Floating-Rate Note Cash Flows and Probability Measures

Summary

The document distinguishes valuing a floating-rate note from estimating its expected coupon cash flows. For valuation under a single-curve framework, one can derive forward rates from the yield curve, use them to estimate future coupons, and discount those payments. The response says this approach works for valuation, but it does not provide a numerical example or a detailed pricing procedure.

For expected cash flows, the probability measure matters. Under the forward measure associated with a coupon payment, the relevant forward rate is its expected rate. Under the money-market measure, the expected floating payment is slightly higher because of convexity. The discussion does not specify a particular interest-rate model or quantify the adjustment; its main lesson is that forward rates are not measure-independent forecasts of floating payments.

Key ideas

• Forward rates can be used to project coupons and discount cash flows when valuing a floating-rate note.
• Expected coupon cash flows depend on the probability measure used.
• Under the corresponding forward measure, the forward rate is the expected rate for that payment period.
• Under the money-market measure, convexity makes the expected floating cash flow slightly higher than the forward rate.

Tags

# Expected Cash flows of a Floating Rate Note


# Expected Cash flows of a Floating Rate Note












How would one calculate the expected cash flows of a floating rate note?

Given a yield curve corresponding to the underlying of a floating rate note, would it be sufficient to compute the forward rates and use them to calculate the future value of the coupon payments? This would be in line with the classical (textbook) single yield curve valuation of the FRN, but I wonder what the industry approach would be.

Would one still do it in this way or would one take an interest rate model (which?), simulate many scenarios and take the averages like Monte Carlo? Are there other ways? Let's assume defaults are not of interest.

## Answer by dm63 (score 3, accepted)

https://quant.stackexchange.com/a/33641

If you are trying to value the FRN, plugging in the forward rates and then discounting is a method that works.

If you are trying (as you specifically say) to calculate the expected cash flows, then you have to specify which probability measure you are in. In the forward measure for each cash flow, the forward rate is the expected value. However in the money market measure, the expected floating cash flow for each date is slightly higher than the forward rate due to the convexity effect alluded to by @will

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