Hi, and thanks for your question.
First, it is not possible for an accurate valuation to be done of your shotgun over the internet. This needs to be done, in person, with a reputable gun collector or expert in your area. I can however give you a few pointers! There is a great website you can go to for a good amount of information on these guns, you'll find it at http://www.parkerguns.org/.
Click on "Parker Identification" on the left menu and you can get some interesting facts and technical specs about your gun. Just by inputting your serial number, it appears your gun was manufactured in 1880, rather than 1875 which you say is stamped on the gun. Older Parker Brothers guns, in good condition and of suitable desire, can be worth quite a bit. Here is a current listing for a 10 gauge made in 1887 that's listed at $9,500 http://www.gunsamerica.com/976981614/Guns/Shotguns/Parker-Shotguns/PARKER_BROS_10_GA_QUALITY_ONE_SXS_HAMMER_SPORTING_GUN.htm
That said, this gun is in pristine shape and is one of the best models made. There is also a parker gun of similar vintage listed at just under $1,000. Once you check out the identification guides at parkerguns.org you can find out a few more things about your gun and what quality it was, which, despite its current condition, will dictate its value.
Their site also has a forum where you can interact with Parker experts
and enthusiasts who could possibly value your gun with all the information, but will most likely tell you to get it evaluated in person as well. Antique and vintage gun dealers are always interested in seeing something like this and are usually happy to give a few minutes of their time to look at an old gun with a rich past.
Thanks again for coming to just answer! Please let me know if you need more information by pressing REPLY or if this information was helpful to you please press ACCEPT. Best wishes!