A BSDE approach to fair bilateral pricing under endogenous collateralization

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• 作者：Tianyang Nie ; Marek Rutkowski
• 关键词：Collateral ; Fair pricing ; Funding costs
• 刊名：Finance and Stochastics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：20
• 期：4
• 页码：855-900
• 全文大小：1,125 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Quantitative Finance
  Finance and Banking
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Economic Theory
  Probability Theory and Stochastic Processes
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1122
• 卷排序：20

文摘

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.