Papers

I write papers on many subjects in quantitative finance: risk modelling, pricing functions, risk and performance contributions, and so on and so forth. Most papers contain original research that I believe is at the state of the art in the field. In this category you can also find the thesis of my former students.


Since the main purpose of these papers is to spread the knowledge to as many people as possible I try to write them devoid of the academic jargon . Therefore even thought, with the proper modifications, most of these papers could be published in a refereed journal, I usually choose not to do that.  Also for the same reason, I encourage you to notify me when the concepts in the papers are not expressed clearly or if you think that something important is missing.

List of related posts:


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 […]


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 […]


Portfolio risk management with efficiently simulated scenarios

Abstract We describe a method–used, among others, by financial-software firm StatPro–to perform portfolio risk analysis based on a two-tier client/server approach. The risk server computes the numerical simulations of single-asset prices for a wide universe of investable instruments. The risk clients, using the server outcome, compute portfolio cash risk scenarios, stress-test simulations, and bid/ask liquidity […]


Relative portfolio risk decomposition and attribution

Abstract In a related paper, see reference [4], we compute the risk decomposition of a portfolio with respect to a generic homogeneous risk measure. In this paper we extend those results to the risk decomposition of an active portfolio: a portfolio measured against a benchmark. We find that all the results obtained for the portfolio […]


Risk decomposition for portfolio simulations

Abstract We describe a method, suitable for numerical simulations, to compute the risk contributions for a generic portfolio of asset. The standard results in the covariance framework provide risk components computed from the derivative of the risk function with respect to the asset exposure. Those results are generalized to a generic positively-homogeneous risk measure, but […]


Average-maturity model for asset backed securities

Abstract We describe an average-maturity method to model pre-payments of asset-backed securities for which it may or may not be present an expiration date. Despote the model simplicity it is applicable to a wide range of securities. Keywords: interest-rate derivatives, abs, asset-backed securities, statistical models, interest rates, deriva- tives, pricing functions, bond pricing Pdf file: […]


Pricing simple credit derivatives

Abstract We provide an introduction to the pricing of credit derivatives. Default probability is defined and modeled using a piecewise constant hazard rate. Credit default swaps are shown as a first example of credit derivatives. It is then shown how to obtain a default probability term structure that is consistent with market quotes of credit-default […]


Pricing simple interest-rate derivatives

Abstract We introduce the basic concepts of quantitative pricing for interest-rate derivatives without optionality, focusing on the risk-free discount curve. We show how to compute the non-arbitrage value of simple interest-rate derivatives from the knowledge of the discount factor. The type of interest-rate derivatives that can be computed in this way include inter-bank deposits, interest-rate […]


Foundations of the StatPro simulation model

Abstract In this paper we describe the building blocks of the StatPro simulation model: given a financial instrument whose price depends on some basic risk factors through a pricing function, it is possible to obtain the expected distribution of the asset value from the simulation of the underlying risk factors. Therefore, a proper modeling of […]


Integrating default risk in the historical simulation model

Abstract We describe a new model for generating credit risk scenarios in the StatPro Simulation Model. Starting from the historical series of asset swap indices grouped by sector, currency, and rating, we can derive a number of equivalent time series for the zero volatility spreads(or z-spreads). The current credit risk of an asset is modeled […]