# 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.

• You very much need to take into account the correlation of discounting with the payments - if it's on the same rate them the correlation is very high. – will Apr 11 '17 at 20:44
• @will your comment makes little sense to me – SmallChess Apr 11 '17 at 23:48
• @SmallChess if you have some future payment based on a random variable, then what you normally do is take the expected value of the future payment, and then discount it using the zero curve - i.e. $\mathbb{E}[X]P$ where $P$ is the discount factor. This is often fine as the discount factor is not correlated with the variable. If the above random variable was the OIS rate though, then it will be correlated with the discounting. The result is that when you have a higher rate, such that you'd get more money, it is more strongly discounted, and when it is lower, it is less strongly discounted. – will Apr 12 '17 at 6:42

## 1 Answer

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

• Thanks, as I am only interested in the future value (i.e. no discounting), the measure shouldn't be of interest here, right? – p.vitzliputzli Apr 12 '17 at 11:05
• I think anytime you take expected values you have to specify probability measure. How do you calculate it otherwise? – dm63 Apr 12 '17 at 13:30
• Well, I agree about the necessity of a probability measure for expected values, but what would you suggest in my case? I have the possibility to compute the future values in a deterministic way by calculating the forward rates out of the current spot curve or by using a stochastic interest rate model and a simulation. I don't know what the advantage of a simulation would be. – p.vitzliputzli Apr 12 '17 at 14:20
• If you do a simulation, you will have to choose a drift term. That is basically equivalent to choosing a probability measure. – dm63 Apr 12 '17 at 20:07
• Undoubtedly the most commonly used method would be to take the forward rates. – dm63 Apr 13 '17 at 2:53