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 payout 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.
Mark-to-market
This is the value of a financial instrument according to current market
rates.
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 modelled in terms of
simple Libor rates (which are lognormally distributed with respect to forward
measure) rather than instantaneous forward rates. This allows the modeller 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 derivatives, or may arise from other
sources, such as implied volatility or time decay.
Martingale
A probabilistic interpretation of the payout of a "fair game." The expected
gain at any point in the future is equal to the actual gain now.
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 behaviour 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
A medium-term note is a debt instrument with a maturity of between three and
seven years, which may pay fixed or variable coupons. These notes can be used to
construct structured notes by embedding derivatives to create structured coupons
which appeal to investors.
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 on to 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
amortisation 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.
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.
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 modelling, 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.
Municipal swap
A swap in which the floating payments are based on an index of tax-exempt US
municipal bonds, such as J.J. Kenny.
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