how to estimate the market implied zero coupon volatility

[Ferdinando M. Ametrano-3]

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

[Ferdinando M. Ametrano-3]

At 08:33 AM 10/10/2003 +0200, Perissin Francesco wrote:
>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.

thank you Francesco... I should have been more precise.

I'm already using a calibrated Hull and White model to estimate eurodollar
futures convexity adjustment. What I am now trying to do is to estimate
this convexity adjustment with an alternative approach that won't need a
complete (calibrated) yield curve model.

The idea is to evaluate the convexity adjustment requiring that the
eurodollar stripped yield curve would correctly price the observed market
swap prices. The convexity adjustment of the IMM_T1 eurodollar future
depends on:
a) the volatility of the underlying IMM_T1->T2 forward rate
b) the volatility of the discount factor D(IMM_T1)
c) their correlation.

There is no problem about the volatility of the underlying IMM_T1->T2
forward rate (a), which can be extracted from the caplet vol curve. If I
could estimate in a quick and easy way the volatility of the discount
factor D(IMM_T1) (b) then I could use the swaps (1Y, 2Y, 3Y, 4Y, 5Y, 7Y,
10Y) for the estimation of a piecewise constant correlation function (c).

I don't need accurate estimation of (b) since the correlation function will
ensure the swap price matching. So I'm looking for the quickest way... a
crude non-historical approach that doesn't need a calibrated model.

I think I cannot use the swaps for estimating (b)+(c) together with a
piecewise constant function, while it shouldn't be a problem to assume that
just the correlation (c) is piecewise constant

ciao -- Nando