hedging / at the money forward option

a bank offers a 1-year term product in which the customer is given anannual rate. but the customer has an embedded option to redeem anytime after 3 months and he will receive whatever interest he has accrued up until then. the bank is trying ot hedge of the customer redeeming early. can someone plz help me understand any of the following paragraph, in basic terms: i dont seem to understand any of it. i dont know how an at the money forward option works , and how this is a way to hedge this term product. any ideas? thanks! "Note that all certificates issued on a particular day will be hedged with identical instruments. The best hedge would be to purchase an ATM (at the money) forward option on the swap curve. This option would then be exercised by the bank if the investor cashed in his certificate. With the embedded option modeled in this way, the bank’s hedge slippage can not be affected by yield curve shape or level, but only by delta hedging slippage and by differences between assumed and actual rational exercise. "

Ack. First, a forward option is usually an forward contract without a fixed expiration date. For example, you might be able to take delivery anytime between 3 months and 1 year. Of course, here that doesn’t really work because the amount that the customer can get is not fixed but is accruing daily. So the guy who wrote that pompous thing is just wrong (which is why he used that pompous language). A forward option on the swap curve sounds about like an American swaption to me and it doesn’t sound like “the best hedge” to me either. The “embedded” is a misplaced adjective, the next clause is wrong, the delta hedging is irrelevant, and the last phrase means that the customer may not exercise his option when he should so you might make money on your hedge. I think I might read something different.

Of course, the question of how best to hedge such a thing with normally traded derivatives is kind of an interesting question…

thx joey. could you also plz explain what delta hedge slippage is? and why is embedded is a misplaced adjective? also, how do i know if this at the money forward option is a call or a put?

A forward option isn’t really a call or put; it’s a forward contract and the option part is about time. For example, suppose that I make a deal with you that you will deliver 10 Million Euros to me at an exchange rate of 0.65 anytime between 4 and 6 months from now when I say (I have no idea what the rate ought to be). You’re going to deliver those Euros to me, it’s just a matter of when. “delta hedge slippage”, I guess, is the real world cost of recreating a derivative by trading in the underlier. So if I want a put option I can either buy a put option or I can go short delta shares of the stock and keep re-adjusting my position everytime delta changes. There’s just no chance that my return will be the same because the world gets in the way and the difference would be slippage. “Embedded” is misplaced because the we’re talking about hedging the option not talking about hedging the bond. Once we have identified the option (to put the bond) there’s no reason to talk about the “embedded” option except to sound pompous. I guess I don’t object to it much, except that I object to the whole paragraph because you didn’t understand it. There’s nothing terribly complicated going on here and the author didn’t really give you any good information but the text is hard to read and filled with jargon that is irrelevant. How about this - “Note that all certificates issued on a particular day will be hedged with identical instruments. Each certificate gives the investor an option to exchange the certificate for the accrued interest on any day between 3 months and the 1-year maturity date. The appropriate hedge for this risk is a security that allows the bank to take a loan at I(t) where I(t) = forward interest rate at time t for a loan of length 1 yr - t which the bank could exercise at any time t between 3 months and 1 yr. Such a derivative would be a forward option on a LIBOR loan (or something, I dunno). We could get one of those geeky quant guys downstairs to tell us how much that option is worth and how to synthetically create one from interest rate securities. If we did what that geeky guy told us, our return would be the same as if the bank had taken loans without options except that our hedging won’t work perfectly and the person who gave us the loan won’t have access to the geeky guy downstairs so he probably won’t do the right thing anyway”.

I guess it’s the interest rate of the loan not the forward rate that is the appropriate hedge, right. I’ll have to ask the geeky guy downstairs.

thanks a lot joey, appreciate all the help!