SSRN Author: Damiano BrigoDamiano Brigo SSRN Content
http://www.ssrn.com/author=268434
http://www.ssrn.com/rss/en-usSat, 11 Oct 2014 02:41:56 GMTeditor@ssrn.com (Editor)Sat, 11 Oct 2014 02:41:56 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0New: An Initial Approach to Risk Management of Funding CostsIn this note we sketch an initial tentative approach to funding costs analysis and management for contracts with bilateral counterparty risk in a simplified setting. We depart from the existing literature by analyzing the issue of funding costs and benets under the assumption that the associated risks cannot be hedged properly. We also model the treasury funding spread by means of a stochastic Weighted Cost of Funding Spread (WCFS) which helps describing more realistic financing policies of a financial institution. We elaborate on some limitations in replication-based Funding/Credit Valuation Adjustments we worked on ourselves in the past, namely CVA, DVA, FVA and related quantities as generally discussed in the industry. We advocate as a different possibility, when replication is not possible, the analysis of the funding profit and loss distribution and explain how long term funding spreads, wrong way risk and systemic risk are generally overlooked in most of the current literature ...
http://www.ssrn.com/abstract=2507447
http://www.ssrn.com/1342269.htmlFri, 10 Oct 2014 07:53:22 GMTREVISION: The Arbitrage-Free Multivariate Mixture Dynamics Model: Consistent Single-Assets and Index Volatility SmilesWe introduce a multivariate diffusion model that is able to price derivative securities featuring multiple underlying assets. Each asset volatility smile is modeled according to a density-mixture dynamical model while the same property holds for the multivariate process of all assets, whose density is a mixture of multivariate basic densities. This allows to reconcile single name and index/basket volatility smiles in a consistent framework. Our approach could be dubbed a multidimensional local volatility approach with vector-state dependent diffusion matrix. The model is quite tractable, leading to a complete market and not requiring Fourier techniques for calibration and dependence measures, contrary to multivariate stochastic volatility models such as Wishart. We prove existence and uniqueness of solutions for the model stochastic differential equations, provide formulas for a number of basket options, and analyze the dependence structure of the model in detail by deriving a number ...
http://www.ssrn.com/abstract=2226053
http://www.ssrn.com/1338149.htmlWed, 24 Sep 2014 13:31:18 GMTREVISION: Inflation Securities Valuation with Macroeconomic-Based No-Arbitrage DynamicsWe develop a model to price inflation and interest rates derivatives using continuous-time dynamics that have some links with macroeconomic monetary DSGE models equipped with a Taylor rule: in particular, the reaction function of the central bank, the bond market liquidity, inflation and growth expectations play an important role. The model can explain the effects of non-standard monetary policies (like quantitative easing or its tapering) and shed light on how central bank policy can affect the value of inflation and interest rates derivatives.
The model is built under standard no-arbitrage assumptions. Interestingly, the model yields short rate dynamics that are consistent with a time-varying Hull-White model, therefore making the calibration to the nominal interest curve and options straightforward. Further, we obtain closed forms for both zero-coupon and year-on-year inflation swap and options. The calibration strategy we propose is fully separable, which means that the ...
http://www.ssrn.com/abstract=2417983
http://www.ssrn.com/1322205.htmlSun, 27 Jul 2014 04:41:18 GMTREVISION: Optimal Execution Comparison Across Risks and Dynamics, with Solutions for Displaced DiffusionsWe solve a version of the optimal trade execution problem when the mid asset price follows a displaced diffusion. Optimal strategies in the adapted class under various risk criteria, namely value-at-risk, expected shortfall and a new criterion called "squared asset expectation" (SAE), related to a version of the cost variance measure, are derived and compared. It is well known that displaced diffusions (DD) exhibit dynamics which are in-between arithmetic Brownian motions (ABM) and geometric Brownian motions (GBM) depending of the choice of the shift parameter. Furthermore, DD allows for changes in the support of the mid asset price distribution, allowing one to include a minimum permitted value for the mid price, either positive or negative. We study the dependence of the optimal solution on the choice of the risk aversion criterion. Optimal solutions across criteria and asset dynamics are comparable although differences are not negligible for high levels of risk aversion and low ...
http://www.ssrn.com/abstract=2247951
http://www.ssrn.com/1303922.htmlSat, 10 May 2014 06:05:21 GMTREVISION: Consistent Iterated Simulation of Multi-Variate Default Times: A Markovian Indicators CharacterizationWe investigate under which conditions a single simulation of joint default times at a final time horizon can be decomposed into a set of simulations of joint defaults on subsequent adjacent sub-periods leading to that final horizon. Besides the theoretical interest, this is also a practical problem as part of the industry has been working under the misleading assumption that the two approaches are equivalent for practical purposes. As a reasonable trade-off between realistic stylized facts, practical demands, and mathematical tractability, we propose models leading to a Markovian multi-variate survival -- indicator process, and we investigate two instances of static models for the vector of default times from the statistical literature that fall into this class. On the one hand, the "looping default' case is known to be equipped with this property, and we point out that it coincides with the classical "Freund distribution' in the bivariate case. On the other hand, if all sub-vectors
http://www.ssrn.com/abstract=2274369
http://www.ssrn.com/1302066.htmlFri, 02 May 2014 06:09:16 GMTNew: Nonlinear Valuation Under Collateral, Credit Risk and Funding Costs: A Numerical Case Study Extending Black-ScholesWe develop an arbitrage-free framework for consistent valuation of derivative trades with collateralization, counterparty credit gap risk, and funding costs, following the approach first proposed by Pallavicini and co-authors in 2011. Based on the risk-neutral pricing principle, we derive a general pricing equation where Credit, Debit, Liquidity and Funding Valuation Adjustments (CVA, DVA, LVA and FVA) are introduced by simply modifying the payout cash-flows of the deal. Funding costs and specific close-out procedures at default break the bilateral nature of the deal price and render the valuation problem a non-linear and recursive one. CVA and FVA are in general not really additive adjustments, and the risk for double counting is concrete. We introduce a new adjustment, called a Non-linearity Valuation Adjustment (NVA), to address double-counting. Our framework is based on real market rates, since the theoretical risk free rate disappears from our final equations. The framework ...
