Interpreting NPV in MAC Swap Futures Pricing

Summary

The document asks what “NPV of the deliverable swap” means in the quoted price of a MAC swap future. It contrasts the discounted-cash-flow meaning of net present value with an expectation of future cash flows, using a stock futures price as an analogy. The central issue is whether the swap’s cash flows in the futures price are discounted and, if so, under which pricing convention or measure.

The text provides no answer, derivation, or supporting evidence; it is a narrowly framed question for interest-rate practitioners. It therefore identifies a conceptual ambiguity rather than teaching a resolved pricing method. Readers should not infer that swap futures are priced exactly like stock futures: the relationship between futures and forward values can depend on settlement, margining, discounting, and the contract’s specific definition of the deliverable swap value. The document is most useful as a prompt to investigate contract conventions and the precise meaning assigned to NPV in the quoted formula.

Key ideas

• The question distinguishes discounted swap cash flows from an undiscounted expectation of future cash flows.
• The author asks how the deliverable swap’s NPV enters the MAC swap futures price.
• The document does not resolve the pricing question or provide a derivation.
• Contract conventions and discounting assumptions are necessary context for interpreting the formula.

Tags

# MAC swap futures


# MAC swap futures












I recently asked a question about SOFR swap futures - unfortunately didn't receive any replies on that, maybe because SOFR is still relatively new.

So I'll try MAC swap futures (https://www.cmegroup.com/trading/interest-rates/files/mac-swap-correlations.pdf). I'm assuming these are more familiar to IR quants and traders, and I'll limit it to one particular question which is really confusing me and I think it could be a matter of jargon.

The price of a MAC swap future can be written as 100 + NPV of deliverable swap.

Now this is what confuses me: what is meant exactly by NPV of the swap?

If I hear NPV I think of discounted (future) cashflows, i.e. $(constant +) E_0^\mathbb Q [ \sum_i (B_0/B_{T_i})CFs (T_i) ]$ where $CFs(T)$ stand for cashflow at time $T$ and $B_t$ is the money market account / risk-free.

However, wouldn't the futures price of an asset, for example a swap involving cashflows, be priced as $(constant +) E_0 [ \sum_i CFs(T_i) ]$ - note the absence of $B_0/B_{T_i}$ - just as the futures price of a stock $S$ is $E_0^\mathbb Q [ S_T ]$?

Hence my question: what is meant by NPV?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.