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I’m not sure that’s the right way to look at it. SVR has a 1 month fix period so any volatility in rates is passed onto the customer.
The SVR spread is only minimally driven by risk premium (prime resi mtge cost of risk is <50 bps), it’s really an elasticity charge (ie benefit from cost plus hassle to refi).
Really what they should do is say “SVR = gilts + 430 bps” or whatever it is and then strip the curve to get the implied 1 month spot rate for each payment period after the fix ends. That’s what I was alluding to in my comment.
Of course they won’t put in writing that SVR is linked to rates otherwise they open themselves up to litigation based on the high SVRs of the last 10 years.
Only insofar as the variable rate includes a risk premium above the risk free rate, of which volatility in the interest rate curve is a factor.
It's the fixed rate that is most dependent on forward rates.
It doesn't really make sense to measure lifetime payments based on anything other the current variable rate - otherwise you're looking at a level of sophistication beyond most people's needs, with reval curves, discount curves and the like.