A BSDE approach to fair bilateral pricing under endogenous collateralization
- 271 Downloads
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.
KeywordsCollateral Fair pricing Funding costs
Mathematics Subject Classification (2010)60G35 91G20 91G80
The research of T. Nie was supported by the Fundamental Research Fund of Shandong University (2015HW023). The research of M. Rutkowski was supported by the DVC Research Bridging Support Grant “A BSDE Approach to Models with Funding Costs”.
- 2.Bichuch, M., Capponi, A., Sturm, S.: Arbitrage-free pricing of XVA—Part I: Framework and explicit examples. Working paper (2015). Available online at https://arxiv.org/abs/1501.05893
- 3.Bichuch, M., Capponi, A., Sturm, S.: Arbitrage-free pricing of XVA—Part II: PDE representation and numerical analysis. Working paper (2015). Available online at https://arxiv.org/abs/1502.06106
- 5.Brigo, D., Capponi, A., Pallavicini, A., Papatheodorou, V.: Collateral margining in arbitrage-free counterparty valuation adjustment including re-hypothecation and netting. Working paper (2011). Available online at https://arxiv.org/abs/1101.3926
- 6.Brigo, D., Francischello, M., Pallavicini, A.: Invariance, existence and uniqueness of solutions of nonlinear valuation PDEs and FBSDEs inclusive of credit risk, collateral and funding costs. Working paper (2015). Available online at https://arxiv.org/abs/1506.00686
- 9.Burgard, C., Kjaer, M.: Funding costs, funding strategies. Risk 26(12), 82–87 (2013) Google Scholar
- 21.Nie, T., Rutkowski, M.: Fair bilateral prices under funding costs and exogenous collateralization. Math. Finance (2016, to appear). Available online at https://arxiv.org/abs/1410.0448
- 23.Pallavicini, A., Perini, D., Brigo, D.: Funding, collateral and hedging: uncovering the mechanics and the subtleties of funding valuation adjustments. Working paper (2012). Available online at http://arxiv.org/abs/1210.3811
- 26.Piterbarg, V.: Funding beyond discounting: collateral agreements and derivatives pricing. Risk 23(2), 97–102 (2010) Google Scholar