Related papers: Two Curves, One Price: Pricing & Hedging Interest …
The crisis that affected financial markets in the last years leaded market practitioners to revise well known basic concepts like the ones of discount factors and forward rates. A single yield curve is not sufficient any longer to describe…
We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between…
The general problem of asset pricing when the discount rate differs from the rate at which an asset's cash flows accrue is considered. A pricing kernel framework is used to model an economy that is segmented into distinct markets, each…
In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the…
We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework in Pallavicini et al (2011), and the related collateralized…
This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American…
We present a general derivation of the arbitrage-free pricing framework for multiple-currency collateralized products. We include the impact on option pricing of the policy adopted to fund in foreign currency, so that we are able to price…
The paper reviews origins of the approach to pricing derivatives post-crisis by following three papers that have received wide acceptance from practitioners as the theoretical foundations for it - [Piterbarg 2010], [Burgard and Kjaer 2010]…
This article presents FVA and CVA of a bilateral derivative in a coherent manner, based on recent developments in fair value accounting and ISDA standards. We argue that a derivative liability, after primary risk factors being hedged,…
In traditional financial markets, yield curves are widely available for countries (and, by extension, currencies), financial institutions, and large corporates. These curves are used to calibrate stochastic interest rate models, discount…
The role of collateral in derivative pricing has evolved beyond credit risk mitigation, particularly following the global financial crisis, when funding costs and basis spreads became central to valuation practices. This development…
We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure,…
Derivative pricing is about cash flow discounting at the riskfree rate. This teaching has lost its meaning post the financial crisis, due to the addition of extra value adjustments (XVA), which also made derivatives pricing and valuation a…
The notion of a credit spread curve is fundamental in fixed income investing, but in practice it is not `given' and needs to be constructed from bond prices either for a particular issuer, or for a sector rating-by-rating. Rather than…
An uncollateralized swap hedged back-to-back by a CCP swap is used to introduce FVA. The open IR01 of FVA, however, is a sure sign of risk not being fully hedged, a theoretical no-arbitrage pricing concern, and a bait to lure market risk…
The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In…
This article presents a generic framework for modeling the dynamics of forward curves in commodity market as commodity derivatives are typically traded by futures or forwards. We have theoretically demonstrated that commodity prices are…
In this paper, we study the pricing of contracts in fixed income markets under volatility uncertainty in the sense of Knightian uncertainty or model uncertainty. The starting point is an arbitrage-free bond market under volatility…
This paper analyzes the pricing of collateralized derivatives, i.e. contracts where counterparties are not only subject to financial derivatives cash flows but also to collateral cash flows arising from a collateral agreement. We do this…
The inclusion of DVA in the fair-value of derivative transactions has now become standard accounting practice in most parts of the world. Furthermore, some sophisticated banks are including an FVA (Funding Valuation Adjustment), but since…