ITA can't price an RTW, but you can get the base fare from EF, and then use ITA to get an estimate of taxes and fees for various routes.

Ex-LHR base prices:
Results from https://www.ExpertFlyer.comFare Information Search:

Departing LHR on 09/17/18 for LHR
Flying AA
Viewing in currency USD
Validated Results

Fare Basis Airline Booking Trip Type Fare Cabin Effective Expiration Min/Max Advanced
Class Date Date Stay Purchase Req
LCIRAT17 AA L Round-Trip 1940.39 (USD) E 07 / --
LCIRAT21 AA L Round-Trip 2228.05 (USD) E 07 / --
LGLOB26 AA L Round-Trip 2353.57 (USD) E -- / 12M
LONE3 AA L Round-Trip 2353.57 (USD) E -- / 12M
LGLOB29 AA L Round-Trip 2745.83 (USD) E -- / 12M
LONE4 AA L Round-Trip 2745.83 (USD) E -- / 12M
LCIRAT25 AA L Round-Trip 2745.83 (USD) E 07 / --
LGLOB34 AA L Round-Trip 3334.22 (USD) E -- / 12M
LONE5 AA L Round-Trip 3334.22 (USD) E -- / 12M
LGLOB39 AA L Round-Trip 3922.62 (USD) E -- / 12M
LONE6 AA L Round-Trip 3922.62 (USD) E -- / 12M
DCIRAT17 AA D Round-Trip 5751.86 (USD) B 07 / --
DCIRAT21 AA D Round-Trip 6614.84 (USD) B 07 / --
DONE3 AA D Round-Trip 7153.55 (USD) B -- / 12M
DCIRAT25 AA D Round-Trip 7549.73 (USD) B 07 / --
DGLOB34 AA D Round-Trip 8106.74 (USD) B -- / 12M
DONE4 AA D Round-Trip 8106.74 (USD) B -- / 12M
DONE5 AA D Round-Trip 9035.09 (USD) B -- / 12M
ACIRAT17 AA A Round-Trip 9779.08 (USD) F 07 / --
DONE6 AA D Round-Trip 10329.56 (USD) B -- / 12M
ACIRAT21 AA A Round-Trip 11217.38 (USD) F 07 / --
AONE3 AA A Round-Trip 12545.84 (USD) F -- / 12M
ACIRAT25 AA A Round-Trip 12655.67 (USD) F 07 / --
AGLOB34 AA A Round-Trip 14475.76 (USD) F -- / 12M
AONE4 AA A Round-Trip 14475.76 (USD) F -- / 12M
AONE5 AA A Round-Trip 16125.88 (USD) F -- / 12M
AONE6 AA A Round-Trip 18563.13 (USD) F -- / 12M


Ex-OSL base prices:
Results from https://www.ExpertFlyer.comFare Information Search:

Departing OSL on 09/17/18 for OSL
Flying AA
Viewing in currency USD
Validated Results

Fare Basis Airline Booking Trip Type Fare Cabin Effective Expiration Min/Max Advanced
Class Date Date Stay Purchase Req
LCIRAT17 AA L Round-Trip 1924.01 (USD) E 07 / --
LGLOB26 AA L Round-Trip 2094.42 (USD) E -- / 12M
LONE3 AA L Round-Trip 2094.42 (USD) E -- / 12M
LCIRAT21 AA L Round-Trip 2311.48 (USD) E 07 / --
LGLOB29 AA L Round-Trip 2481.53 (USD) E -- / 12M
LONE4 AA L Round-Trip 2481.53 (USD) E -- / 12M
LCIRAT25 AA L Round-Trip 2792.48 (USD) E 07 / --
LGLOB34 AA L Round-Trip 2878.60 (USD) E -- / 12M
LONE5 AA L Round-Trip 2878.60 (USD) E -- / 12M
LGLOB39 AA L Round-Trip 3275.55 (USD) E -- / 12M
LONE6 AA L Round-Trip 3275.55 (USD) E -- / 12M
DCIRAT17 AA D Round-Trip 5144.04 (USD) B 07 / --
DCIRAT21 AA D Round-Trip 5718.57 (USD) B 07 / --
DONE3 AA D Round-Trip 6364.52 (USD) B -- / 12M
DCIRAT25 AA D Round-Trip 6480.16 (USD) B 07 / --
DGLOB34 AA D Round-Trip 6967.11 (USD) B -- / 12M
DONE4 AA D Round-Trip 7039.99 (USD) B -- / 12M
DONE5 AA D Round-Trip 8039.16 (USD) B -- / 12M
DONE6 AA D Round-Trip 9069.43 (USD) B -- / 12M
ACIRAT17 AA A Round-Trip 9072.22 (USD) F 07 / --
ACIRAT21 AA A Round-Trip 9940.70 (USD) F 07 / --
ACIRAT25 AA A Round-Trip 10929.42 (USD) F 07 / --
AONE3 AA A Round-Trip 11162.88 (USD) F -- / 12M
AGLOB34 AA A Round-Trip 12881.00 (USD) F -- / 12M
AONE4 AA A Round-Trip 12881.00 (USD) F -- / 12M
AONE5 AA A Round-Trip 14348.05 (USD) F -- / 12M
AONE6 AA A Round-Trip 16516.93 (USD) F -- / 12M