Marginal Value of Fund (MVF) rate is an internal rate used for any internal lending or borrowing of funds within an organization. A MVF swap is a swap whose floating legs is based on the MVF rate.
MVF rates are blended and excessive averaged LIBOR rates over specified moving historical periods. The MVF swap’s floating leg is settled monthly with daily average of MVF rates over each period. The swap can be correctly booked in Infinity system provided that the floating forward rate can be estimated with satisfactory.
MVF curve is constructed so that forward 1-DAY MVF rates can be estimated from the curve. The creation of the curve consists of two-step processes. In step 1, so-called MVF rate equivalent cash rates are generated. The MVF curve is finally generated by using regular curve algorithm. The constructed curve is then used to price barriers (see https://finpricing.com/lib/EqBarrier.html)
Although MVF swaps are based on a blended and excessive averaged LIBOR rates, swap terms do not exceed five years. This implies that the convexity adjustments may not be significant. Therefore, the pricing of the MVF swaps may be still within the vanilla interest rate swap pricing framework.
Expected future 1-MTH and 3-MTH LIBOR rates are respectively estimated by the forward rates via USD LBR 1M and USD LBR 3M curves, which are supposed to be the best market curve for forecasting 1-MTH and 3-MTH LIBOR rates.
However, there is no such analogues corresponding to 2-MTH LIBOR rates. We consider cases where 2-MTH LIBOR rates are forecasted by USD LBR 1M and USD LBR 3M. We use USD LBR 3M as discount curve since underlying instruments of this curve are most liquid in the market With the help of the notations defined above, let us define
Thus, the MVF rate at the time t can be defined where index weights here are given by
An MVF FRA, with the forward period of [fwdStt; fwdEnd], the notional principal of notl, position index of β, and the strike rate of RX, has the matured payoff given Now, let t0 be a valuation date and T be the settlement date of the FRA, where T ¸ fwdEnd. Then the present value of the MVF FRA, denoted by mvfPVt0 , can be given where dF is the discounting factor from the settlement date back to the valuation date. Clearly, the key part in pricing the MVF swap is to calculation the expectation of MVF rate, i.e., Et0 [MVFt]. With the definition of MVF rate, we have