Financial Derivative Terms - L

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Leg Currency: The currency used to define the cash flows of swap leg.
Leg Type: The type of cash flow payments that each party must swap (fixed, floating, etc).
Leverage: The use of borrowed money or various financial instruments to increase the potential return of an investment; however, leverage magnifies both gains and losses and therefore, risk is also increased.
LIBOR Curve: A plot of different LIBOR rate terms over a specific period of time.
LIBOR Market Model: An interest rate model based on evolving LIBOR market forward rates. The objects modeled using LMM are market-observable quantities (LIBOR forward rates). The LIBOR Market Model can be used to price any instrument whose pay-off can be decomposed into a set of forward rates. It assumes that the evolution of each forward rate is lognormal. Each forward rate has a time dependent volatility and time dependent correlations with the other forward rates being evolved. After specifying these volatilities and correlations, an instrument can be priced using Monte Carlo simulation to evolve the forward rates.
LIBOR Market Model Calibration Parameters: A calibrated model is a model whose parameters have values that are consistent with market observations. Calibration involves finding values of the parameters such that the model is able to reproduce (as close as possible) the prices of “calibration instruments" observed in the market. Values of the LIBOR Market Model parameters (forward rate volatilities and correlations) are found by calibrating the model to market-quoted Black volatilities of caps and European-style swaptions. The resulting values of the parameters (forward rate volatilities and correlations) are used when evolving the state variables (forward rates) for the purpose of pricing interest rate derivatives that may or may not have prices available in the market.
LIBOR-in-Arrears Derivative: In a LIBOR-in-Arrears swap/note, the current floating payment is based on the LIBOR rate for the next period and applied retroactively to the entire period.
Linear Interpolation: A method of interpolation that assumes a straight line exists between two X,Y) data points.
Local Volatility: Given the prices of call or put options across all strikes and maturities, we may deduce the volatility which produces those prices via the full Black-Scholes equation. Unlike the naive volatility produced by applying the Black-Scholes formulae to market prices, the local volatility is the volatility implied by the market prices and the one factor Black-Scholes.
Log Volatility: A historical volatility calculation method that assumes that stock prices are lognormally distributed (the rate of change in a price series is continuous).

This is one of the assumptions used in the Black-Scholes option pricing model. The historical volatility of the Black-Scholes model is the standard deviation of the natural logarithms of the prices on consecutive trading dates and is called the log volatility.
Lognormal Distribution: A pattern of frequency of occurrence where the logarithm of a variable follows a normal distribution pattern in order to describe returns over one or more years.
Lognormal Random Walk: An industry standard model which describes movements of stock prices are independent of one another and the size and direction are random except for the fact that stock prices tend to increase over time. The lognormal distribution becomes a normal distribution when the values of the variable are switched to the natural logarithms of the values of the variable.
London Interbank Offered Rate (LIBOR): An interest rate at which banks can borrow funds, in marketable size, from other banks in the London interbank market. The LIBOR is fixed on a daily basis by the British Bankers’ Association. The LIBOR is derived from a filtered average of the world’s most creditworthy banks’ interbank deposit rates for larger loans with maturities between overnight and one full year.
Long Position: The amount of a security that is owned.
Lookback Options: Options that allow the option holder the right to purchase the underlying asset at the lowest price (call option), or sell the underlying asset at the highest price (put option) over a specified period. At expiration, the investor looks back and chooses the largest in-the-money amount that occurred over the life of the option. Lookback options are never out-of-the-money.

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