Does anyone out there have any experience in delta hedging a swaption portfolio? I've developed a model that uses forward starting swaps as the hedge instruments but it's performance is somewhat less than optimal. The problem sounds simple enough but I'm seeing that one's choice for a delta measure has a huge impact on hedge performance. Hull (2000) suggests shocking each of the zero rates by a basis point and then hedging each of the deltas. Fine, but that seems like a hell of a lot of hedging transactions if one has to rebalance frequently. Throw gamma into the mix and you've got an operational nightmare! He also suggests carrying out PCA and hedging the first two or three factors. Is there a preferred way to hedge interest rate derivatives, or calculate delta for that matter? What kind of hedging mechanism would a desk use? How much misspecification would a desk tolerate? There seems to be a void in the literature on this subject. I've nearly worn out my copy of PWiQF trying to find the solution. Hull doesn't say much more that what I stated above. Any other reading suggestions that deal specifically with interest rate derivative hedging?I would really appreciate it if anyone could give me some tips on how to maximize my hedge effectiveness.

Not sure about the second/third order complexities, but the first thing to say about initially delta hedging a swaption portfolio is KEEP IT SIMPLE - use the instruments with the best liquidity (and hence usually the lowest transaction costs) , especially if you are running a portfolio. Why would you hedge with a forward starting swap? If you are hedging (e.g.) the purchase of a two into five year receivers, you can delta hedge by receiving twos and paying sevens. However, depending on your portfolio, you might not bother, in the first instance, to hedge at the exact maturities; you may simply hedge the net long exposure by paying in sevens alone. You might even want to hedge with futures/bonds.The practicalities of hedging delta depend on each of the particular interest rate markets - there will be no 'perfect' rule. What is definitely true is that it will differ markedly from the academic examples which assume minimal or non-existent transaction costs, and hence continuous rebalancing. Hope this helps - I'm sure you'll get a more advanced analysis soon!

Thanks for the help.I suppose that my choice of hedging instruments is somewhat arbitrary. My goal is to simply replicate price movements in the swaption using linear instruments. I want to earn no profit at any point in time. If I use par swaps, wouldn't I lose my self-financing property? Let me know if I'm way off on this. Thanks again.

Ryan,Both methodologies are used in hedging swaptions. Bumping up the zero curve (or more accurately the input rate used to calculate the zero curve) is a widely used methodology. Sungard's Infinity and other systems use this approach known as "Partial Differential Hedge" or the "Risk-Point" method by Dattatreya. Using PCA analysis improves this analysis which assumes only a parallel shift in the term structure by incorporating other types of changes in the yield curve. Also, you have to consider the possibility of strong correlations between the different time buckets on the curve, which could allow you to reduce the amount of hedging instruments. I would agree with thefatman as to your choice of hedging instruments. Keep it simple by breaking down the swaption into its cashflows, and see what best replicates them, i.e. futures (and bonds).

Are futures and bonds recommended because because they make up the underying of the option (FRAs for the fixed leg of the swap) or because of liquidity concerns, or both? If swaps are used in a delta-hedge framework, is the practitioner concerned about having to tear up swaps that were entered into at the previous rebalancing event? Thanks.

<i>Are futures and bonds recommended because because they make up the underying of the option (FRAs for the fixed leg of the swap) or because of liquidity concerns, or both? If swaps are used in a delta-hedge framework, is the practitioner concerned about having to tear up swaps that were entered into at the previous rebalancing event? </i>Futures and bonds are (potentially) recommended because they can do the job of hedging you against interest rate risks! Of course, each time you stray away from the 'true underlying' (in this case the swap market) you will encounter some basis risk - but this may well be a risk worth taking on in exchange for better liquidity.I am looking at this from the perspective of a market maker with a large portfolio. This will require constant monitoring and rebalancing - individual trades will not be monitored, only the overall sensitivities of the portfolio, albeit in many dimensions. (NB - Some individual exotics may need monitoring, or large positions at particular strikes). If speed of execution is important (and it often is), then it may be easier to execute bond or futures trades to hedge your exposure to rates. <I>Later</i> you may eliminate the spread risk by executing a spread trade in the market, swapping your futures/bond risk, for swap positions. The practitioner doesn't generally care too much about 'tearing up' swaps. In the first instance, many banks are set up such that to the extent that an options desk execute swaps to hedge, they will do so via an internal trade - so no-one cares too much about unwinds etc. But to be honest, why bother to unwind at all? Just overlay the five year receivers you do today on top of the five year payers you executed last week and manage the residual positions.Hope this helps.TFM

