CARMA MODEL

Several processes are developed to model the combined behavior of many dependent time series, such as the CARMA model.

Several processes are developed to model the combined behavior of many dependent time series, such as the CARMA model (Continuous Auto-regressive Moving Average), which is the continuous-time analogs of the discrete-time ARMA model.

The main target of our project, CARMA MODEL, is to extend this model and use it with a new application for bounds.

Thanks to their applicability to irregularity spaced and continuous observations and high-frequency data, they have turned out to be a powerful tool in the modeling.

Considering CARMA model as a mathematical one, we exposed the different functions and tools that are required to make the system work by identifying parameters. We exposed the different types of constraints that might limit the proper functioning of the system. We focused on the fulfillment of our requirements to build an operational system by some simulations and discuss then the numerical aspects.

We plan to improve the capacity of CARMA process trying to describe short and forward interest rates of coupon bonds and other options such as swaps.

The main difficulty in our project was in what extension to other financial products are concerned. Indeed, we do not know if it was possible to extend the model as it was made only for the zero-coupon bond, and even if we succeed, if the reasoning is coherent, if our process is not nonsense from real or mathematical point of view.

Moreover, another important constraint was the encoding and the realisation of the model and this part was the most difficult part that stopped our progression in the project because we don’t have any knowledge in Visual Basic on Excel. But even if we haven’t encoding the model, we know that this model is for the zero coupons, so we want to make it work for the model with coupon, but also for SWAPS.

In this case, it will raise two different problematic therefore two different publications: for both products, which would be a real plus for our project. We generalize the VASICEK interest rate model (CARMA (1, 0)) by changing parameters. Indeed, one factor model is weak. Therefore, using the Multi-factor Continuous –time autoregressive moving-average model for the short and forward interest rates, will allow us not only to calculate the price of a zero coupon bond but also will help meet our need to make it possible for swaps.

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