RE: how to estimate the market implied ze ro coupon volatility

[Perissin Francesco]

Hi Nando
Never done such a thing, but I would consider a traded instrument which is quite close to the discount bond, i.e. a cap. Now, I would try one of the following ways:

1) take an historical series of cap volatility and yield curves, and perform calibrations on a simple model with analytical formulas, i.e. Hull&White. Now you have the short rate volatilities, which you can use for calculating analytically discount bond options. The current version of QL, as you know, is able to perform all of these steps.

2) try out if there's an analytical relationship between cap prices and discount bond options, in the B&S world, but I know you and I am sure that if you knew this, you wouldn't have written this e-mail!! In this way you would avoid introducing the calibration errors.

3) consider also that there exist options on Libor rates, but they are less liquid than caps, and I dont know price sources for them. Even for them, you should have the problem of tranlating their vols into discount bond option vols.

ciao
Francesco

-----Original Message-----
From: Ferdinando Ametrano [[hidden email]]
Sent: giovedì, 9 ottobre 2003 18:50
To: QuantLib-users
Subject: [Quantlib-users] how to estimate the market implied zero coupon volatility

I need to evaluate the volatility of a zero coupon (price or yield, or
discount factor... as you prefer).

I know I can perform historical analysis of the yield yield term structure
curve, but I would also like to estimate some kind of market implied
volatility.

I know that zero coupon volatility is not directly priced by the market (no
zero-coupon swaptions), but even a raw implied (non-historical)estimation
would be enough for me.

Any suggestion?

thank you

ciao -- Nando

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