Unformatted text preview: b) Now consider an HJM model, driven by the risk-neutral Brownian motion f W , in which the volatility σ ( t, T ) is of the form σ ( t, T ) = g ( t ) h ( T ) for two bounded and strictly positive deterministic functions g and h . Write down the dynamics of the forward rates f ( t, T ) and of the short rate R t = f ( t, t ) under the risk-neutral measure. Then Fnd deterministic functions θ ( t ), κ ( t ), and ξ ( t ) such that R t satisFes dR t = κ ( t )( θ ( t ) − R t ) dt + ξ ( t ) d f W t . That is, R t solves the SDE of a general one-factor Hull & White model. Exercise 2. Exercise 10.9 on page 458 in Steve Shreve’s book. 1...
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- Spring '08
- Probability theory, Upson, Steve Shreve, rate process Rt