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We investigate a compound Poisson infinite factor diffusion model which describes the relationship between the infinite-dimension random risk resource and the corresponding stochastic process. We derive the no-arbitrage condition on the drift of instantaneous forward rates in the compound model and study the impact of random jump on the price of the zero-coupon bond.

In the study of the stochastic process, the expansion from single-factor model to multiple-factor model greatly improves its capability to describe the dynamic properties. For the term structure of interest rates, multiple-factor expansion enables itself to more flexibly describe the relationship between different maturities and their corresponding risk-free interest rates. The term structure curve contains rich information about the economy status and financial markets. The literatures have witted extensive researches on this topic for recent decades. For instance, the HJM model in [

In this paper, according to the stochastic string model presented in [

The paper is organized as follows. Section

For a probability space

the term structure curve would parallel shift which limits its capability to generate richer class of dynamics and shapes of the term structure of interest rates,

it does not permit consistency with term structure innovation along with the time.

One way to extend the model is by introducing the

Assume that the dynamics of the instantaneous forward rates at

Information burst, some emergency events, crises, and monetary target adjustment may cause the return and price of asset jump. There are more and more empirical lines of evidence which show that the interest rate models should incorporate the jump risk. The difference of the asset price of continuous path will disappear as the change of time converges to zero. We know that in the jump model, the difference does not converge to zero, although its probability of jump occurrence will converge to 0. Eberlein et al. [

Based on the continuous path of instantaneous forward rate used in Santa-Clara and Didier [

Applying the decomposition theorem of a compound Poisson process (see [

Assume that the market is complete, so that the existence and uniqueness of the risk market price are guaranteed. It can be proved that the continuous part of random risk factor is independent of the jump risk factor.

For the continuous risk resource part, define

If the market is complete, the arbitrage-free condition of the instantaneous forward rate satisfies

The price at time

When

Under the risk-neutral measure

Under the risk-neutral measure

We show that (

In (

The compound Poisson infinite diffusion model developed in Section

We consider the price of the short-term interest rate futures. Assume that the financial market is shocked by two kinds of random risk resource: one is continuous risk factor of

Under the risk-neutral measure

Note that the zero-coupon bond price is a function of instantaneous forward rates

Thanks are due to the referees whose meaningful suggestions are very helpful to revise the paper. This work is supported by the Fundamental Research Funds for the Central Universities (JBK130401).