# Future

is an agreement to buy or sell an underlying, typically a commodity, at some specified time in the future. The holder is obliged to trade at the future date. The difference between a forward and a future is that forwards are OTC and

futures are exchange traded. Therefore futures have standardized contract terms and are also marked to market on a daily basis. Being exchange traded they also do not carry any credit risk exposure.

# Hawai'ian option

is a cross between Asian and American.

# Himalayan option

is a multi-asset option in which the best performing stock is thrown out of the basket at specified sampling dates, leaving just one asset in at the end on which the payoff is based. There are many other, similar, mountain range options.

# HYPER option

High Yielding Performance Enhancing Reversible options are like American options but which you can exercise over and over again. On each exercise the option flips from call to put or vice versa. These can be priced by introducing a price function when in the call state and another when in the put state. The Black-Scholes partial differential equation is solved for each of these, subject to certain optimality constraints.

# Index amortizing rate swap

is just as a vanilla swap, an agreement between two parties to exchange interest payments on some principal, usually one payment is at a fixed rate and the other at a floating rate. However, in the index amortizing rate swap the size of the principal decreases, or amortizes, according to the value of some financial quantity or index over the life of the swap. The level of this principal may be determined by the level of an interest rate on the payments dates. Or the principal may be determined by a non-fixed income index. In the first example we would only need a fixed-income model, in the second we would also need a model for this other quantity, and its correlation with interest rates. In an index amortizing rate swap the principal typically can amortize on each payment date. On later payment dates this principal can then be amortized again, starting from its current level at the previous payment date and *not* based on its original level. This makes this contract very path dependent. The contract can be priced in either a partial differential equation framework based on a one- or two-factor spot-rate based model, or using Monte Carlo simulations and a LIBOR market-type model.

# Interest rate swap

is a contract between two parties to exchange interest on a specified principal. The exchange may be fixed for floating or floating of one tenor for floating of another tenor. Fixed for floating is a particularly common form of swap. These instruments are used to convert a fixed-rate loan to floating, or vice versa. Usually the interval between the exchanges is set to be the same as the tenor of the floating leg. Furthermore, the floating leg is set at the payment date before it is paid. This means that each floating leg is equivalent to a deposit and a withdrawal of the principal with an interval of the tenor between them. Therefore all the floating legs can be summed up to give one deposit at the start of the swap s life and a withdrawal at maturity. This means that swaps can be valued directly from the yield curve without needing a dynamic model. When the contract is first entered into the fixed leg is set so that the swap has zero value. The fixed leg of the swap is then called the par swap rate and is a commonly quoted rate. These contracts are so liquid that they define the longer-maturity end of the yield curve rather than vice versa.

# Inverse floater

is a floating-rate interest-rate contract where coupons go down as interest rates go up. The relationship is linear (up to any cap or floor) and *not* an inverse one.