Maturity and Exposure

[brian.field]

Gregory seems a bit inconsistent with respect to whether maturity effects exposure.

Clearly, the longer the term of the agreement, i.e., the more distant the maturity, the greater the future uncertainty. Also, the greater the root(t) term, so it must affect exposure.

He states above formula 13.3 that "...the exposure is a rather simple increasing function reflecting the fact that, as time passes, there is an increasing uncertaintly about the value of the final exchange."

Yet, a few lines later, he states under formula 13.3 in the text,"....that the maturity of the contract does not influence the exposure (except for the obvious reason that there is zero exposure after this date.)

Can you help me understand that @David Harper CFA FRM ?

Thanks!

 

[David Harper CFA FRM]

Hi @brian.field At first I thought you identified a typo (Gregory's errata as here @ http://www.cvacentral.com/books/credit-value-adjustment/errata/ ) but when I pulled up the referenced Chapter 8 Appendix (copy here at http://www.cvacentral.com/books/credit-value-adjustment/errata/ ) I realized that the forward contract's maturity does not appear in the his exposure model. Rather, consistent with Figure 8.8 (is that maybe Fig 13.8 in your version? The literal source is Chapter 8 of the book), the exposure starts at zero because the contract value is immediately zero, then it increases over time. His exposure model is Brownian motion: dV(t) = µdt + σdW(t). So, for example, if the contract is a 3-year forward contract, his model simply starts with zero exposure that is an increasing function of time ("as time passes, there is an increasing uncertainty"), but that function is only drift and volatility; the 3-year maturity does not really alter the exposure model!

Then his parenthetical--i.e., "(except for the obvious reason that there is zero exposure after this date.)"--acknowledges that (in my example), the increasing function would terminate (drop down to zero) at the 3-year interval. Unlike an interest rate swap which exhibits amortization (decreasing function) after diffusion, the forward is just diffusion then termination at peak. In this way, I think the difference is how first quote refers to time (as the x-axis) in contrast to the literal maturity of the contract in the second quote. Let me know what you think? Thanks!