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Hi,There is an approximation to the standard deviation of the error in P&L when delta hedging a call or put in the Black Scholes world that is a function of how many times you rehedge and vegahttp://www.ederman.com/new/docs/risk-non_conti ... edge.pdfIs there a similar expression for the standard deviation of the error in P&L when delta hedging a swaption using the Black model, if so is there a reference that someone can point me to.Cheers,Tony

I would think all you need to do is input the swaption vega in the approximation Have in mind that it is a only standard deviation under assumption of discrete hedging under geometric Brownian motion. In practice the real standard deviation will be much larger due to stochastic-vol and in particular jumps in underlying asset (when delta hedging fails = risk increases).Also the Derman approximation only gives you standard deviation of P&L, worst case even under geometric Brownian motion can be much worse.

Hi e3321534,This is a very interesting question. While the problem is not completely dissimilar to the situation in Derman's article, there are a few differences. But first let's look at how you price the option: V(0) = Ann(0) * E[ Max(S(T)-K,0) ], where the expectation is done in the Annuity measure. Things to note: 1. numeraire is not deterministic2. you can't invest in the modelled quantity: the swap rate is not an asset3. so the best way to do delta hedging would be to enter forward swap agreements4. but in the real life that swap is no available either5. which means that you really need to do delta hedging using some other swapsTo my knowledge this analysis has not been done so far, or at least has not been published. Now, to simplify the problem, you can ignore the technical fact that forward swaps are not available, and try to figure out the P&L assuming forwards swaps are available. The problem is that the swap P&L does not only depend on the forward swap rate, but on the rate between now and the start of the swap as well. So the simplest setting I can think of is: - assume that the forward rate between now and the start of the swap (swaption expiry) is constant, call it R; calculate R0- call the swap rate is S; you know S0k- write the simplified formula for the annuity in terms of R and S- you need to diffuse R and S; S will be a martingale, you can choose if it's arithmetic or geometric Brownian motion- postulate a vol for R and a correlation between R and S - figure out the diffusion for R (the non-arbitrage condition similar to the HJM condition) - do a Monte Carlo and repeat Derman's exercise, i.e. keep track of the P&L- play with various parameters until you reach a good empirical understanding of the total hedging error- then try to see if you can prove your results analytically.Best of luck,V.

QuoteOriginally posted by: e3321534Is there a similar expression for the standard deviation of the error in P&L when delta hedging a swaption using the Black model, if so is there a reference that someone can point me to.Some related literature:R Ahmad, P Wilmott. Which Free Lunch Would You Like Today, Sir? Wilmott magazine, 2005. http://www.wilmottwiki.com/wiki/uploads ... 93105.pdfM Henrard. Swaptions: 1 price, 10 deltas, and... 6 1/2 gammas. Wilmott Magazine, pp. 48-57, November 2005. http://ideas.repec.org/p/wpa/wuwpfi/0407018.html