are types of barrier option for which the payoff is contingent on a barrier level being hit/missed before expiration.

LIBOR-in-arrears swap

is an interest rate swap but one for which the floating leg is paid at the same time as it is set, rather than at the tenor later. This small difference means that there is no exact relationship between the swap and bond prices and so a dynamic model is needed. This amounts to pricing the subtle convexity in this product.

Lookback option

is a path-dependent contract whose payoff depends on the maximum or minimum value reached by the underlying over some period of the option s life. The maximum/minimum may be sampled continuously or discretely, the latter using only a subset of asset prices over the option's life. These contracts can be quite expensive because of the extreme nature of the payoff. There are formula for some of the simpler lookbacks, under the assumption of a lognormal random walk for the underlying and non-asset-dependent volatility. Otherwise they can be valued via finite-difference solution of a path-dependent partial differential equation in two or three dimensions, or by Monte Carlo simulation.

Mortgage Backed Security (MBS)

is a pool of mortgages that have been securitized. All of the cash flows are passed on to investors, unlike in the more complex CMOs. The risks inherent in MBSs are interest rate risk and prepayment risk, since the holders of mortgages have the right to prepay. Because of this risk the yield on MBSs should be higher than yields without prepayment risk. Prepayment risk is usually modelled statistically, perhaps with some interest rate effect. Holders of mortgages have all kinds of reasons for prepaying, some rational and easy to model, some irrational and harder to model but which can nevertheless be interpreted statistically.

Outperformance option

is an option where the holder gets the best performing out of two or more underlyings at expiration. This option can be valued theoretically in a lognormal random walk, constant parameter world, since it is not path dependent and there is a closed-form solution in terms of a multiple integral (in the same number of dimensions as there are underlyings). This amounts to a numerical quadrature problem which is easily achieved by Monte Carlo or quasi Monte Carlo methods. The theory may be straightforward but the practice is not since the price will depend on the correlations between all of the underlyings, and these parameters are usually quite fickle.

Parisian option

is a barrier option for which the barrier feature (knock in or knock out) is only triggered after the underlying has spent a certain prescribed time beyond the barrier. The effect of this more rigorous triggering criterion is to smooth the option value (and delta and gamma) near the barrier to make hedging somewhat easier. It also makes manipulation of the triggering, by manipulation of the underlying asset, much harder. In the classical Parisian contract the 'clock' measuring the time outside the barrier is reset when the asset returns to within the barrier. In the Parisian contract the clock is not reset but continues ticking as long as the underlying is beyond the barrier. These contracts are strongly path dependent and can be valued either by Monte Carlo simulation or by finite-difference solution of a three-dimensional partial differential equation.

Pass through

is a security which collects payments on various underlying securities and then passes the amounts on to investors. They are issued by Special Purpose Vehicles and can be made to avoid appearing on balance sheets. This achieves a variety of purposes, some rather nefarious.

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