The correct answer is option 3: 2016. The Insolvency and Bankruptcy Board of India (IBBI) was established in the year 2016.

Option 1: 2014 - This is not the correct answer. The IBBI was not established in 2014.

Option 2: 2015 - This is not the correct answer. The IBBI was not established in 2015.

Option 4: 2017 - This is not the correct answer. The IBBI was not established in 2017.

In summary, the correct answer is option 3: 2016. The IBBI was established in that year.