Gregory, Chapter 8 (PFE)

[Unusualskill]

Hi @David Harper CFA FRM and @Nicole Seaman ,

May I ask why swap is most likely to results in a peaked shape for the exposure profile represented by potential future exposure? Thank you, appreciate your help!

 

[David Harper CFA FRM]

under a simple assumption where the yield is i.i.d. (such that yield volatility scales with the square root of time), mathematically it peaks at exactly one-third (1/3rd) its tenor (life); the local maximum is the solution to a differentiation. It goes up (amortizes) due to the rate uncertainty, but then down (diffuses) because there is no principal at risk (exchanged).