Multiple-Random Field HJM-framework

In the following, we compute the price of bond options assuming these two types of Random Fields as correlated sources of uncertainty, while dZ(t T) leads to anon-differential and dU (t, T) to a T-differential type of term structure model. Note that the computation of the particular option price differs only in the proposed type of correlation function. 

The direct modeling of the term structure dynamics using a finite-factor HIM model (see chapter (5)) allows us to fit the initial term structure perfectly. Although the initial term structure is a model input, it does not permit consistency with the term structure fluctuations over time. Using e.g. a one-factor HJM-framework (see section (5.3.3)) implies that we are only able to model parallel shifts in the term structure innovations. When we relax this restriction through a multi-factor model this typically does not imply that we are able to capture aU possible fluctuations of the entire term structure. 

Starting from the following multiple-Field dynamics of the forward rates 

applying ltd s lemma to the bond price dynamics P e) = e leads to 

the absence of arbitrage opportunities implies tbat the drift term of the bond price dynamics equals the risk-free interest rate. This implies 

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Multiple-Random Field HJM-framework Given the following relation... 

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