Chapter 7: Common Contracts 307
Cashflows are when money changes hands during the life
of the contract (as opposed to an initial premium or a
final payoff). When there is a cashflow the value of the
contract will instantaneously jump by the amount of the
cashflow.
- When a contract has a discretely paid cashflow you
should expect to have to apply jump conditions. This
also means that the contract has time dependence,
see above. - Continuously paid cashflows mean a modification,
although rather simple, to the governing equation.
Path dependence is when an option has a payoff that
depends on the path taken by the underlying asset, and
not just the asset’s value at expiration. Path dependency
comes in two varieties, strong and weak.
Strong path dependent contracts have payoffs that
depend on some property of the asset price path in
addition to the value of the underlying at the present
moment in time; in the equity option language, we can-
not write the value asV(S,t). The contract value is
a function of at least one more independent variable.
Strong path dependency comes in two forms,discretely
sampledandcontinuously sampled, depending on
whether a discrete subset of asset prices is used or
a continuous distribution of them.
- Strong path dependency means that we have to work
in higher dimensions. A consequence of this is that
our code may take longer to run.
Weak path dependence is when a contract does depend
on the history of the underlying but an extra state
variable is not required. The obvious example is a bar-
rier option.