Self-Funding Portfolios and Collateralised Derivative Pricing

12 Pages Posted: 6 Jan 2013

See all articles by Miguel Carrion Alvarez

Miguel Carrion Alvarez

Banco Santander, Global Risk Methodology

Eulogio Yustas

Model Risk Internal Audit, Banco Santander; Banco Santander - Boadilla del Monte

Date Written: January 5, 2013

Abstract

A general framework is proposed for including the effects of collateral management in derivative pricing. Comprehensive yet simple formulas are obtained allowing the impact of different types of collateral agreements to be incorporated in valuations. The approach centers on analysing the self-financing condition on portfolios which explicitly include the market funding of derivative, collateral and hedging positions. Major simplifications, including a martingale pricing formula, are obtained when funding and collateral are in the form of cash, but the general framework aims at greater generality. The functional dependence of the collateral balance on the value of the derivative also plays a central role in the analysis. The “institutional” implications for liquidity management (pertaining to derivative desk funding, bank treasury “transfer pricing,” and the interplay with the repo market) are briefly considered.

Keywords: collateral, funding, Black-Scholes-Merton, martingale pricing, discounting

JEL Classification: G12

Suggested Citation

Carrion Alvarez, Miguel and Yustas, Eulogio and Yustas, Eulogio, Self-Funding Portfolios and Collateralised Derivative Pricing (January 5, 2013). Available at SSRN: https://ssrn.com/abstract=2196713 or http://dx.doi.org/10.2139/ssrn.2196713

Miguel Carrion Alvarez (Contact Author)

Banco Santander, Global Risk Methodology ( email )

Ciudad Grupo Santander
Boadilla del Monte, 28660
Spain

Eulogio Yustas

Banco Santander - Boadilla del Monte ( email )

Ciudad Financiera Grupo Santander
Avenida de Cantabria s/n
Boadilla del Monte, Madrid 28660
Spain

Model Risk Internal Audit, Banco Santander ( email )

Ciudad Financiera Grupo Santander
Avenida de Cantabria s/n
Boadilla del Monte, Madrid 28660
Spain

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