Financial analysts use the following differential equation to model the interest rate process of a market economy
d(f(r)) = (θ(t) – a(r)) dt +σ(t) dz
where dz models the randomness of the economy.
a) The Ho-Lee process uses f(r) = r, a(r) = 0, and θ(t) = R(t) + σ(t). Solve the Ho-Lee equation if σ(t) = 0 and R(t) = 0.05t.
b) Another process has f(r) = In r and
a(r) = In r. Solve this equation assuming.
θ(t) = R(t) + σ(t), σ(t) = 0, and
R(t) = 0.05t.
(Solutions for σ ≠ 0 are called stochastic solutions and are beyond the scope of this text.)
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