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What does SWIFT mean in trade finance?
SWIFT is the short form of "Society for Worldwide Interbank Financial Telecommunication". Swift defines its role in international financial transactions on its website as follows. “Our role is two-fold. We provide the proprietary communications platform, products and services that allow our customers to connect and exchange financial information securely and reliably. We also act as the catalyst that brings the financial community together to work collaboratively to shape market practice, define standards and consider solutions to issues of mutual interest.” 
In simple terms swift has two main roles in international financial transactions, firstly SWIFT provide a secure communications platform by which financial institutions can communicate each other reliably and fastly and secondly SWIFT establishes standard message formats which can be used on secure SWIFT platforms. Today banks use SWIFT platform to communicate each other when sending a wire transfer, issuing a letter of credit, advising a discrepancy message etc. Each of these message formats have a different code, which is called swift message types. For example a bank must use MT700 Issue of a Documentary Credit when issuing a letter of credit and MT 734 advice of a refusal when giving its refusal message. (MT means Message Type)

On below table you can find main swift  message types used in letters of credit transactions.

Message Type
Explanation
MT 700      
Issue of a Documentary Credit 
MT 701      
Issue of a Documentary Credit 
MT 705        
Pre-Advice of a Documentary Credit
MT 707        
Amendment to a Documentary Credit
MT 710        
Advice of a Third Banks Documentary Credit
MT 711        
Advice of a Third Banks Documentary Credit
MT 720        
Transfer of a Documentary Credit
MT 721        
Transfer of a Documentary Credit
MT 730        
Acknowledgement
MT 732        
Advice of Discharge
MT 734       
Advice of a Refusal 
MT 740        
Authorization to Reimburse
MT 742       
Reimbursement Claim 
MT 747        
Amendment to an Authorisation to Reimburse
MT 750        
Advice of Discrepancy
MT 752        
Authorisation to Pay, Accept or Negotiate
MT 754        
Advice of Payment/Acceptance/Negotiation
MT 756        
Advice of Reimbursement or Payment

Important Note : According to the current letters of credit rules, UCP 600, a letter of credit will be deemed to be operative letter of credit if it is transmitted via an authenticated electronic platform such as SWIFT.