Understanding Financial Calculation Rules

Pricing Rules for Rate Sensitivity

For rate sensitivity (behavioral) models to accurately assess delta rates, you need to define the pricing rules that the model uses. For example, you can define a pricing index as a single rate from a particular yield curve such as the seven-year Chicago Mercantile Trade US Treasury; or you can use more complex indices based on more than one rate from more than one yield curve to describe how you reprice products in response to changes in interest rates.

You can also assign alternative pricing rules to subsets of the financial product based upon criteria that you define. For example, for certificates of deposit (CD) above 100,000 USD in Arizona, you might want to assign an additional 50 points to the rate that is derived from the product pricing index. However, for CDs that are below 100,000 USD in New York, you might want to use a different pricing index. You have flexibility in defining the pricing structure of financial products, according to regions, balances, products, and so on.

Conventional Financial Measures Calculations

The Financial Calculator application engine calculates a number of conventional financial measures for a pool of instruments. The financial measures that are supported are:

• Net Present Value: NPV is the fair value that should be paid for the financial instrument. A common way of determining this value is to obtain the expected value of the series of discounted cash flows that are projected from current date to maturity.

  for single path analysis, where t equals time.

  for multi-path analysis, where I equals 1 through N number of paths, and where t equals time. DF is discount factor, and CF is cash flow. For example, CF_ti is the cash flow at time t for pathI and similarly for DF_ti.

  Other equations exist for determining NPV.

• Effective Duration: The measure of the sensitivity of NPV to parallel shifts of rates that takes into account changes of projected cash flows.

• Effective Convexity: The measure of sensitivity of duration with respect to parallel shift rate changes as a second order effect on NPV.

  where NPV^- is the NPV in the case of decreasing rate paths. NPV⁺ is the NPV in the case of the increasing rate paths. Delta R is the size of the parallel shift of the interest rates.

• Cash Flow Duration: The weighted average time of projected cash flows weighted by the discounted cash flows.

  where DF_t is discount factor for timet and CF_t is cash flows at timet. NPV is net present value of cash flows.

• Modified Duration: A modification of cash flow duration, taking into account the internal rate of return.

  Modified cash flow duration = [Duration / (1 + IRR / Frequency)], where IRR equals the internal rate of return, and frequency is the frequency of the payments per year. For example, for semiannual payments, the value is 2.

• Average Life: The time necessary for principal to be reduced by one half of its current value. You should not select average life for products that do not have an initial balance such as credit cards, savings accounts, and lines of credit.

• Dollar Duration: A measure of the change in the dollar price of an instrument.

• Internal Rate of Return: (IRR) represents the interest rate at which NPV is book plus accrued income.