Standard desk practice for hedging swaps/swaptions is usually something like the following.First let's exclude options & subsequent vega risk.To obtain today's (LIBOR) yield curve, the swap desk has selected a set of N "stripping instruments" (for USD, the instrument set consists of Eurodollar deposits to the first future, 20 or so Eurodollar futures, the 6y, 7y, 10y, 15y, 20y, 25y, and 30y swap rates ... the exact set varies with institution & may include FRAs), and fed these to the stripper. From these instruments, the stripper determines the discount factor df(t), which is the value today of 1 dollar delivered on date t. Throughout the day, the instrument prices and swap rates are updated on a more or less continous basis.Knowing the discount factors, one can price any swap, either spot starting or forward starting, as well as FRAs, depositis, Eurodollar futures, amortizing swaps, ... ie, all the so called delta instruments that a swap trader may be dealing with. This means that the value of the swap book is a function of the N deposit rates, futures prices, swap rates, ... that went into the stripper. We now figure out our "bucket deltas:" for each instrument used in the stripper, we bump the rate/price of that instrument, re-strip the curve to find a new set of discount factors, and then re-price all deals in our book; the difference between this value and the base case is our bucket delta to that particular instrument. We then repeat for all instruments to get all our bucket deltas. The swap (delta) trader keeps track of all these risksand hedges them out bucket by bucket. He may leave, say, some 12y risk open, offsetting it with 10y and 15y risk, but this is the trader's call.The reason that futures are used in the front part of the curve is that the first 5 years of futures are quite liquid, and can be bought or sold freely without chewing up bid-ask spread.Options (caps, floors, swaptions, range notes, inverse floaters, Bemudans, exotics) are no different. To get the (bucket) delta risks, strips the yc to find the discount factors, and prices all the deals in the book(s) to get the base value. Then one-by-one, one bumps the stripping instruments, re-strips the curve, re-prices all the deals in the book(s), and subtract out the base value to get the book's risk to that particular stripping instrument.To hedge this risk, one simply hands it off to the swap trader, who consolidates it with the delta risks from the swap/FRAs/futures etc. in his book. Typically the swap trader is responsible for hedging these delta risks. Usually one has thousands of deals, and all there delta risk is expressed in terms of the 30 or so stripping instruments.To get the "gamma risk" in the swap world one usually executes a parallel shift of the yield curve by, say +10bps, and then determines the price and bucket deltas of the shifted curve. One then repeats this at, say, -10bps, +20bps, -20bps, etc. until one is comfortable.Can one do better by using factor analysis and hedging only the dominant motions instead of all possible movements? Maybe, but one is always leaving some risk open on the table unless the factors add up to 100% of the probability ... in fact one is taking a proprietary view. This is why it is the trader's call.

Thanks guys, this isextremely useful.One more question. Say the trader detemines the deltas for 10 points along the curve. Would he then, using 10 hedging insturments, solve the system of 10 equations and 10 unknowns, or is this just a purely theoretical approach that's never used in practice?

In real life, we manage swaptions / caps and floors books.... So you look at individual delta / gamma / vega buckets, but you manage the whole. Let us say you buy a 5y5y payer swap today, you might not hedge with receiving in 10 yrs swap and paying in 5 years... You will look at your position to find out, maybe you will end up buying back some bunds you are short, or receiving truck loads of 2 yrs swap to compensate for the movements of your position on the curve following big moves in the market... No science, just a question of expectations, and global book positionning...