Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 211 / 2 / c

Table of contents
- Solution c

Solution

Buy one maturity-

(T - 1)

bond. When it pays one at

T - 1

, use all proceeds to buy

1/ P_{T - 1}^{T}

maturity-

T

bonds. Short

1 + f

maturity-

T

bonds. The terminal payoff is

\frac{1}{P _{T - 1}^{T}} - (1 + f) = r_{T} - f .

Its initial replication cost is

ξ_{0} = P_{0}^{T - 1} - (1 + f) P_{0}^{T},

which vanishes for

f = P_{0}^{T - 1} / P_{0}^{T} - 1

.

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