Risksvr™ handles forward events generically. This approach is unique and covers all existing floating events: From simple plain vanilla floating legs handled in the LIBOR Swap market to complex bundled structures that contain averaging and compounding events.

This architecture presents numerous advantages over the simplifications that are part of accepted methodologies such as the one presented by RiskMetrics and detailed in the RiskMetrics Technical Document No4 on Page 110.

Generic Floating Leg Events Handled by Risksvr™

In this framework, every floating rate event requires TWO Interest Rate Curves:

These two curves can be:

• Identical

• of Different Credit Standing: (Government Curve and Swap Reset Index)

• of Different Nature, such as TRS, Equity Swaps, Equity Default Swaps, CDS, etc
  

These two Interest Rate Curves can be separated into

1. A reference reset  index,  from which the level is used to observe (or deduce through arbitrage-free calculation)  the reset event of a floating leg. 
   One or a series of resets events will then be used to create a Coupon Payment.
   
   
   

2. A discount rate index is defined as any interest rate (and its associated term structure and zero coupon rate curve) that will be used to discount future cash flow payments.
   
   In this framework ,forward rates and zero coupon bond prices cannot be used interchangeably.

This distinction is often overlooked because it is assumed interest rate swaps and floating rate notes are LIBOR based and LIBOR rates will be used to fix the coupon rates and discount the coupon payment.

This leads to the following simplification, which assumes reset reference index and discount curve are identical in nature and frequency.

 For a detailed explanation, please refer to Page 110 of the RiskMetrics Technical Document No 4.1996.

          Floating Leg=

N        = is the Notional Principal of the payment event.

t         = is the effective date of the trade (i.e. the valuation date of the leg).
 = is the x period Forward rate set at time y.
  = is the x period spot rate starting at time y.                

The assumption that reference index and discount rates are one and the same gives us the well known short-cut that allows payment discount and future coupons to cancel each other by using the standard relationship between discount rates and forward rates.

           If we assume reference and discount rates are identical, then the floating Leg collapses conveniently:

Drawbacks: Lost Credit and Market Risk

This approach assumes the Floating rate carries solely a reset risk on the next reset coupon. It also assumes notional principal will be constant.

This is bad, since it assumes there is no forward spread risk. From a Risk Management perspective, this simplification offers the speed necessary to revalue large books at the enterprise level, but it also forgoes potential sources of market and credit risk, especially when dealing with long term instruments. 
Spread risk was indeed the main factor in the near demise of  LTCM! 

The relationship between forward and discount rates will not hold if either the frequency, day count convention or the interest rate on which the forward rate is based are different than the one used to discount the payment. In practice, this happens most of the time since the forward period is determined between begin and end dates of the reset period, whereas the discount period is computed between coupon payment dates.

In order to provide a generic framework from which we can price any type of floating event, we introduce the following generic expression:

Thus, for each payment i= 1, 2, …, n.

N                     = Notional principal value of payment.
dc_i                       = the day count factor applicable.

ResetDate(k)        = the date when the coupon is reset for event k.
BeginDate(k)        = the begin date of the coupon accrual. (2 business days after reset, 
                            except with ON swaps) for event k.
EndDate(k)           = the end date of the coupon accrual for event k.
PaymentDate(i)     = the date on which payment occurs (2 business days after reset).

     = the discount rate for the payment date.
R(t,x,y,z)                = the y, z period rate, reset at time x and observed at time t
   based on the reset reference index. 

R can either be a single rate or the result of multiple rates observed during the payment period which are then averaged and or compounded (see below). R can either be the rate observed in the market or if not yet observed a rate implied from risk-neutral arbitrage assumption between forward rates. 

Alternatively, the expression can be generalized by replacing rates with zero coupon rates.

=Z< is the discount rate for the payment period x starting at date y.

where:

R                 = Reset for period. (R & f are used interchangeably).
r_i                     = individual averaging reset or fwda_i (individual forward rate  extracted by
 arbitrage-free relationship between spots and forwards).
n                 = Number of averaging resets.

The De-annualized reset rate and  spread rate are then simply applied to the prescribed compounding method above.