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Low-volatility investing is an investment style that buys stocks or securities with low volatility and avoids those with high volatility. This investment style exploits the low-volatility anomaly. According to financial theory risk and return should be positively related, however in practice this is not true. Low-volatility investors aim to achieve market-like returns, but with lower ris

In probability theory and related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes. In particular, it allows the computation of derivatives of random variables. Malliavin calculus is also called the stochastic calculus of variations. P. Malliavin firs

In finance, margin is the collateral that a holder of a financial instrument has to deposit with a counterparty (most often a broker or an exchange) to cover some or all of the credit risk the holder poses for the counterparty. This risk can arise if the holder has done any of the following:

In mathematical finance, Margrabe's formula is an option pricing formula applicable to an option to exchange one risky asset for another risky asset at maturity. It was derived by William Margrabe in 1978. Margrabe's paper has been cited by over 2000 subsequent articles.

In finance, the Markowitz model ─ put forward by Harry Markowitz in 1952 ─ is a portfolio optimization model;

In finance, moneyness is the relative position of the current price (or future price) of an underlying asset (e.g., a stock) with respect to the strike price of a derivative, most commonly a call option or a put option. Moneyness is firstly a three-fold classification:

In mathematical finance, a Monte Carlo option model uses Monte Carlo methods to calculate the value of an option with multiple sources of uncertainty or with complicated features. The first application to option pricing was by Phelim Boyle in 1977 (for European options). In 1996, M. Broadie and P. Glasserman showed how to price Asian options by Monte Carlo. An important development was

In statistics, a moving average (rolling average or running average or moving mean or rolling mean) is a calculation to analyze data points by creating a series of averages of different selections of the full data set. Variations include: simple, cumulative, or weighted forms.

In portfolio theory, a mutual fund separation theorem, mutual fund theorem, or separation theorem is a theorem stating that, under certain conditions, any investor's optimal portfolio can be constructed by holding each of certain mutual funds in appropriate ratios, where the number of mutual funds is smaller than the number of individual assets in the portfolio. Here a mutual fund refer

A naked option or uncovered option is an options strategy where the options contract writer (i.e., the seller) does not hold the underlying asset to cover the contract in case of assignment (like in a covered option). Nor does the seller hold any option of the same class on the same underlying asset that could protect against potential losses (like in an options spread). A naked option i

Net volatility refers to the volatility implied by the price of an option spread trade involving two or more options. Essentially, it is the volatility at which the theoretical value of the spread trade matches the price quoted in the market, or, in other words, the implied volatility of the spread.

In financial markets, an option naming convention is a method of identifying which of many possible options is being quoted or traded.

In finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options—as well as others where the payoff is calculated similarly—are referred to as "vanilla options". Options where the payoff is calculated differe

In finance, the time value (TV) (extrinsic or instrumental value) of an option is the premium a rational investor would pay over its current exercise value (intrinsic value), based on the probability it will increase in value before expiry. For an American option this value is always greater than zero in a fair market, thus an option is always worth more than its current exercise value.

Option strategies are the simultaneous, and often mixed, buying or selling of one or more options that differ in one or more of the options' variables. Call options, simply known as Calls, give the buyer a right to buy a particular stock at that option's strike price. Opposite to that are Put options, simply known as Puts, which give the buyer the right to sell a particular stock at the

An overnight indexed swap (OIS) is an interest rate swap (IRS) over some given term, e.g. 10Y, where the periodic fixed payments are tied to a given fixed rate while the periodic floating payments are tied to a floating rate calculated from a daily compounded overnight rate over the floating coupon period. The OIS term is not overnight; it is the underlying reference rate that is an over

In finance, perpetual futures, also known as perpetual swaps or colloquially as perps, are contract agreements to non-optionally buy or sell an asset at an unspecified point in the future. Perpetual futures are cash-settled, and they differ from regular futures in that they lack a pre-specified delivery date and can thus be held indefinitely without the need to roll over contracts as the

Pin risk occurs when the market price of the underlier of an option contract at the time of the contract's expiration is close to the option's strike price. In this situation, the underlier is said to have pinned. The risk to the writer (seller) of the option is that they cannot predict with certainty whether the option will be exercised or not. So the writer cannot hedge their position

Portfolio optimization is the process of selecting an optimal portfolio (asset distribution), out of a set of considered portfolios, according to some objective. The objective typically maximizes factors such as expected return, and minimizes costs like financial risk, resulting in a multi-objective optimization problem. Factors being considered may range from tangible (such as assets, l

