I am currently trying to find out different ways of calibrating a Ho-Lee model (special case of the Hull-White model) to price various types of derivatives, say 1) futures, 2) cap/floors and 3) more exotic derivatives (I already know this model would not be the first choice to do so but it's only for illustration purposes).

The question is the following. What would be the best way of calibrating volatility in all the 3 cases above, most significantly 1) and 2) ? To be sure, I would be calibrating the volatility of the short rate, and in no case forward volatility?

I am a bit confused to I appreciate market practitioner's view on the subject. Thanks in advance!

This model has one single volatility parameter, so if you insist on "calibrating" it you have a choice between picking one instrument and backing out the vol that will give you the exact price or use whatever available instruments you have and minimize some measure of mispricing, which usually translates into some kind of sum of squared errors. Or, if your currency of focus is USD, you can peg it at 80 bps per year, and you are probably not going to be too far off... As a minor history lesson, Ho-Lee is not a special case of anything, really, and most definitely not Hull-White. They published the first interest rate modeling paper that took the initial term structure as an input and focused on how to generate an arbitrage-free dynamic process of the whole yield curve. Subsequent work by Heath, Jarrow and Morton shortly thereafter somewhat swamped their contribution, by generalizing the idea to continuous time and an arbitrary number of factors, in the process addressing (mostly successfully) some stochastic processes problems not previously dealt with in finance related research. 

@bearish thanks for your answer, I was actually thinking of HJM and not Hull-White, and it's certainly wrong to say that Ho-Lee would be a special case of HJM. 

Going back to fitting a yield curve to Ho-Lee, I can see that it is possible to fit the model "perfectly" using a closed form solution of the time-dependent drift parameter for today's yield curve. However, the formula contains the volatility term, which takes me back to my original question (and your answers too) which I'll break up in two smaller ones:

1. Imagine I am trying to price a futures contract starting at T using the Ho-Lee model. I can write the fair price of such contract as the value of a forward contract for that same period of time minus a convexity adjustment, which depends on sigma defined as "standard deviation of the change in the short-rate interest rate in 1 year". What is the best way of obtaining the correct sigma then?
2. Suppose I just want to fit the yield curve entirely using Ho-Lee. As mentioned above, there is a closed-form solution for the time-dependent drift term depending on volatility. Would I have to combine this knowledge with least-squared error minimization (as you suggest) to obtain sigma ? Would it be possible to instead use BS cap vols for the same time period or does that make no sense?

Getting a bit confused now as you can see!