AbstractsPhysics

A bank borrowing some money has to give some securities to the lender, which is called collateral. Different kinds of collateral can be posted, like cash in different currencies or a stock portfolio depending on the terms of the contract, which is called a Credit Support Annex (CSA). Those contracts specify eligible collateral, interest rate, frequency of collateral posting, minimum transfer amounts, etc. This guarantee reduces the counterparty risk associated with this type of transaction. If a CSA allows for posting cash in different currencies as collateral, then the party posting collateral can, now and at each future point in time, choose which currency to post. This choice leads to optionality that needs to be accounted for when valuing even the most basic of derivatives such as forwards or swaps. In this thesis, we deal with the valuation of embedded optionality in collateral contracts. We consider the case when collateral can be posted in two different currencies, which seems sufficient since collateral contracts are soon going to be simplified. This study is based on the conditional independence approach proposed by Piterbarg [8]. This method is compared to both Monte-Carlo simulation and finite- difference method. A practical application is finally presented with the example of a contract between Natixis and Barclays.