A dual-currency note (DC) pays coupons in the investor's domestic currency with the notional in the issuer's domestic currency. A reverse dual-currency note (RDC) is a note which pays a foreign interest rate in the investor's domestic currency. A power reverse dual-currency note (PRDC) is a structured product where an investor is seeking a better return and a borrower a lower rate by tak

Precautionary saving is saving (non-expenditure of a portion of income) that occurs in response to uncertainty regarding future income. The precautionary motive to delay consumption and save in the current period rises due to the lack of completeness of insurance markets. Accordingly, individuals will not be able to insure against some bad state of the economy in the future. They anticip

In finance and mathematics, predictive modelling is the use of statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event, regardless of when it occurred. For example, predictive models are often used to detect crimes and identify suspects, after the crime has taken place.

A property derivative is a financial derivative whose value is derived from the value of an underlying real estate asset. In practice, because individual real estate assets fall victim to market inefficiencies and are hard to accurately price, property derivative contracts are typically written based on a real estate property index. In turn, the real estate property index attempts to a

In finance, a put or put option is a derivative instrument in financial markets that gives the holder (i.e. the purchaser of the put option) the right to sell an asset (the underlying), at a specified price (the strike), by (or on) a specified date (the expiry or maturity) to the writer (i.e. seller) of the put. The purchase of a put option is interpreted as a negative sentiment about th

In financial mathematics, the put–call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to (and hence has the same value as) a single forward contract at this strike price and expiry. This is because if the p

In finance, a Rainbow option is a derivative whose payoff depends on multiple underlying risky assets. Each underlying asset is referred to as a color of the rainbow. It contrasts with a simple option that is exposed to one source of uncertainty, such as the price of underlying asset.

A ratio spread or frontspread is a multi-leg options position. Like a vertical, the ratio spread involves buying and selling options on the same underlying security with different strike prices and the same expiration date. In this spread, the number of option contracts sold is not equal to a number of contracts bought. An unequal number of options contracts gives this spread certain u

In financial economics, rational pricing is the assumption that asset pricing models must reflect the arbitrage-free price of the asset

A real estate derivative is a financial instrument whose value is based on the price of real estate. The core uses for real estate derivatives are: hedging positions, pre-investing assets and re-allocating a portfolio. The major products within real estate derivatives are: swaps, futures contracts, options (calls and puts) and structured products. Each of these products can use a differ

Realized variance or realised variance (RV, see spelling differences) is the sum of squared returns. For instance, the RV can be the sum of squared daily returns for a particular month, which would yield a measure of price variation over this month. More commonly, the realized variance is computed as the sum of squared intraday returns for a particular day.

In finance, recovery swaps, recovery locks, or recovery default swaps (RDS) are derivative contracts related to credit default swaps, and reference a bond issuance as its underlying. They are designed to provide a hedge against the uncertainty of recovery in default.

In finance, risk reversal (also known as a conversion when an investment strategy) can refer to a measure of the volatility skew or to a trading strategy.

In actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key quantities of interest are the probability of ruin, distribution of surplus immediately prior to ruin, and deficit at time of ruin.

A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written

In finance, a single-stock future (SSF) is a type of futures contract between two parties to exchange a specified number of stocks in a company for a price agreed today (the futures price or the strike price) with delivery occurring at a specified future date, the delivery date. The contracts can be later traded on a futures exchange.

In finance and the stock market, slippage is the difference between the execution price expected by the trader (usually the one indicated by the trading software) and the one at which the transaction actually happens. Market impact, liquidity, and frictional costs may contribute to slippage.

The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating a stochastic process. The Snell envelope is named after James Laurie Snell.

The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside variance equally. Though both ratios measure an investment's risk-adjusted return, they do s

In finance, a spot contract, spot transaction, or simply spot, is a contract of buying or selling a commodity, security or currency for immediate settlement (payment and delivery) on the spot date, which is normally two business days after the trade date. The settlement price (or rate) is called spot price (or spot rate). A spot contract is in contrast with a forward contract or futures

In finance, a spread option is a type of option where the payoff is based on the difference in price between two underlying assets. For example, the two assets could be crude oil and heating oil; trading such an option might be of interest to oil refineries, whose profits are a function of the difference between these two prices. Spread options are generally traded over the counter, rath

In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field of mathematical finance to evaluate derivative securities, such as options. The name derives from the models' treatment of the underlying security's volatility as a random process, governed by state variables such as the price leve

In finance, a stock market index future is a cash-settled futures contract on the value of a particular stock market index. The turnover for the global market in exchange-traded equity index futures is notionally valued, for 2008, by the Bank for International Settlements at US$130 trillion.

