Fair Bilateral Pricing Under Funding Costs and Exogenous Collateralization

35 Pages Posted: 16 Mar 2018

See all articles by Tianyang Nie

Tianyang Nie

Shandong University

Marek Rutkowski

The University of Sydney - School of Mathematics and Statistics

Date Written: April 2018

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.

Keywords: BSDE, collateral, fair pricing, funding costs, hedging, PDE

Suggested Citation

Nie, Tianyang and Rutkowski, Marek, Fair Bilateral Pricing Under Funding Costs and Exogenous Collateralization (April 2018). Mathematical Finance, Vol. 28, Issue 2, pp. 621-655, 2018. Available at SSRN: https://ssrn.com/abstract=3141579 or http://dx.doi.org/10.1111/mafi.12145

Tianyang Nie (Contact Author)

Shandong University

27 Shanda Nanlu
South Rd.
Jinan, 250100
China

Marek Rutkowski

The University of Sydney - School of Mathematics and Statistics ( email )

Sydney, New South Wales 2006
Australia

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