# Any resources or literature on interpolation schemes for future dates?

I have a whole stack of the popular option trading/modelling books (Natenburg, Sinclair, Hull, etc.) None of them however address the idea of pricing or modelling values at a point in the "future". That is moving curve anchor dates or horizon dates forward along the various curves (vol, rates, forwards, etc.)

For instance suppose I have the zero rate curves for USDMXN and I want to run this experiment (assume all dates are valid market dates):

1. Today, Nov 16, determine the forward outright point for a Dec 15 expiry and call that X.
2. Today, Nov 16, determine the forward outright point for a Jan 14 expiry call that Y.
3. Today, Nov 16, set anchor date for curves to Dec 15 and move current spot to X, (some systems seem to require that you do this, other's do not, effectively we want to move spot to the place on the forward curve that we previously witnessed it top be in step 1, such that when we interpolate to Jan 14 our starting point is equivalent.)
4. Today, Nov 16, determine the current forward outright point for Jan 14 AS IF the current date was Dec 15 as given by the future anchor date and call that Z

My expectation is that Y == Z, and this is in fact what I see from a various of off the shelf products (including BBG).

Simple interpolation schemes work fine for standard price curves, but they don't work for discount curves, given that you need to find the rate value that allows appreciation in a shorter period (Dec to Jan) but with the same target (in this case Y) as the longer period (Nov to Jan).

edit:

My objective is this: Have an interpolation scheme for forward points that calculates the forward correctly, from zero rate curves, irrespective of where the anchor t is.

$$F_{t,T} = S_t\frac{D^f_{t,T}}{D^d_{t,T}}$$

• I am not sure I fully understand the question. If I "simulate" a world of 15.12., then the 14.01. contract will be only of 1 month length (not 2), making it more equal to X rather than Y? Moreover, I am not sure what you mean by shifting "current spot to X" --> that would only work for past dates? Could you clarify a bit more? Other than that, converting points to yields you would easily obtain (1+x)*(1+z)=(1+y). Converting this to discount factors is easy, but I feel your question is a bit more advanced? Nov 16 '20 at 15:16
• @KevinT I've added a bit for clarity, hopefully it helps. I understand that if I were looking at options or actual trades, the contracts would be different (1M vs 2M), I'm actually only interested in determining an outright forward for a specific date, from two DIFFERENT anchor dates, using the same curve data. That's what I was trying to show in my example. Nov 17 '20 at 13:26