FORECAST function to interpolate using index match given blank cells

After half a day, I will venture a response.

1) Are you required to use Excel for this? Gnumeric has a built in INTERPOLATION() function that is usually easier to use for interpolation problems than anything in Excel. I checked the helpfile, and it claims that INTERPOLATION() knows how to ignore blanks. If I assume the behavior that it will use when it ignores blanks, I would expect Gnumeric's INTERPOLATION() function to work quite easily for this. A lookup function to return the values from the desired "observation date" row [INDEX(...MATCH(),0)], and then put that into the main INTERPOLATION() function. I don't have immediate access to Gnumeric for testing, but I would expect something like =INTERPOLATION('raw data'!B1:M1,INDEX(B2:M254,MATCH(C3,'raw data'!A2:A254,0),0),C5) would work.

2) I have noted before that the hardest part of interpolation in Excel is the lookup part (if you must use Excel or other spreadsheet that does not include a built in interpolation function). In this case, the difficulty is further complicated by the irregular "shape" of the source data caused by the blanks. My thought here would be to do something to get rid of the blanks for each observation date so I have lookup vectors for each row that can be used to find the desired expiration date. Are you required to do all of the interpolation in a single cell, or are you open to a solution that uses multiple helper columns (I'm always inclined towards helper columns and doubt I could come up with a single cell mega formula for this). The approach I used:
2a) I used a SMALL(IF(...)) array function to identify which dates had values for each row in "Raw Data" and create a horizontal lookup vector for dates. =SMALL(IF($B2:$M2="","",$B$1:$M$1),O$1) [copy/paste/fill into columns O:Z] where O1:Z1 contain the numbers 1 to 12.
2b) A lookup function to get values =INDEX($B2:$M2,MATCH(O2,$B$1:$M$1,0)) into AB2 and copied into columns AB:AM.
2c) I like to get slope and intercept for each pair of points rather than use the FORECAST() function, so I add two more sets of helper columns to calculate slope and intercept. =SLOPE(AB2:AC2,O2:P2) into column AO:AZ. =INTERCEPT(AB2:AC2,O2:P2) into columns BB:BM
2d) With the lookup stuff set up, I can go to output and use a MATCH() function to find the desired row number based on observation date, another MATCH() function to get the column number based on expiration date, then two INDEX() functions to return the corresponding slope and intercept. Plug slope and intercept into y=m*expiration date+b to complete the interpolation.

Obviously, something using a built in interpolation function that knows how to ignore blanks is a lot easier. If you are opposed to all of the helper cells in the Excel solution, perhaps someone else will come along with a solution that can fit into a single cell.

After testing in Gnumeric, it doesn't work exactly as I expected. I'm not sure why, but it doesn't do very well with the blanks. This worked, though (and is still a lot easier than what I did in Excel):

1) For some reason, it handled blanks just fine when on the same tab, so I added a helper column to interpolate across each row at the expiration date in Raw Data. =INTERPOLATION($B$1:$M$1,B2:M2,Output!$C$5) in column O
2) Then a simple lookup function in Output to return the value at the specified observation date. =VLOOKUP(C3,'Raw Data'!$B$2:$M$254,15,TRUE).

Hopefully something in all of that helps.