Exchange Edge is using self-signed certificate for the SMTP services and for subscribe new Exchange synchronization between Hub and Edge servers.
Self-signed certificates are only valid for one year.
To display certificate used by Exchange Server run this command:
Get-ExchangeCertificate | fl
To renew a self-signed certificate for Exchange Edge you can use Exchange Management Shell command:
Get-ExchangeCertificate | New-ExchangeCertificate
To [...]

Useful links:

The OpenSSL Project: http://www.openssl.org/
OpenSSL for Windows: http://www.slproweb.com/products/Win32OpenSSL.html

 
We want to get an official SSL certificate from well-known public Certificate Authority (CA). We have to generate a certificate request, for example using OpenSSL.
 
Steps to request a certificate – to generate a CSR file (Certificate Signing Request)
1. Creating a private key
You need to create a private key [...]