July 27th, 2012, 10:24 am
Possibly I am assuming two things where only one exists, but there seem to be two factors involved with the standard convexity adjustments between futures and rates. Since I know nothing about Girsanov's Theorem or Martingale measures, much of the literature on the web is not that helpful to me. The two different elements seem to be: 1. Futures pay-offs are linear, whereas swaps/FRA's are convex. If I have a long FRA position and an offsetting long futures position, the profit on the FRA will always be greater than the loss on the futures, with the degree of profit being a (thoroughly complex) function of the volatility of the rate. 2. Futures are marked to market daily. So in the same example above, if rates rise, the futures position loses money that needs to be borrowed at higher rates. Similarly if rates fall, profits can only be reinvested at lower rates. No such issues exist for the FRA.This latter effect seemed to be the one most commonly noted by people like Hull, but surely the first effect exists even if there is no daily marking to market? isn't this why CMS rates are not simply the same as implied forwards, as the duration of the hedge (forward term swaps) must be different to the short-dated duration of the payoffs? I have limited mathematical ability and I'm trying to explain convexity adjustments (to people who are also mathematically challenged) in conceptual terms similar to the ones above.Can anyone help?Fatman