Παράγωγα με εγγύηση: αποτίμηση με αναπροσαρμογή της αξίας χρηματοδότησης
KeywordsΕγγυήσεις ; Αναπροσαρμογή αξίας χρηματοδότησης ; Μοντέλο Cox, Ross & Rubinstein ; Μοντέλο Piterbarg ; Κίνδυνος αθέτησης ; Περίοδος αναπροσαρμογής ; Προβλεπτική ικανότητα ; Collateral ; Funding value adjustment (FVA) ; Cox, Ross & Rubinstein model ; Piterbarg’s model ; Default risk ; Margin periods ; Forecasting
This thesis aims the pricing of derivatives with collateral and their comparison with derivatives with non-collateral. The credit crisis of 2008 changed the traditional manner of pricing derivatives. Firstly, by posting collateral in a trade to mitigate the counterparty credit risk, and by the realization that banks are not risk-free and they cannot borrow at the risk-free rate. This led banks to introduce the controversial adjustment to derivative prices, known as funding value adjustment (FVA), which is interlinked with collateral posting. Firstly, we extend Cox, Ross and Rubinstein model to include collateral and funding value adjustment. Then we prove that this model is a discrete analogue of the Piterbarg’s partial different equation (PDE) model, which has included collateral. We show a diagrammatic representation of the two models with and without collateral and that the prices of both models coincide. Also, we see that there is a default risk for different margin periods of collateral. Finally, we conduct parameter estimation and study the forecasting power of the models.