In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of a derivative instrument such as an option to changes in one or more underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters. Collectively these have also been called the risk sensitivities, risk measures or hedge parameters.
In financial mathematics, the implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model, will return a theoretical value equal to the price of said option. A non-option financial instrument that has embedded optionality, such as an interest rate cap, can also have an implied volatility. Implied volatility, a forward-looking and subjective measure, differs from historical volatility because the latter is calculated from known past returns of a security. To understand where implied volatility stands in terms of the underlying, implied volatility rank is used to understand its implied volatility from a one-year high and low IV.
Market risk is the risk of losses in positions arising from movements in market variables like prices and volatility. There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the most commonly used types of market risk are:
A hedge is an investment position intended to offset potential losses or gains that may be incurred by a companion investment. A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, gambles, many types of over-the-counter and derivative products, and futures contracts.
Volatility risk is the risk of an adverse change of price, due to changes in the volatility of a factor affecting that price. It usually applies to derivative instruments, and their portfolios, where the volatility of the underlying asset is a major influencer of option prices. It is also relevant to portfolios of basic assets, and to foreign currency trading.
Rational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.
In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields.
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates. In general, the higher the duration, the more sensitive the bond price is to the change in interest rates. Bond convexity is one of the most basic and widely used forms of convexity in finance. Convexity was based on the work of Hon-Fei Lai and popularized by Stanley Diller.
In finance, the beta is a statistic that measures the expected increase or decrease of an individual stock price in proportion to movements of the stock market as a whole. Beta can be used to indicate the contribution of an individual asset to the market risk of a portfolio when it is added in small quantity. It refers to an asset's non-diversifiable risk, systematic risk, or market risk. Beta is not a measure of idiosyncratic risk.
Monte Carlo methods are used in corporate finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining the distribution of their value over the range of resultant outcomes. This is usually done by help of stochastic asset models. The advantage of Monte Carlo methods over other techniques increases as the dimensions of the problem increase.
Financial risk management is the practice of protecting economic value in a firm by managing exposure to financial risk - principally operational risk, credit risk and market risk, with more specific variants as listed aside. As for risk management more generally, financial risk management requires identifying the sources of risk, measuring these, and crafting plans to mitigate them. See Finance § Risk management for an overview.
Financial risk is any of various types of risk associated with financing, including financial transactions that include company loans in risk of default. Often it is understood to include only downside risk, meaning the potential for financial loss and uncertainty about its extent.
In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: Mathematical finance § Derivatives pricing: the Q world for discussion of the mathematics; Financial engineering for the implementation; as well as Financial modeling § Quantitative finance generally.
In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date. For interest rate derivatives lattices are additionally useful in that they address many of the issues encountered with continuous models, such as pull to par. The method is also used for valuing certain exotic options, where because of path dependence in the payoff, Monte Carlo methods for option pricing fail to account for optimal decisions to terminate the derivative by early exercise, though methods now exist for solving this problem.
The following outline is provided as an overview of and topical guide to finance:
The RiskMetrics variance model was first established in 1989, when Sir Dennis Weatherstone, the new chairman of J.P. Morgan, asked for a daily report measuring and explaining the risks of his firm. Nearly four years later in 1992, J.P. Morgan launched the RiskMetrics methodology to the marketplace, making the substantive research and analysis that satisfied Sir Dennis Weatherstone's request freely available to all market participants.
Fixed-income attribution is the process of measuring returns generated by various sources of risk in a fixed income portfolio, particularly when multiple sources of return are active at the same time.
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. Options are typically acquired by purchase, as a form of compensation, or as part of a complex financial transaction. Thus, they are also a form of asset and have a valuation that may depend on a complex relationship between underlying asset price, time until expiration, market volatility, the risk-free rate of interest, and the strike price of the option. Options may be traded between private parties in over-the-counter (OTC) transactions, or they may be exchange-traded in live, public markets in the form of standardized contracts.
Valuation risk is the risk that an entity suffers a loss when trading an asset or a liability due to a difference between the accounting value and the price effectively obtained in the trade.
A Credit valuation adjustment (CVA), in financial mathematics, is an "adjustment" to a derivative's price, as charged by a bank to a counterparty to compensate it for taking on the credit risk of that counterparty during the life of the transaction. CVA is one of a family of related valuation adjustments, collectively xVA; for further context here see Financial economics § Derivative pricing. "CVA" can refer more generally to several related concepts, as delineated aside. The most common transactions attracting CVA involve interest rate derivatives, foreign exchange derivatives, and combinations thereof. CVA has a specific capital charge under Basel III, and may also result in earnings volatility under IFRS 13, and is therefore managed by a specialized desk.
