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Swaptions
A swaption is an option granting its owner the right but not the obligation to enter into an underlying swap. Although options can be traded on a variety of swaps, the term "swaption" typically refers to options on interest rate swaps. Types of swaptions There are two types of swaption contracts (analogous to put and call options): *A payer swaption gives the owner of the swaption the right to enter into a swap where they pay the fixed leg and receive the floating leg. *A receiver swaption gives the owner of the swaption the right to enter into a swap in which they will receive the fixed leg, and pay the floating leg. In addition, a "straddle" refers to a combination of a receiver and a payer option on the same underlying swap. The buyer and seller of the swaption agree on: *The premium (price) of the swaption *Length of the option period (which usually ends two business days prior to the start date of the underlying swap), *The terms of the underlying swap, including: **Notion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hull–White Model
In financial mathematics, the Hull–White model is a model of future interest rates. In its most generic formulation, it belongs to the class of no-arbitrage models that are able to fit today's term structure of interest rates. It is relatively straightforward to translate the mathematical description of the evolution of future interest rates onto a tree or lattice and so interest rate derivatives such as bermudan swaptions can be valued in the model. The first Hull–White model was described by John C. Hull and Alan White in 1990. The model is still popular in the market today. The model One-factor model The model is a short-rate model. In general, it has the following dynamics: :dr(t) = \left theta(t) - \alpha(t) r(t)\right,dt + \sigma(t)\, dW(t). There is a degree of ambiguity among practitioners about exactly which parameters in the model are time-dependent or what name to apply to the model in each case. The most commonly accepted naming convention is the following: * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Model (finance)
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 (any time) 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. Equity and commodity derivatives In general the approach is to divid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Swap (finance)
In finance, a swap is an agreement between two counterparties to exchange financial instruments, cashflows, or payments for a certain time. The instruments can be almost anything but most swaps involve cash based on a notional principal amount.Financial Industry Business Ontology Version 2 Annex D: Derivatives, EDM Council, Inc., Object Management Group, Inc., 2019 The general swap can also be seen as a series of forward contracts through which two parties exchange financial instruments, resulting in a common series of exchange dates and two streams of instruments, the ''legs'' of the swap. The legs can be almost anything but usually one leg involves cash flows based on a |
Swap (finance)
In finance, a swap is an agreement between two counterparties to exchange financial instruments, cashflows, or payments for a certain time. The instruments can be almost anything but most swaps involve cash based on a notional principal amount.Financial Industry Business Ontology Version 2 Annex D: Derivatives, EDM Council, Inc., Object Management Group, Inc., 2019 The general swap can also be seen as a series of forward contracts through which two parties exchange financial instruments, resulting in a common series of exchange dates and two streams of instruments, the ''legs'' of the swap. The legs can be almost anything but usually one leg involves cash flows based on a |
Black–Derman–Toy Model
In mathematical finance, the Black–Derman–Toy model (BDT) is a popular short-rate model used in the pricing of bond options, swaptions and other interest rate derivatives; see . It is a one-factor model; that is, a single stochastic factor—the short rate—determines the future evolution of all interest rates. It was the first model to combine the mean-reverting behaviour of the short rate with the log-normal distribution, and is still widely used. History The model was introduced by Fischer Black, Emanuel Derman, and Bill Toy. It was first developed for in-house use by Goldman Sachs in the 1980s and was published in the ''Financial Analysts Journal'' in 1990. A personal account of the development of the model is provided in Emanuel Derman's memoir '' My Life as a Quant''. Formulae Under BDT, using a binomial lattice, one calibrates the model parameters to fit both the current term structure of interest rates (yield curve), and the volatility structure for interest rate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ho–Lee Model
In financial mathematics, the Ho–Lee model is a short-rate model widely used in the pricing of bond options, swaptions and other interest rate derivatives, and in modeling future interest rates. It was developed in 1986 by Thomas Ho and Sang Bin Lee. Under this model, the short rate follows a normal process: :dr_t = \theta_t\, dt + \sigma\, dW_t The model can be calibrated to market data by implying the form of \theta_t from market prices, meaning that it can exactly return the price of bonds comprising the yield curve. This calibration, and subsequent valuation of bond options, swaptions and other interest rate derivatives, is typically performed via a binomial lattice based model. Closed form valuations of bonds, and " Black-like" bond option formulae are also available.Graeme West, (2010)''Interest Rate Derivatives'', Financial Modelling Agency. As the model generates a symmetric ("bell shaped") distribution of rates in the future, negative rates are possible. Further, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bermudan Option
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 differently are categorized as "exotic options". Exotic options can pose challenging problems in valuation and hedging. American and European options The key difference between American and European options relates to when the options can be exercised: * A European option may be exercised only at the expiration date of the option, i.e. at a single pre-defined point in time. * An American option on the other hand may be exercised at any time before the expiration date. For both, the payoff—when it occurs—is given by * \max\, for a call option * \max\, for a put option where K is the strike ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 differently are categorized as "exotic options". Exotic options can pose challenging problems in valuation and hedging. American and European options The key difference between American and European options relates to when the options can be exercised: * A European option may be exercised only at the expiration date of the option, i.e. at a single pre-defined point in time. * An American option on the other hand may be exercised at any time before the expiration date. For both, the payoff—when it occurs—is given by * \max\, for a call option * \max\, for a put option where K is the strike pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Underlying
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. Some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the Chicago Mercantile Exchange, while most insurance contracts have developed into a separate industry. In the United States, after the financial crisis of 2007–2009, there has been increased pressure to move derivatives to trade on exchanges. Derivatives are one of the t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. 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. Definition and application An option is a contract that allows the holder the right to buy or sell an underlying asset or financial instrument at a specified strike ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Contract
In finance, a forward contract or simply a forward is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on at the time of conclusion of the contract, making it a type of derivative instrument.John C Hull'', Options, Futures and Other Derivatives (6th edition)'', Prentice Hall: New Jersey, USA, 2006, 3 The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a short position. The price agreed upon is called the ''delivery price'', which is equal to the forward price at the time the contract is entered into. The price of the underlying instrument, in whatever form, is paid before control of the instrument changes. This is one of the many forms of buy/sell orders where the time and date of trade is not the same as the value date where the securities themselves are exchanged. Forwards, like other derivative securities, can b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Price
The forward price (or sometimes forward rate) is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, the forward price can be expressed in terms of the spot price and any dividends. For forwards on non-tradeables, pricing the forward may be a complex task. Forward price formula If the underlying asset is tradable and a dividend exists, the forward price is given by: : F = S_0 e^ - \sum_^N D_i e^ \, where :F is the forward price to be paid at time T :e^x is the exponential function (used for calculating continuous compounding interests) :r is the risk-free interest rate :q is the convenience yield :S_0 is the spot price of the asset (i.e. what it would sell for at time 0) :D_i is a dividend that is guaranteed to be paid at time t_i where 0< t_i < T. Proof of the forward price formula The two questions here are what price the short position (th ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
