How to Determine the Total Return Swap Notional Value at Each Reset Period?

Say my asset leg of a quarterly reset TRS is: $$V_{asset}(t) = \sum_{\tau=0.25}^{T}\bigg(N(t,\tau) \cdot \frac{F(t,\tau)-F(t,\tau-0.25)}{F(t,\tau-0.25)} \cdot Z(t,\tau)\bigg)$$ and my funding leg is $$V_{funding} = \sum_{\tau=0.25}^{T} \bigg(N(t,\tau) \cdot \big(y(t,\tau,0.25)+ s\big) \cdot Z(t,\tau) \bigg)$$ It would be nice if the notional $$N$$ would just be set at TRS issue and remained constant, but according to market convention it is not.

How on earth do I calculate $$N(t,\tau)$$?

• What I've seen so far (not my field of expertise though) is to scale nominal based on what you called $F(t, \tau)$, i.e., the asset's (spot/forward) prices. AFAIK people basically apply two versions of this: (1) fix it at the assets initial price $F(t)$ and then rescale with $F(t, \tau)/F(t)$; (2) fix it at the previous reset date $F(t, \tau-0.25)$ and then rescale with $F(t, \tau)/F(t, \tau-0.25)$. – KevinT Jan 19 at 16:57