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Lecture

Interest Rate Derivatives: Caps and Floors

Description

This lecture covers interest rate derivatives focusing on caps and floors, which protect against high and low rates, cap-floor parity, pricing under forward measures, Black's and Bachelier's price formulas, caplets, floors, cap/floor quotes in terms of implied volatilities, and the challenges of matching volatility curves in interest rate models.

Official source

Ontological neighbourhood

Economics

Microeconomics: Financial economics

Related concepts (32)

Local volatility

A local volatility model, in mathematical finance and financial engineering, is an option pricing model that treats volatility as a function of both the current asset level and of time . As such, it is a generalisation of the Black–Scholes model, where the volatility is a constant (i.e. a trivial function of and ). Local volatility models are often compared with stochastic volatility models, where the instantaneous volatility is not just a function of the asset level but depends also on a new "global" randomness coming from an additional random component.

Volatility smile

Volatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter (implied volatility) that is needed to be modified for the Black–Scholes formula to fit market prices. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices (and thus implied volatilities) than what is suggested by standard option pricing models. These options are said to be either deep in-the-money or out-of-the-money.

Implied volatility

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 (such as Black–Scholes), will return a theoretical value equal to the current market 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.

Interest rate swap

In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a "linear" IRD and one of the most liquid, benchmark products. It has associations with forward rate agreements (FRAs), and with zero coupon swaps (ZCSs). In its December 2014 statistics release, the Bank for International Settlements reported that interest rate swaps were the largest component of the global OTC derivative market, representing 60%, with the notional amount outstanding in OTC interest rate swaps of

381 trillion, and the gross market value of

14 trillion.

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.

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Swaptions: Interest Rate Models

Covers swaptions, moneyness, callable bonds, pricing formulas, and implied volatilities.

Interest Rate Derivatives: Calibration Example

Covers the calibration of interest rate models using a two-factor Gaussian HJM model and the computation of Black and Bachelier cap vegas.

Forward Measures: Interest Rate Models

Explores forward measures, option pricing, and bond option pricing in interest rate models.

Estimating the Term Structure: Exact Methods

Explores exact methods for estimating the term structure in interest rate models, emphasizing the importance of choosing the right discount curve.

Heath-Jarrow-Morton Framework: Interest Rate Models

Explores the Heath-Jarrow-Morton framework for interest rate models and discusses bond price dynamics and a Vasiček short rate model.