When you create an API using Gateway and map a custom domain, AWS API Gateway makes an entry in cloudfront distribution
source: http://docs.aws.amazon.com/apigateway/latest/developerguide/how-to-custom-domains.html
For every API you create, API Gateway sets up an Amazon CloudFront distribution for the API. Requests with the default API URL are routed through the corresponding CloudFront distribution. Similarly, for every custom domain name, API Gateway sets up a CloudFront distribution. An API request with the custom domain name is routed through the custom domain name's CloudFront distribution.
However the cloudfront IPs can change when AWS updates the ip ranges.
As a user of the API, how do I bind a static IP to the custom domain mapped to Gateway so that I need not update firewall egress settings whenever AWS updates the IP ranges?