In finance, a straddle strategy involves two transactions in options on the same underlying, with opposite positions. One holds long risk, the other short. As a result, it involves the purchase or sale of particular option derivatives that allow the holder to profit based on how much the price of the underlying security moves, regardless of the direction of price movement.

In finance, a strangle is an options strategy involving the purchase or sale of two options, allowing the holder to profit based on how much the price of the underlying security moves, with a neutral exposure to the direction of price movement. A strangle consists of one call and one put with the same expiry and underlying but different strike prices. Typically the call has a higher stri

In finance, the strike price (or exercise price) of an option is a fixed price at which the owner of the option can buy (in the case of a call), or sell (in the case of a put), the underlying security or commodity. The strike price may be set by reference to the spot price, which is the market price of the underlying security or commodity on the day an option is taken out. Alternatively,

In finance, a synthetic position is a way to create the payoff of a financial instrument using other financial instruments.

Tax loss harvesting (TLH) refers to a category of tax-efficient investment strategies that seek to accelerate the realization of capital losses and defer the realization of capital gains.

A Tobin tax was originally defined as a tax on all spot conversions of one currency into another. It was suggested by James Tobin, an economist who won the Nobel Memorial Prize in Economic Sciences. Tobin's tax was originally intended to penalize short-term financial round-trip excursions into another currency. By the late 1990s, the term Tobin tax was being applied to all forms of shor

In finance, a total return swap (TRS), total rate of return swap (TRORS), or cash-settled equity swap is a financial contract that transfers both the credit risk and market risk of an underlying asset.

The trinomial tree is a lattice-based computational model used in financial mathematics to price options on equity. It was developed by Phelim Boyle in 1986. It is an extension of the binomial options pricing model, and is conceptually similar. It can also be shown that the approach is equivalent to the explicit finite difference method for option pricing.

A turbo warrant (or callable bull/bear contract) is a kind of stock option. Specifically, it is a barrier option of the down and out type. It is similar to a vanilla contract, but with two additional features: It has a low vega, meaning that the option price is much less affected by the implied volatility of the stock market, and it is highly geared due to the possibility of knockout. Th

In finance, a price (premium) is paid or received for purchasing or selling options.

Value at risk (VaR) is a measure of the risk of loss of investment/capital. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses.

The Vanna–Volga method is a mathematical tool used in finance. It is a technique for pricing first-generation exotic options in foreign exchange market (FX) derivatives.

A variance swap is an over-the-counter financial derivative that allows one to speculate on or hedge risks associated with the magnitude of movement, i.e. volatility, of some underlying product, like an exchange rate, interest rate, or stock index.

In finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of one-factor short-rate model as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives, and has also been adapted for credit markets. It was introduced in 1977 by Oldřich Vašíček, an

In finance, volatility arbitrage (vol arb) is a term for financial arbitrage techniques directly dependent and based on volatility.

Volatility risk

In finance, a volatility swap is a forward contract on the future realised volatility of a given underlying asset. Volatility swaps allow investors to trade the volatility of an asset directly, much as they would trade a price index. Its payoff at expiration is equal to

The volatility tax is a mathematical finance term first published by Rick Ashburn, CFA in a 2003 column, and formalized by hedge fund manager Mark Spitznagel, describing the effect of large investment losses (or volatility) on compound returns. It has also been called volatility drag, volatility decay or variance drain. This is not literally a tax in the sense of a levy imposed by a gov

In finance, a warrant is a security that entitles the holder to buy or sell stock, typically the stock of the issuing company, at a fixed price called the strike price.

Weather derivatives are financial instruments that can be used by organizations or individuals as part of a risk management strategy to reduce risk associated with adverse or unexpected weather conditions. Weather derivatives are index-based instruments that usually use observed weather data at a weather station to create an index on which a payout can be based. This index could be total

A year-on-year inflation-indexed swap (YYIIS) is a standard derivative product over inflation rate. The underlying is a single consumer price index (CPI). The first swap of this kind was traded through the inter-dealer broker network in November 1999.

In finance, a zero coupon swap (ZCS) is an interest rate derivative (IRD). In particular it is a linear IRD, that in its specification is very similar to the much more widely traded interest rate swap (IRS).

A zero-coupon inflation swap (ZCIS), also called a zero-coupon inflation-indexed swap (ZCIIS), is a standard derivative product whose payoff depends on the inflation rate realized over a given period of time. The underlying asset is a single consumer price index (CPI).