Hi,I am testing the hedging performance of several term structure models in a simulation that generates evolutions of swaption implied volatilities and forward rates under the physical measure.I was wondering the following: Can I analyze the delta hedging performance of my models with regard to a derivative whose real world price I do not know?In most papers on the subject a replicating portfolio is constructed which has the same initial price and the same delta as the derivative to be hedged. This would not be possible without knowing the price, of course.But say I want to hedge a barrier option which cannot be priced analytically in my real world framework but whose sensitivities can be computed analytically in my hedging models. I could replicate the option delta without replicating the option price. Then I could delta hedge the option until expiry and compare the standard deviations of the option payoff and of my hedging portfolios.Would this make sense?

You can do it, but I'm doubtful what it tells you. Your average option payoff in the simulation will be a "model actuarial value". Say my P-model for a stock price, say SPX, is GBM. I conduct your hedging experiment on my model against a vanilla otm put option, say 10% otm.I learn that I can replicate the model average option payoff with an average error or 10% and std dev. of 30%.So what? Then I go to the actual listed SPX options market and see the price of that 10% otm option was 3x what my model actuarial value was.The same sort of gross disparity could hold for your barrier option.

Thank you very much for your quick response. The thing is, I am a little confused with one thing in my project. A short while ago I had a correspondence with a well-known author in the field. He suggested I analyze a specific barrier option which can be priced using a static replication approach. But unfortunately the static replication does not work without further assumptions. In particular, for the replication at time [$]t_0[$] I need the prices[$]C(S({T_1}) = K_u, K = K_u, T_1, T_2),[$]i.e. the future time [$]T_1[$] price of a vanilla option starting at time [$]T_1[$] with strike [$]K_u[$] given the underlying's future value is [$]K_u[$] (ATM). In my P-model this future price is not given.In my hedging models I can make assumptions for these conditional future implied volatilities, but I have no true market price (in my real world model). The professor said I should just make assumptions and I was wondering how much my results actually depend on these assumptions, and if the real world prices really matter or if I could even do completely without computing them.Of course I could also Monte Carlo simulate the option price in my real world simulation. P.S.: My hesitation with regard to the assumptions has a reason. My P-model is not as simple as assuming the real world evolves according to Black Scholes/Hull White or some other term structure model or SDE. I am basically using a process which extracts statistical information about actual historical evolutions of rates and implied volatilities and any assumption I am making at this point is a step away from using pure historical data.

Well, first of all, let me stress that rates are not my area, so I have only general comments. I understand that you are using some historical data. But, it's not all clear to me what you are trying to accomplish. If the purpose is to derive some values for certain barrier options by a static replication scheme and then do something of economic consequence with those,say for an employer, then I think my previous comments stand. Your derived values could be "way off" andapparently you have no data to test that.If it's more an academic exercise, comparing how a hedging scheme derived under one model might perform againsttheoretical prices derived from that model or another model, then that is a more controlled environment. As your professor said, go ahead and make assumptions. It should be possible to test their effect by introducing othermodels where they are omitted/violated. For example, if the static replication only holds under a diffusion assumption,see what happens when you have jumps.

Thank you. This is a purely academic exercise. My goal is to take various term structure models and let them compete for the best delta and delta + vega hedge within a simulation that evolves forward rates and the swaption implied volatility surface under the physical measure. What has been done before in the literature is mostly look at how well models would have hedged in the one available market history or create virtual market data by simulating a more or less arbitrary diffusion or using a term structure model. What I am basically doing is taking historical market data and simulating synthetic market histories (comprising swaption implied volatilities + rates) that capture the statistical properties of the one real market history (such as jumps).Currently I am trying to decide which derivatives I want to hedge and examine in this framework. Of course I can just do the swaptions that are given. But I would also like to find an additional derivative. That's why in the other thread I asked whether there is any other derivative that can be priced analytically if one knows only cap and swaption swaption prices, independent of any model.But now I think it wouldn't be so bad to just make assumptions for the barrier option in the real world simulation and apply the static hedging approach.