标题：A BSDE approach to fair bilateral pricing under endogenous collateralization
作者：Nie, Tianyang; Rutkowski, Marek
作者机构：[Nie, Tianyang] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.; [Rutkowski, Marek] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006 更多
通讯作者：Rutkowski, M;Rutkowski, M
通讯作者地址：[Rutkowski, M]Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia;[Rutkowski, M]Warsaw Univ Technol, Fac Math & Informat Sci, PL-00661 Warsaw, P 更多
来源：FINANCE AND STOCHASTICS
关键词：Collateral; Fair pricing; Funding costs
摘要：Nie and Rutkowski (Int. J. Theor. Appl. Finance 18: 1550048, 2015; Math. Finance, 2016, to appear) examined fair bilateral pricing in models with funding costs and an exogenously given collateral. The main goal of this work is to extend results from Nie and Rutkowski (Int. J. Theor. Appl. Finance 18: 1550048, 2015; Math. Finance, 2016, to appear) to the case of an endogenous margin account depending on the contract's value for the hedger and/or the counterparty. Comparison theorems for BSDEs from Nie and Rutkowski (Theory Probab. Appl., 2016, forthcoming) are used to derive bounds for unilateral prices and to study the range for fair bilateral prices in a general semimartingale model. The backward stochastic viability property, introduced by Buckdahn et al. (Probab. Theory Relat. Fields 116: 485-504, 2000), is employed to examine the bounds for fair bilateral prices for European claims with a negotiated collateral in a diffusion-type model. We also generalize in several respects the option pricing results from Bergman (Rev. Financ. Stud. 8: 475-500, 1995), Mercurio (Actuarial Sciences and Quantitative Finance, pp. 65-95, 2015) and Piterbarg (Risk 23(2): 97-102, 2010) by considering contracts with cash-flow streams and allowing for idiosyncratic funding costs for risky assets.