direction.
A range note is a structured note, which pays a coupon for each day that the underlying spot stays within a prespecified range (sometimes called the accrual corridor).
A trading strategy whereby the value of a portfolio after rebalancing is equal to its value at any previous time.
The Sharpe ratio describes the extent to which an investment compensates for extra risk. This ratio is also called the risk-return ratio. The higher the ratio, the higher the risk compensation an investment offers.
A path-dependent option that allows the investor to lock in profits if he thinks the market has reached a high (for a call) or low (for a put). The strike is set at the price at which the investor shouts.
Technology that determines to which exchanges orders or trades are sent. Smart routers can be programmed to send out pieces of large orders (after they are broken up by a trading algorithm) so as to get cost-effective trade execution.
The current interest rate appropriate for discounting a cash flow of some given maturity.
A model that contains a random variable the outcome of which is based on probability.
Volatility of an underlying assumed to be driven by a stochastic process.
An option strategy in which the buyer takes a long position on a call and a put on the same underlying asset with same strike and maturity. Straddle is a good investment strategy if the investor expects a large movement in the price of the underlying asset but is not sure about the direction of the movement.
An option strategy similar to Straddle. The buyer goes long on an out of the money call and an out of the money put with same strike and maturity.
Exercise price for a put or call option.
A digital option that pays out a proportion of the assets underlying a portfolio if the asset lies between a prespecified range at the expiry of the option.
A contract between two parties to exchange cash flows in the future based on agreed predetermined formulas.
A contract that gives its holder the option to enter into a swap on a later date.
Change is option price on decrease of one day from time to maturity.
A model in which the basic assumption is that prices or rates can move to one of three possible values over any short time period. At any time step the price or rate direction can be upward, neutral, or downward.
A barrier option which gets activated only when the underlying asset price rises above the prespecified barier level.
A barrier option which gets deactivated when the underlying asset price rises above rge prespecified barrier level.
Equities realize better returns if their current value is higher than their current price. A value strategy makes use of valuation ratios to select stocks that are attractively priced relative to their fundamentals. Frequently used ratios are price-to-book and price-earnings ratios.
A common option, such as a European put or call.
Rate of change of option vega with respect to the change in the underlying asset.
A simple swap agreement where one party pays fixed and the counter party pays floating rate.
Value At Risk (VAR) represents the total proportion of market value that is at risk or faces risk due to speculation, due to uncertainty in market caused by presence of an external or un-systemic risk or internal risk parameter or systemic risk. Algorithmic trading is able to capitalize on VAR estimation, to capitalize on risk estimation, and bring down value of traded security in the market.
The rate of change in the price of a derivative security relative to the volatility of the underlying security.
Implied volatility versus strike graph is typically smile shaped and hence called a ‘volatility smile’. The underlying distribution is found to be leptokurtic and hence the observed option prices of out of the money options are found to be higher.
Weighted average cost of capital (WACC)
Expected return on a portfolio of all a firm’s securities. Used as a hurdle rate for capital investment. Often the weighted average of the cost of equity and the cost of debt The weights are determined by the relative proportions of equity and debt in a firm’s capital structure.
Fifth letter of a Nasdaq stock symbol indicating that listing is a mutual fund.
The interest rate that will make the present value of the future cashflows from an investment equal to the price of thr investment.
Applies mainly to convertible securities. Difference in current yield between the convertible and the underlying common.
Term structure of yield rates.
A portfolio constructed to have zero systematic risk, that is, having a beta of zero.
A term structure of yields for zero-coupon bonds – zero rates versus maturity dates.
Zero-Coupon Bond, Or Zero
A bond without interim coupon payments. It is sold at at a discount to the notional and on maturity the notional is returned.