Marco Marchioro

Learning Quantitative Finance with QuantLib

Preview of White Papers

In this page I will upload the most-recent changes to the StatPro white papers. The actual official version of these paper is published on the StatPro website under the page "White Papers".  If you like the paper, you think there is a mistake, or just want to leave a comment please use the Contact Me page

Portfolio risk management with efficiently simulated scenarios


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 spreads. We focus on the risk-client implementation and describe the details needed to compute the different scenario types for a portfolio of heterogeneous assets. It is also shown how it is necessary to treat differently bond-like instruments that always have a positive quote, futures that are settled on a margin account, and swap-like contracts that may have a positive or a negative net-present value. Finally we show how the computation of daily simulations can be used to estimate risk for longer time horizon, even when the financial instrument considered have special bounding constraints.

PDF file: portfolio-simulated-scenarios.2.0.pdf 

Pricing Simple Credit Derivatives


This paper gives 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 swaps. Portfolio credit derivatives are also considered: the loss distribution is computed in both the homogeneous and non-homogeneous cases and is used to compute the price of a collateralized debt obligations. Finally, the generation of simulated scenarios for base correlation is briefly discussed. 

PDF file:  intro-credit-derivatives.pdf

Pricing Simple Interest-Rate Derivatives


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 swaps, and foreign-exchange forward contracts. Finally, we describe in details the bootstrap of the discount curve from a series of quoted deposit and swap rates. 

PDF file:  intro-fixed-income-derivatives.pdf

Average-maturity Model for Asset Backed Securities


We describe an average-maturity method to model prepayment for asset-backed securities for which it may or may not be present an expiration date.

PDF file: abs-avarage-maturity-model.pdf

Integrating default risk in the historical simulation model


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 using the z-spread so computed. In order to simulate the change of credit risk from one day to another we employ two different procedures depending on the availability of a default probability structure for the given issuer. The first method, namely the static method, relies purely on the issuer rating for obtaining the spread scenarios. The second method, namely the dynamic method, interpolates a fractional rating to accurately position the given issuer between ratings. Interestingly, the dynamic method gives an immediate response to event risk since the approach reflects the risk that is embedded in the market-quoted default probability structure.

PDF file: default-risk-hist-simulations.pdf

Foundations of the Statpro Simulation Model


This is the first in a series of papers describing the StatPro simulation model. In this paper we describe the basic building blocks of the whole 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 asset value from the expected distribution of the underlying risk factors. Therefore, a proper modeling of each possible risk factor is an essential feature of the model. The model here described has been implemented by StatPro in its SRM product and has been proven to be reliable and robust.

PDF file: foundation-simulation-model.pdf

Risk Decomposition for Portfolio Simulations


We describe a method to compute the decomposition of portfolio risk in additive asset components suitable for numerical simulations. The standard results in the covariance framework provide risk components computed from the derivative of the risk function with respect to the asset exposure. These results are generalized to a generic positively-homogeneous risk measure, but cannot be easily applied to value at risk because of the resulting instabilities. We show how introducing a new risk measure, the unbiased average value at risk, it is possible to split exactly the portfolio risk into stable additive components. The results obtained in this paper are general, stable, and can be used in portfolios containing products belonging any asset class. The risk-decomposition results are generalized to the computation of risk components at segment levels. Finally, we show a real-world application of the described method with a numerical example.

PDF file:  portfolio-risk-decomposition.pdf

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