Hull White Tree pricing help

This example is taken from here:

http://www.mathworks.com/help/fininst/swaptionbyhw.html

Rates =0.075 * ones (10,1);
Compounding = 2;
StartDates = ['jan-1-2007';'jul-1-2007';'jan-1-2008';'jul-1-2008';'jan-1-2009';...
'jul-1-2009';'jan-1-2010'; 'jul-1-2010';'jan-1-2011';'jul-1-2011'];
EndDates =['jul-1-2007';'jan-1-2008';'jul-1-2008';'jan-1-2009';'jul-1-2009';...
'jan-1-2010';'jul-1-2010';'jan-1-2011';'jul-1-2011';'jan-1-2012'];

    ValuationDate = 'jan-1-2007';

    % define the RatesSpec
    RateSpec = intenvset('Rates', Rates, 'StartDates', StartDates, 'EndDates',...
    EndDates, 'Compounding', Compounding);

    % use HWVolSpec to compute the interest-rate volatility
    Volatility = 0.05*ones(10,1);
    AlphaCurve = 0.01*ones(10,1);
    AlphaDates = EndDates;
    HWVolSpec = hwvolspec(ValuationDate, EndDates, Volatility, AlphaDates, AlphaCurve);

% use HWTimeSpec to specify the structure of the time layout for an HW interest-rate tree
HWTimeSpec = hwtimespec(ValuationDate, EndDates, Compounding);

% build the HW tree
HWTree = hwtree(HWVolSpec, RateSpec, HWTimeSpec);

% use the following arguments for a 1-year swap and 3-year swaption
ExerciseDates = 'jan-1-2010';
SwapSettlement = ExerciseDates;
SwapMaturity   = 'jan-1-2012';
Spread = 0;
SwapReset = 2 ;
Principal = 100;
OptSpec = 'put';
Strike= 0.04;
Basis=1;

% price the swaption
PriceSwaption = swaptionbyhw(HWTree, OptSpec, Strike, ExerciseDates, ...
Spread, SwapSettlement, SwapMaturity,'SwapReset', SwapReset, ...
'Basis', Basis,'Principal', Principal)

Now how do I fix this if my point of valuation is not January 1st 2007 but December 1st 2006 or December 28th 2006 ?

Do the Timespec for building the tree have to be equally spaced? I tried to simply add the extra date to the current TimeSpec but that didn't work.

For a December 1st 2006 valuation date, I tried to construct the following time spec:

    TimeSpec = hwtimespec(ValuationDate, daysadd(ValuationDate,30*(1:60),6), Compounding)

But that only worked when I changed the 'SwapReset' in swaptionbyhw from 4 to 12. Which I am not sure makes sense since these swaps reset every 3 months or 4 times a year.

Also, I don't know how to proceed if the ValuationDate was say Dec-15-2009, just 15 days prior to exercise date. Will I have to build my tree at 15 day intervals? Will my SwapReset be 24 times a year?