Convexity Adjustments for Daily Averaged Interest Rate Swaps

Summary

The document raises a pricing issue for an interest rate swap whose floating leg averages rates observed daily during each accrual period. The payment is based on the average of forward rates for short intervals, discounted to the payment date. Since individual rate periods can mature before or after that payment date, their timing differs from the standard reset and payment arrangement.

That mismatch motivates a convexity adjustment, connecting the problem to established treatments of unnaturally timed forward rate resets and average-rate swaps. The source frames the issue and points toward relevant theory, but does not derive an adjustment formula, specify a model, or provide numerical examples. Any practical calculation would therefore need additional assumptions about rate dynamics, discounting, and the precise averaging and payment conventions.

Key ideas

• Daily averaging makes the floating leg depend on rates observed across multiple short intervals.
• The payment date may not coincide with the natural maturity dates of the constituent rates.
• This timing mismatch can require a convexity adjustment in swap valuation.
• The document identifies related theoretical cases but does not provide a formula or model-specific calculation.

Tags

# Convexity Adjustment for Average Rate IRS


# Convexity Adjustment for Average Rate IRS












Suppose that one want to price an Interest Rate Swap with daily averaging, i.e. the floating leg looks like

$$Floating~Leg = \sum\limits_{i=1}^N P(T_i)\cdot\frac{\sum_{k=1}^m F(t_k, t_k+\delta)}{m}, ~T_{i-1}\leq t_k< T_i$$

It seems like some sort of convexity adjustment is needed there since some of rates are maturing before the natural payment time and some are maturing afterwards. In essense this a mix of cases discussed in Brigo & Mercurio book (13.8.5 Forward Rate Resetting Unnaturally and Average-Rate Swaps) and this question.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.