Fair bilateral pricing under funding costs and exogenous collateralization. (18th April 2017)

• Record Type: Journal Article
• Authors: Nie, Tianyang; Rutkowski, Marek
• Is Part Of: Mathematical finance. Volume 28:Number 2(2018)
• Page Start: 621
• Page End: 655
• Publication Date: 2017-04-18
• Subjects: BSDE -- collateral -- fair pricing -- funding costs -- hedging -- PDE; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12145
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: Bielecki and Rutkowski introduced and studied a generic nonlinear market model, which includes several risky assets, multiple funding accounts, and margin accounts. In this paper, we examine the pricing and hedging of contract from the perspective of both the hedger and the counterparty with arbitrary initial endowments. We derive inequalities for unilateral prices and we study the range of fair bilateral prices. We also examine the positive homogeneity and monotonicity of unilateral prices with respect to the initial endowments. Our study hinges on results from Nie and Rutkowski for backward stochastic differential equations (BSDEs) driven by continuous martingales, but we also derive the pricing partial differential equations (PDEs) for path‐independent contingent claims of a European style in a Markovian framework.