• 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 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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