MANDARIN COLLAR
The Mandarin Collar combines a range forward with the purchase of a range binary structure, such that should the spot stay within the prescribed range, the proceeds of the range forward are enhanced by the pay-out amount of the range binary. If either of the limits trades at any time, the range binary is terminated, but the underlying exposure remains hedged by the range forward. The graph displays the payoff of a long exposure hedged using a Mandarin Collar; the choice of name should be apparent from this picture.
MARGIN
See
future
MARGRABE OPTION
See
outperformance option
MARK to market
To mark-to-market is to calculate the value of a financial instrument (or portfolio of such instruments) based on the current market rates or prices of the underlying. Marking-to-market on a daily (or more frequent) basis is often recommended in risk management guidelines.
See also
accrual accounting,
hedge accounting
MARKET MODEL OF INTEREST RATES
A special case of the Heath-Jarrow-Morton model due to Brace, Gatarek and Musiela in which the term structure of interest rates is modeled in terms of simple Libor rates (which are lognormally distributed with respect to forward measure) rather than instantaneous forward rates. This allows the modeler to exclude the possibility of negative interest rates from the model and obtain prices for caps, floors and swaptions consistent with the Black-Scholes framework. The model can be calibrated using readily available market data: forward or swap rates volatilities and correlations, and is particularly suited to path-dependent instruments.
MARKET RISK
Exposure to a change in the value of some market variable, such as interest rates or foreign exchange rates, equity or commodity prices. For holders of a derivatives position, market risk may be passed through from a change in the value of the underlying to the price of the derivative, or may arise from other sources, such as implied volatility or time decay.
MARKET VALUE
See
replacement cost
MARKING-TO-MARKET
See
mark to market
MARTINGALE
A probabilistic interpretation of the payoff of a “fair game.” The expected gain at any point in the future is equal the actual gain now.
See also
geometric Brownian motion.
MEAN REVERSION
The phenomenon by which interest rates and volatility appear to move back to a long-run average level. Interest rates’ mean-reverting tendency is one explanation for the behavior of the term structure of volatility. Some interest rate models incorporate mean reversion, such as Vasicek and Cox-Ingersoll-Ross, in which high interest rates tend to go down and low ones up.
MEDIUM-TERM NOTE (MTN)
A medium-term note is a debt instrument with a maturity of between three and seven years which pays fixed coupons. While these notes are themselves plain vanilla instruments, they can be used to construct structured notes by embedding derivatives to create structured coupons which appeal to investors.
MERTON MODEL OF CREDIT RISK
See
Credit Risk Models
MId-market
The mid-point between the “bid” and “offer” market rate/price, commonly used as a basis for pricing swaps.
MINI-MAX FLOATER
See
collared floater
MINI-PREMIUM OPTION
The purchaser of a mini-premium option (also known as a step-payment or installment option) pays no initial premium. Instead, a fixed premium becomes payable if the market spot rate subsequently trades through each of a number of predetermined trigger levels for the spot rate. While this offers hedgers protection at zero cost, the total premium paid if all the triggers are activated will be greater than the premium for the equivalent plain vanilla option. However, in this case, the spot rate would have moved in favor of the hedger’s underlying position.
See also
binary option,
contingent premium option
MIN-MAX
London Metal Exchange vernacular for a collar – selling an option, in order to fund the purchase of an opposite option.
MIRAGE OPTION
A European-style option paying the compounded value of returns of an underlying asset over a specified number of time periods of specified length, where payoffs from a certain number of the best and worst performing periods are excluded from the payoff.
MODIFIED DURATION
See
duration
MONEY-BACK OPTION
An option that will repay at least the original option premium at expiry. However, the leverage of the option is greatly reduced compared with a standard option: effectively the premium is simply the interest forgone on the original principal.
See also
rebate
MONTE CARLO SIMULATION
A method of determining the value of a derivative by simulating the evolution of the underlying variable(s) many times over. The discounted average outcome of the simulation gives an approximation of the derivative’s value. This method may be used to value complex derivatives, particularly path-dependent options, for which closed-form solutions have not been or cannot be found. Monte Carlo simulation can also be used to estimate the value-at-risk (VAR) of a portfolio. In this case, a simulation of many correlated market movements is generated for the markets to which the portfolio is exposed, and the positions in the portfolio revalued repeatedly in accordance with the simulated scenarios. The result of this calculation will be a probability distribution of portfolio gains and losses from which the VAR can be determined. The principal difficulty with Monte Carlo VAR analysis is that it can be very computationally intensive.
MORTGAGE SWAP
An asset swap attached to fixed-rate mortgage payments. Mortgage swaps allow investors to enjoy the flows from a portfolio of mortgages without taking a mortgage asset onto their balance sheet. The principal reduces if and when the outstanding mortgage principal reduces (which can occur if the mortgage holder pays off the mortgage or defaults). Such swaps are complicated because although the fixed-rate receiver receives a higher rate than on a normal swap, the amortization of the principal is not just a function of interest rates. The largest mortgage swap market is in the US; in 1992 and 1993 prepayments accelerated because of historically low interest rates.
See also
index amortizing swap,
prepayment risk,
reverse index amortizing swap
MORTGAGE-BACKED SECURITY
See
asset-backed security
MOVING STRIKE OPTION
An option in which the strike is reset over time, such as an interest rate cap in which the strike is reset for the next period at the current interest rate plus a pre-agreed spread.
Msrb
The Municipal Securities Rulemaking Board was established in 1975 by Congress to develop rules regulating securities firms and banks involved in underwriting, trading, and selling municipal securities- bonds and notes issued by states, cities, and counties or their agencies to help finance public projects. The Board, which is composed of members from the municipal securities dealer community and the public, sets standards for all municipal securities dealers. Like the Financial Industry Regulatory Authority (FINRA), the Board is a self-regulatory organization that is subject to oversight by the Securities and Exchange Commission (SEC).
MULTI-FACTOR MODEL
Any model in which there are two or more uncertain parameters in the option price (one-factor models incorporate only one cause of uncertainty: the future price). Multi-factor models are useful for two main reasons. Firstly, they permit more realistic modeling, particularly of interest rates, although they are very difficult to compute. Secondly, multi-factor options (for example, spread options) have several parameters, each with independent volatilities, and also the correlation between the underlyings must be dealt with separately.
MULTI-FACTOR OPTION
Any option whose pay-out is linked to the performance of more than one asset. Such options include outside barrier options, outperformance options, portfolio options, multiple strike options and spread options. Their value is usually strongly dependent on the correlation between the underlying assets. A multi-factor option is synonymous with a multi-colored rainbow option.
MULTIPLE STRIKE OPTION
See
outperformance option
MUNICIPAL SWAP
A swap in which the floating payments are based on an index of tax-exempt US municipal bonds, such as SIFMA.
See also
tax-exempt swap
MUTUAL OFFSET SYSTEM
A margining system for derivatives exchanges in which positions on different exchanges can offset each other. This means that if a participant has a long position on one exchange but a short position on the other in a fungible (compatible) contract, they can pay reduced margin on one exchange because their total exposure has been reduced by netting over the two exchanges.
For example, the Singapore International Monetary Exchange (Simex) has two mutual offsets, one with the Chicago Mercantile Exchange for Eurodollar futures, and another with the International Petroleum Exchange, for Brent crude oil futures.