Delta neutralIn finance, delta neutral describes a portfolio of related financial securities, in which the portfolio value remains unchanged when small changes occur in the value of the underlying security. Such a portfolio typically contains options and their corresponding underlying securities such that positive and negative delta components offset, resulting in the portfolio's value being relatively insensitive to changes in the value of the underlying security.
Put optionIn 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 the future value of the underlying stock. The term "put" comes from the fact that the owner has the right to "put up for sale" the stock or index.
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. Options are typically acquired by purchase, as a form of compensation, or as part of a complex financial transaction.
Hedge (finance)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.
Call optionIn finance, a call option, often simply labeled a "call", is a contract between the buyer and the seller of the call option to exchange a security at a set price. The buyer of the call option has the right, but not the obligation, to buy an agreed quantity of a particular commodity or financial instrument (the underlying) from the seller of the option at or before a certain time (the expiration date) for a certain price (the strike price). This effectively gives the owner a long position in the given asset.
Derivative (finance)In finance, a derivative is a contract that derives its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the underlying. Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements for speculation, or getting access to otherwise hard-to-trade assets or markets.
Hedge fundA hedge fund is a pooled investment fund that trades in relatively liquid assets and is able to make extensive use of more complex trading, portfolio-construction, and risk management techniques in an attempt to improve performance, such as short selling, leverage, and derivatives. Financial regulators generally restrict hedge fund marketing to institutional investors, high net worth individuals, and accredited investors. Hedge funds are considered alternative investments.
Greeks (finance)In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in 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 (as are some other finance measures). Collectively these have also been called the risk sensitivities, risk measures or hedge parameters. The Greeks are vital tools in risk management.
Bond valuationBond valuation is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate. In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist.
Rational pricingRational 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. Arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets. Where this mismatch can be exploited (i.
Mathematical financeMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.
Binomial options pricing modelIn finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting. The binomial model was first proposed by William Sharpe in the 1978 edition of Investments (), and formalized by Cox, Ross and Rubinstein in 1979 and by Rendleman and Bartter in that same year.
Real options valuationReal 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 examine the opportunity to invest in the expansion of a firm's factory and the alternative option to sell the factory.
GreeksThe Greeks or Hellenes (ˈhɛliːnz; Έλληνες, Éllines ˈelines) are an ethnic group and nation native to Greece, Cyprus, southern Albania, Anatolia, parts of Italy and Egypt, and to a lesser extent, other countries surrounding the Eastern Mediterranean and Black Sea. They also form a significant diaspora (), with many Greek communities established around the world. Greek colonies and communities have been historically established on the shores of the Mediterranean Sea and Black Sea, but the Greek people themselves have always been centered on the Aegean and Ionian seas, where the Greek language has been spoken since the Bronze Age.
Risk-neutral measureIn mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure. This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market, a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure.
Asset pricingIn financial economics, asset pricing refers to a formal treatment and development of two main pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from either general equilibrium asset pricing or rational asset pricing, the latter corresponding to risk neutral pricing.
Finite difference methods for option pricingFinite difference methods for option pricing are numerical methods used in mathematical finance for the valuation of options. Finite difference methods were first applied to option pricing by Eduardo Schwartz in 1977. In general, finite difference methods are used to price options by approximating the (continuous-time) differential equation that describes how an option price evolves over time by a set of (discrete-time) difference equations. The discrete difference equations may then be solved iteratively to calculate a price for the option.
Greeks in TurkeyThe Greeks in Turkey (Rumlar ) constitute a small population of Greek and Greek-speaking Eastern Orthodox Christians who mostly live in Istanbul, as well as on the two islands of the western entrance to the Dardanelles: Imbros and Tenedos (Gökçeada and Bozcaada). They are the remnants of the estimated 200,000 Greeks who were permitted under the provisions of the Convention Concerning the Exchange of Greek and Turkish Populations to remain in Turkey following the 1923 population exchange, which involved the forcible resettlement of approximately 1.
Market neutralAn investment strategy or portfolio is considered market-neutral if it seeks to avoid some form of market risk entirely, typically by hedging. To evaluate market neutrality requires specifying the risk to avoid. For example, convertible arbitrage attempts to fully hedge fluctuations in the price of the underlying common stock. A portfolio is truly market-neutral if it exhibits zero correlation with the unwanted source of risk. Market neutrality is an ideal, which is seldom possible in practice.
Butterfly (options)In finance, a butterfly (or simply fly) is a limited risk, non-directional options strategy that is designed to have a high probability of earning a limited profit when the future volatility of the underlying asset is expected to be lower (when long the butterfly) or higher (when short the butterfly) than that asset's current implied volatility. A long butterfly position will make profit if the future volatility is lower than the implied volatility.
