FAIR BILATERAL PRICES IN BERGMAN’S MODEL WITH EXOGENOUS COLLATERALIZATION

Tianyang Nie () and Marek Rutkowski ()
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Tianyang Nie: School of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China
Marek Rutkowski: School of Mathematics and Statistics, University of Sydney, Sydney, Camperdown NSW 2006, Australia

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 07, 1-26

Abstract: We examine the pricing and hedging of general contracts in an extension of the market model proposed by [B-1995]. We study both problems from the perspectives of the hedger and the counterparty with arbitrary initial endowments. We derive inequalities satisfied by unilateral prices of a contract and we give the range for its fair bilateral prices. Our study hinges on results for backward stochastic differential equations (BSDEs) driven by multi-dimensional continuous martingales obtained in Nie & Rutkowski (2014b). We also derive the pricing partial differential equations (PDEs) for path-independent contingent claims of European style in a Markovian framework.

Keywords: Hedging; fair prices; borrowing rate; lending rate; margin agreement; BSDE (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S021902491550048X

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