You are in luck.  I remember a publication from years ago we had at the Lane County Extension Office and found it under the archive files.  Here is the information. 

HOMEMADE LIQUID PECTIN

Homemade pectin can be made from tart cooking apples that are slightly underripe or crab apples. 

MAKING THE PECTIN

Wash fruit and remove the stems. Slice the unpeeled fruit into a large heavy kettle. Leave the cores in the fruit. Remove bruises, worms and damaged parts. 

Apple Pectin (Yield: 1 cup pectin per pound of apples) 
1 pound sliced apples (include both slightly underripe and ripe) 
2 cups water

Bring to a boil in a covered, heavy kettle. Simmer for 20 minutes. Do not overcook the apples. Remove from the heat and let cool slightly. Pour the apple pulp and juice through a damp jelly bag or strainer lined with a damp cloth. Allow to drip into a bowl for 4 hours or overnight. To avoid cloudiness, do not squeeze the bag. Place the juice that dripped from the bag into a heavy kettle and boil rapidly, uncovered, until the volume is reduced by half. This liquid contains the pectin that is now ready to use.

Crab Apple Pectin
2 pounds sliced crab apples (Do not peel or core)
3 cups waterPlace crab apples and water in a heavy saucepan. Simmer 30-40 minutes, adding additional water if needed. Stir to prevent the mixture from sticking. Pour the cooked mixture into a damp jelly bag or cloth, set over a bowl, and let the juices drip from the bag. (Don’t squeeze the bag.) The juice that drips contains the pectin.

STORING THE PECTIN
Homemade pectin may be canned for long term storage. Pout hot pectin into hot half-pint or pint jars, leaving ½ inch headspace. Process jars at a simmering temperature (185° F.) for 15 minutes. Store canned pectin in a cool, dry, dark place and use within a few months. Refrigerate pectin after opening.

USING THE PECTIN
Homemade pectin may replace commercial liquid pectin (⅔ cup homemade pectin equals 1 packet commercial pectin). Follow instructions in pectin packages. If not following a pectin manufacturer’s recipe, use ⅔ cup homemade pectin for each 4 cups of fruit. Lemon juice should be added to prepared fruit that doesn’t taste tart (1 Tablespoon for each cup of juice). Use the test for pectin to estimate pectin content of the fruit. Some fruits (including apricots, figs, peaches, sweet plums, strawberries and pears) that are very low in pectin may require the addition of another cup of homemade pectin solution for each 4 cups of fruit. Try the minimum amount (⅔ cup of pectin) first. Add pectin to prepared fruit in a large kettle and bring to a boil. After 2 to 3 minutes of boiling, add 2 to 3 cups of sugar and boil rapidly until the gelling stage is reached.

Test for Pectin An alcohol test gives a rough estimate of the amount of pectin in fruit juice. In a small dish, put 1 teaspoon juice and 1 Tablespoon 70% rubbing alcohol. Stir slightly to mix. Juice high in pectin will form a solid jelly-like mass that can be lifted with a fork, Juices low in pectin will remain liquid or form only small particles jelly-like lumps. Note: Do not taste this mixture. Rubbing alcohol is poisonous. Keep the container out of reach of children.

I remember years ago trying it.  It was a lot of work but it did work.  We did use a mix of apples, not all green underripe. If you mean all underripe green apples when you said green apples, you certainly could try it.  Not a safety issue.  Good luck.

Thanks for using Ask Extension

Nellie Oehler