http://www.ssrn.com/abstract=2430696
http://www.ssrn.com/1301391.htmlTue, 29 Apr 2014 14:16:09 GMTREVISION: Inflation Securities Valuation with Macroeconomic-Based No-Arbitrage DynamicsWe develop a model to price inflation and interest rates derivatives using continuous-time dynamics that have some links with macroeconomic monetary DSGE models equipped with a Taylor rule: in particular, the reaction function of the central bank, the bond market liquidity, inflation and growth expectations play an important role. The model can explain the effects of non-standard monetary policies (like quantitative easing or its tapering) and shed light on how central bank policy can affect the value of inflation and interest rates derivatives.
The model is built under standard no-arbitrage assumptions. Interestingly, the model yields short rate dynamics that are consistent with a time-varying Hull-White model, therefore making the calibration to the nominal interest curve and options straightforward. Further, we obtain closed forms for both zero-coupon and year-on-year inflation swap and options. The calibration strategy we propose is fully separable, which means that the ...
http://www.ssrn.com/abstract=2417983
http://www.ssrn.com/1294287.htmlMon, 31 Mar 2014 06:11:52 GMTNew: CCP Cleared or Bilateral CSA Trades with Initial/Variation Margins Under Credit, Funding and Wrong-Way Risks: A Unified Valuation ApproachThe introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD trillions. In this article we develop for the first time a comprehensive approach for pricing under CCP clearing, including variation and initial margins, gap credit risk and collateralization, showing concrete examples for interest rate swaps. Mathematically, the inclusion of asymmetric borrowing and lending rates in the hedge of a claim lead to nonlinearities showing up in claim dependent pricing measures, aggregation dependent prices, nonlinear PDEs and BSDEs. This still holds in presence of CCPs and CSA. We introduce a modeling approach that allows us to enforce rigorous separation of the interconnected nonlinear risks into different valuation adjustments where the key pricing nonlinearities are confined to a funding costs component that is ...
http://www.ssrn.com/abstract=2380017
http://www.ssrn.com/1272890.htmlThu, 16 Jan 2014 20:42:22 GMTREVISION: CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ: Re-Hypothecation, CVA, Closeout, Netting, WWR, Gap-Risk, Initial and Variation Margins, Multiple Discount Curves, FVA?We present a dialogue on Funding Costs and Counterparty Credit Risk modeling, inclusive of collateral, wrong way risk, gap risk and possible Central Clearing implementation through CCPs. This framework is important following the fact that derivatives valuation and risk analysis has moved from exotic derivatives managed on simple single asset classes to simple derivatives embedding the new or previously neglected types of complex and interconnected nonlinear risks we address here. This dialogue is the continuation of the ``Counterparty Risk, Collateral and Funding FAQ" by Brigo (2011). In this dialogue we focus more on funding costs for the hedging strategy of a portfolio of trades, on the non-linearities emerging from assuming borrowing and lending rates to be different, on the resulting aggregation-dependent valuation process and its operational challenges, on the implications of the onset of central clearing, on the macro and micro effects on valuation and risk of the onset of ...
http://www.ssrn.com/abstract=2361697
http://www.ssrn.com/1262689.htmlTue, 03 Dec 2013 09:42:32 GMTREVISION: CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ: Re-Hypothecation, CVA, Closeout, Netting, WWR, Gap-Risk, Initial and Variation Margins, Multiple Discount Curves, FVA?We present a dialogue on Funding Costs and Counterparty Credit Risk modeling, inclusive of collateral, wrong way risk, gap risk and possible Central Clearing implementation through CCPs. This dialogue is the continuation of the previous FAQ 'Counterparty Risk, Collateral and Funding FAQ' by Brigo (2011). In this dialogue we focus more on funding costs for the hedging strategy of a portfolio of trades, on the non-linearities emerging from assuming borrowing and lending rates to be different, on the resulting aggregation-dependent valuation process and its operational challenges, on the closeout boundary conditions at default, on the implications of the onset of central clearing, on the macro and micro effects on valuation and risk of the onset of CCPs, on initial and variation margins impact on valuation and on multiple discount curves. Through questions and answers and by referring to the growing body of literature on the subject we present a unified view of valuation (and risk) that ...
http://www.ssrn.com/abstract=2361697
http://www.ssrn.com/1262377.htmlSun, 01 Dec 2013 17:32:57 GMT