Hi
@nansverma In Gregory's Figure 7.14 (where the lines are not very well distinguished), I think for this
illustrated payer (i.e., pay fixed, receive floating) interest rate swap the EE is the upper, positive line, the EFV is the middle (less positive) and the NEE is the negative line. Due to the importance of the "expected future value," I have copied it from Gregory below. But you are basically correct to say EFV is "the expected value of all possible values , which is equivalent to fair value [future M2M] of the swap." Realistically, it will be the average of Monte Carlo simulated
future values. In the case of this swap, it is heavily influenced by the forward interest rate curve. However, it is not necessarily negative or positive because, if both counterparties use the same simulation (assume they are at least roughly similar), a positive EFV for one counterparty will be a negative EFV for the other!
This is unlike the EE and NEE, which are not thusly "symmetrical." Recall the essential counterparty formula: Exposure = max(value, 0) such that negative exposure = min(value, 0). EE and PFE must be positive because they are, respectively, the average and conditional quantile of only positive values (the exposure part of the distribution); similarly, NEE must be negative. I hope that's helpful!
Gregory (emphasis mine):
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