A risk decomposition framework consistent with performance measurements

Abstract We define a framework to compute the risk contributions of a portfolio consistently with a given performance-measurement schema. The framework has a wide array of applications, such as risk attribution, and matches the standard risk decomposition when the portfolio has a linear dependence on the factor exposures. We go beyond the traditional risk-decomposition approach, […]


Projection performance contributions of non-linear portfolios

Abstract We define a theoretical framework to exactly measure the additive risk-driver contributions to the performance of an investment portfolio. The approach is based on first principles, is non local and is especially suitable for non-linear portfolios. We consider a single-period return and assume that the generated cash flows are reinvested in the portfolio itself. […]


Non perturbative key-rate contributions to bond returns

Abstract We show a non-perturbative method to split the bond return into components coming from the different key-rates, the credit spread, the carry term, and another couple of minor components. We explicitly show the results for the case of a fixed-rate coupon bond with a price computed using cash-flow discounting with a yearly-compounded yield curve. […]



Seasonality of dividend point indexes

Abstract We analyse a variety of dividend-point indexes, typically used to determine the payoff of dividend derivatives. We show strong evidence of seasonality patterns for all indexes examined. Since dividend-point reset with irregular time intervals, we find the need to use a different seasonality function for the current or any future period. We determine the […]



Risk measure, XVA Analysis, Cost of Capital and Central Counterparties Workshop

In this workshop, that I had the pleasure to attend, a number of topics were discussed. In primis several valuation adjustments (denoted by the generic name XVA) such as CVA, FVA, and KVA. The level of all the seminars was very high and you needed some previous knowledge of the subject in order to fully […]


Finite difference methods for sensitivity computations

Abstract We describe some basic finite-difference methods to estimate the derivatives of a generic smooth function. For a function of one variable we provide the derivation of the standard forward difference, backward difference, and central difference approximation of the first and second derivatives. We also derive the expression for the second-order cross partial derivative for […]


Introduction to linear commodity derivatives

Abstract We provide an introduction to linear derivatives on common storable commodities. Using no-arbitrage arguments we derive an expression for the quote of commodity future contracts and we highlight the importance of convenience yield. We show a some numerical results for the convenience-yield term structure of few common commodities and focus on the similarities with […]


QuantLib on a Jupiter Notebook

After using QuantLib on excel (see the excellent QuantLibXL addin) for many years I have recently started to use it, as also suggested by Luigi in this video, in a ipython in a jupyter notebook. Moving away from excel was easier than I thought especially thanks to the pandas project. I am still experimenting with these […]