## Present Value

Calculates the present value of at time index t of cash flows from time index t+1 to the end of the projection period using a specified discount rate or yield curve. To develop a variable using the Present Value function, the following parameters must be defined:

*Cash flows*- Selected from dropdown menu of time-indexed numerical variables.*Rate type*- Fixed Rate or Yield Curve selected from dropdown menu.

- Fixed Rate
*Discount Rate*- Should be entered as an annualized discount rate. Monthly cash flows are discounted using a monthly discount rate equal to (1+Discount Rate)^(1/12) -1.

- Yield Curve
*Currency*- Indicates which Currency within an Economic Scenario is associated with the yield curve to be used in the Present Value calculation. The discounting will be calculated using the spot rates for the various durations from the yield curve as of the Time Index at which the present value is being calculated.*Spread*- The annual spread above the yield curve defined within your Scenario Table which is associated with the selected Currency for a given Economic Scenario.

- Fixed Rate

## Annuity Factor

Calculates an annuity factor based on the following parameters:

*Interest Rate*- Annualized monthly discount rate*Decrement Table*- Decrement table used for a life contingent annuity. This can be left blank for an annuity certain.*Payment Frequency*- Monthly, Quarterly, Semiannual or Annual*Payment Timing*- Indicator of payments being made at the End or Beginning of a period*Duration (in months)*- Total maximum months of annuity duration. For a lifetime annuity, this should be left blank. A decrement table must also be provided in order to calculate a lifetime annuity.*Gender*- Male or Female*Age*- Attained age of the annuitant at time index t*Duration*- Duration since annuity inception. This duration value will be used to read from Select & Ultimate decrement tables if one is specified in the decrement table above.

## Internal Rate of Return

Calculates an Internal Rate of Return based on a starting balance and a series of cash flows.

*Initial Value*- The starting balance used in determining the internal rate of return*Cash Flows*- Selected from the dropdown menu of time-indexed numerical variables*Behavior*- "Future Cash Flows Only" excludes cash flows in the current period in the IRR calculation. "Include Current Period Cash Flows" should be selected to include the current period.*On Failure*-Determines how the system should handle a failure to converge. Failure to converge can be reflected as an Error, Warning or the user can select Ignore to ignore the failure.

The Internal Rate of Return formula attempt to solve for a single annual effective interest rate which, when used to discount the Cash Flows from the variable specified, will be exactly equal to the Initial Value.

## Option Price

Calculates the price of a European call or put option using the Black-Scholes formula based on the following parameters:

*Type*- Indicates whether the option is a Call option, which gives the holder the right to buy a stock at a set price, and a Put option**,**which gives the holder the right to sell a stock*Current Price*- The current stock price at the issue of an option*Exercise Price*- The set price at which an option can be bought or sold when it is exercised*Risk-Free Rate*- The annualized risk-free rate used to discount cash flows in calculating the option price*Annual Volatility*- The standard deviation of log returns for a security