1. Cash Flow Engine Reference Guide
  2. Monte Carlo Analytics
  3. The Architecture of the Rate Generator
  4. Computation of Rates and Stochastic Discount Factors

13.2.1 Computation of Rates and Stochastic Discount Factors

At the beginning of an ALM Process, the Rate Generator calculates and stores monthly rates for 360 months and all scenarios.

On request by the Cash Flow engine, the Rate Generator will calculate the rate, that is, the annually compounded yield at any time T for a discount bond maturing at time T, as follows:

  • Compute the future bond price using a closed-form solution (a discretized version of Hull and White solution).
  • Convert discount bond prices into discrete yields.

We limit the simulation horizon to 30 years from the As-of-Date. After that period, rates are set equal to the 30-year rate. Also, the closed-form formula is limited to a 30-year term. Rates with a longer-term are set equal to the 30-year term rate.

The Cash Flow Engine may need rates from another IRC (Index) than the risk-free IRC. In this case, the value of the Interest Rate Code (IRC) with maturity T will be a function of the value of the risk-free IRC.

The Rate Generator pre-computes the stochastic discount factor for every scenario, for the first day of every monthly bucket. The computation can be selected with or without an Option Adjusted Spread (OAS) added. The OAS depends on the Product Dimension member and is expressed in terms of discrete annual compounding rate. For internal code optimization reasons, we limit the maximum OAS value to 5%.