A BSDE approach to fair bilateral pricing under endogenous collateralization
Tianyang Nie , Marek Rutkowski
AbstractResults from Nie and Rutkowski are extended to the case of the margin account, which may depend on the contract’s value for the hedger and/or the counterparty. The present work generalizes also the papers by Bergman, Mercurio and Piterbarg. Using the comparison theorems for BSDEs, we derive inequalities for the unilateral prices and we give the range for its fair bilateral prices. We also establish results yielding the link to the market model with a single interest rate. In the case where the collateral amount is negotiated between the counterparties, so that it depends on their respective unilateral values, the backward stochastic viability property studied by Buckdahn et al. is used to derive the bounds on fair bilateral prices.
|Journal series||Finance and Stochastics, ISSN 0949-2984|
|Publication size in sheets||2.25|
|Keywords in Polish||wsteczne równania stochastyczne, wycena bezarbitrazowa|
|Keywords in English||Collateral, Fair pricing, Funding costs|
|ASJC Classification||; ;|
|Abstract in Polish||W pracy rozszerzono poprzednie wyniki autorów oraz uogólniono wyniki Bergmana, Mercurio i Pitebarga.|
|Score|| = 35.0, 02-02-2020, ArticleFromJournal|
= 35.0, 02-02-2020, ArticleFromJournal
|Publication indicators||= 4; = 5; : 2016 = 1.748; : 2016 = 1.55 (2) - 2016=1.696 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.