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Finance

Monte Carlo methods for option pricing

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

Securities & exchanges

Mortgage-backed security

A mortgage-backed security (MBS) is a type of asset-backed security (an "instrument") which is secured by a mortgage or collection of mortgages. The mortgages are aggregated and sold to a group of individuals (a government agency or investment bank) that securitizes, or packages, the loans together into a security that investors can buy. Bonds securitizing mortgages are usually treated a

Finance

Naked option

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

Securities & exchanges

Net volatility

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.

Networks

Olympics Go! Paris 2024

Olympics Go! Paris 2024 (stylized as Olympics GO! Paris 2024) is a 2024 city-building and sports video game published by nWay and officially licensed with the International Olympic Committee (IOC) to coincide with the 2024 Summer Olympics.

Finance

Option (finance)

In finance, an option is a contract which conveys to its owner, the holder, the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or instrument at a specified strike price on or before a specified date, depending on the style of the option.

Finance

Option naming convention

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

Finance

Option style

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

Finance

Option time value

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.

Finance

Options strategy

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

Finance

Original sin (economics)

Original sin is a term in economics literature, proposed by Barry Eichengreen, Ricardo Hausmann, and Ugo Panizza in a series of papers to refer to a situation in which "most countries are not able to borrow abroad in their domestic currency."

Securities & exchanges

Overnight indexed swap

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

Assets

Perpetual futures

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

Securities & exchanges

Pin risk

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

Securities & exchanges

Power reverse dual-currency note

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

Fiat currencies

Price level

The general price level is a hypothetical measure of overall prices for some set of goods and services (the consumer basket), in an economy or monetary union during a given interval (generally one day), normalized relative to some base set. Typically, the general price level is approximated with a daily price index, normally the Daily CPI. The general price level can change more than on

Securities & exchanges

Property derivative

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

Fiat currencies

Purchasing power parity

Purchasing power parity (PPP) is a measure of the price of specific goods in different countries and is used to compare the absolute purchasing power of the countries' currencies. PPP is effectively the ratio of the price of a market basket at one location divided by the price of the basket of goods at a different location. The PPP inflation and exchange rate may differ from the market e

Finance

Put option

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

Trading basics

Put–call parity

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

Finance

Rainbow option

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.

Securities & exchanges

Ratio spread

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

Securities & exchanges

Real estate derivative

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

Finance

Real options valuation

Real options valuation, also often termed real options analysis, (ROV or ROA) applies option valuation techniques to capital budgeting decisions. A real option itself, is the right—but not the obligation—to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. For example, real options valuation could exami

Finance

Recovery swap

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.

Fiat currencies

Renminbi currency value

Renminbi currency value is a debate affecting the Chinese currency unit, the renminbi (Chinese: 人民币 Code:CNY). The renminbi is classified as a managed floating exchange rate currency "with reference to a basket of currencies", which has drawn attention from nations which have freely floated currencies and has become a source of trade friction with Western nations.

Finance

Risk reversal

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.

Finance

Risk-free rate

The risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payments over a fixed period of time that is assumed to meet all payment obligations.

Securities & exchanges

SABR volatility model

In mathematical finance, the SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the parameters of the model. The SABR model is widely used by practitioners in the financial industry, especially in the interest rate derivative markets. It was developed by Patric

Trading basics

Season ticket

A season ticket or season pass is a ticket valid for multiple events, typically providing access to an entire season of games or performances at a specific venue or within a particular activity, such as sports matches or public transportation services. Season tickets are commonly issued by sports organizations, theaters, and transit authorities to ensure customers have secured access for

Finance

Securities market participants (United States)

Securities market participants in the United States include corporations and governments issuing securities, persons and corporations buying and selling a security, the broker-dealers and exchanges which facilitate such trading, banks which safe keep assets, and regulators who monitor the markets' activities. Investors buy and sell through broker-dealers and have their assets retained b

Securities & exchanges

Single-stock futures

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.

Trading basics

Slippage (finance)

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.

Fiat currencies

Special drawing rights

Special drawing rights (SDRs, code XDR) are a supplementary foreign exchange reserve asset defined and maintained by the International Monetary Fund (IMF). SDRs are the units of account for the IMF, and not a currency; rather, SDR value is based on a basket of currencies, the specific composition of which is reviewed every five years. SDRs represent a claim to currency held by IMF member

Trading basics

Sports betting

Sports betting is the activity of predicting sports results and placing a wager on the outcome.

Finance

Spot contract

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

Securities & exchanges

Spread option

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

Assets

Stablecoin

A stablecoin is a type of cryptocurrency that aims to maintain a stable value relative to a specified asset, a pool or basket of assets. The specified asset might refer to fiat currency, commodity, or other cryptocurrencies. Despite the name, stablecoins are not necessarily stable. Stablecoins rely on stabilization tools such as reserve assets or algorithms that match supply and demand

Securities & exchanges

Stochastic volatility

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

Securities & exchanges

Stock market index future

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.

Finance

Straddle

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.

Securities & exchanges

Strangle (options)

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

Securities & exchanges

Strike price

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,

Securities & exchanges

Swap (finance)

In finance, a swap is a derivative in which two parties agree to exchange one stream of cash flows for another, based on some agreed formula. An example is a floating-for-fixed interest rate swap, which calls for (a) payments by one party based on the product of a floating interest rate and a fixed amount, called the notional, in exchange for (b) payments by the counterparty based on the

Securities & exchanges

Synthetic position

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

Fiat currencies

Tally stick

A tally stick (or simply a tally) was an ancient memory aid used to record and document numbers, quantities, and messages. Tally sticks first appear as animal bones carved with notches during the Upper Palaeolithic; a notable example is the Ishango Bone. Historical reference is made by Pliny the Elder (AD 23–79) about the best wood to use for tallies, and by Marco Polo (1254–1324) who me

Trading basics

Total return swap

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.

Trading basics

Treasury basis trade

Treasury basis trading is a financial strategy that involves taking offsetting positions in a cash market instrument (typically a U.S. Treasury bond) and its related derivative, such as a Treasury futures contract. The strategy seeks to exploit pricing discrepancies between the two instruments, which are expected to converge over time. It is a specialized form of basis trading applied to

Finance

Trinomial tree

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.

Finance

Turbo warrant

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

Fiat currencies

U.S. Dollar Index

The U.S. Dollar Index (USDX, DXY, DX, or, informally, the "Dixie") is an index (or measure) of the value of the United States dollar relative to a basket of foreign currencies, often referred to as a basket of U.S. trade partners' currencies. The Index goes up when the U.S. dollar gains "strength" (value) when compared to other currencies.

Finance

Valuation of options

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

Securities & exchanges

Vanna–Volga pricing

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.

Banking

Variance swap

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.

Finance

Volatility arbitrage

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

Securities & exchanges

Volatility swap

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

Securities & exchanges

Warrant (finance)

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.

Securities & exchanges

Weather derivative

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

Securities & exchanges

Year-on-year inflation-indexed swap

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.

Securities & exchanges

Zero coupon swap

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).

Securities & exchanges

Zero-coupon inflation swap

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).