Chapter 7: Common Contracts 319
amount. Although the option comes into being at a specified
date in the future it is usually paid for as soon as the contract
is entered into. In a Black–Scholes world, even with time-
dependent volatility, these contracts have simple closed-form
formulæ for their values. Provided the strike is set to be a
certain fraction of the underlying at the start date then the
value of a vanilla call or put at that start date is linear in the
price of the underlying, and so prior to the start date there is
no convexity. This means that forward-start options are a way
of locking in an exposure to the volatility from the option’s
start date to the expiration.
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 con-
straints.
Index amortizing rate swap is just as a vanilla swap, an agree-
ment 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,