Chapter 7: Common Contracts 321
Knock-in/out option 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 maxi-
mum/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 formulæ for some
of the simpler lookbacks, under the assumption of a lognor-
mal 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 cashflows are passed on to
investors, unlike in the more complex CMOs. The risks inher-
ent 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 inte-