April 2011
Intermediate to advanced
328 pages
9h 5m
English
Content preview from Risk Analysis in Finance and Insurance, 2nd Edition
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48 Risk Analysis in Finance and Insurance
2.3 Pricing and hedging American options
In a binomial (B,S)-market with the time horizon N,weconsiderase-
quence of contingent claims (f
n
)
n≤N
,whereeachf
n
has the repayment date
n =0, 1,...,N. Managing such a collection is not difficult, as we can straight-
forwardly price each claim f
n
:
C
n
(f
n
)=E
∗
f
n
(1 + r)
n
,
and therefore the price of the whole collection is
C
(f
n
)
n≤N
=
N
n=0
C
n
(f
n
)=E
∗
N
n=0
f
n
(1 + r)
n
.
In elementary financial and actuarial mathematics, a series of deterministic
payments (f
n
) is called an annuity. Thus, using this terminology, the latter
formula gives the price of a stochastic annuity. Note that the ...
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