Can I value the equity leg of an equity swap using the projected forward equity returns?

In other words, for a sequence of times $t_{0}<t_{1}<\ldots<t_{n}$, where $t_{0}$ begins a brand new calculation period and $t_{n}$ is the maturity of the contract, do we have (assuming the payment frequency is the same as the calculation period frequency) $$V_{t}=\sum_{j=1}^{n}\frac{F_{j}-F_{j-1}}{F_{j-1}}\cdot D(0,t_{j})?$$ Here $F_{j}$ is the forward equity price at time $t_{j}$ calculated at time $t_{0}$ and $D(0,t_{j})$ is the discount factor for the period $[t_{0},t_{j}]$

I know that the traditional way to value the equity leg is to think of it as a floating rate bond that resets to par at the end of each payment date. Personally, I find this approach somewhat unintuitive and prefer the projected forward rates viewpoint. Since the two interpretations are equivalent for floating LIBOR legs, I suspect the same is true for the equity legs.

My presumption is that once the value of the equity leg is determined, then a spread $S$ can be added so that $$V_{EquityLeg}=V_{OtherLeg},$$ at inception of the contract.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.