A Guide to Behavioural Modelling for ALM

A Guide to Behavioural Modelling for ALM

Correlation Risk Management and Modelling (2nd edition)

Correlation Risk Management and Modelling (2nd edition)

A Quantitative Framework to Assess the Risk-Reward Profile of Non Equity Products


 In A Quantitative Framework to Assess the Risk-Reward Profile of Non-Equity Products, bestselling author and Head of the Quantitative Analysis Unit at Italian regulator CONSOB, Marcello Minenna sets out a new method for achieving this for non-equity investment products.

By combining techniques commonly used in markets in a consistent and transferable format, Minenna provides the reader with a toolkit to produce the core information that the investors need to make their investment decisions.

This innovative, practical guide offers a way for financial institutions, investors, regulators, issuers and academics to better assess, understand and describe products and make a meaningful comparison between them.

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Faced with myriad choices, retail investors choose between different financial products based on their liquidity attitude, risk appetite, budget constraints and performance objectives.

But how, given the vast range of products and the innumerable ways of describing them, can an investor know the fundamental information to make an enlightened investment decision?

In this new book, Marcello Minenna provides a framework for assessing the risk-return profile of non-equity products. The framework is:

  • practical – it combines commonly used techniques;
  • scalable – it can be applied across a range of products; and
  • transferable – it enables the investor, structurer or regulator to look across and compare performances.

The methodology developed is comprised of three indicators or pillars which will reveal the material risks of the products:

  • Pillar 1: Price unbundling and probabilistic scenarios. This pillar is about understanding what will impact the value of the non-equity financial product over its lifetime.
  • Pillar 2: Degree of risk. This displays the degree of risk that characterises the product throughout the entire investment time horizon (summarising the temporal evolution of the risk) and the variability of the product’s returns over the entire period.
  •  Pillar 3: Recommended investment time horizon. This acts as an indicator which expresses a recommendation regarding the holding period of the product, for instance how long would an investor expect to hold a product before, say, breaking even.

Individual chapters explain each pillar, offering a detailed illustration of the analytical tools underlying each of these indicators. A final chapter applies the three pillars to six non-equity products that feature various solutions of financial engineering (one risk-target, one benchmark, three return-target products and one structured liability). These practical examples show in a concrete way the strict connections and the complementarity of the pillars in revealing the material risks and essential characteristics of any non-equity product.

This information can be easily gathered in a short document of great utility:

  • For issuers and structurers, it represents a practical and useful way to describe a product;
  • For investors, it is a snapshot of the investment’s characteristics to help them decide whether to invest;
  • For regulators, it presents a transparent and consistent way for investments to be described.

Marcello Minenna’s practical guide represents the standardisation of one methodology for assessing the risk-return of financial products. His quantitative approach is a new touchstone for retail investors, issuers, structurers, distributors and regulators, and is essential reading for those working in the measurement and management of risk.

More Information
ISBN 9781906348595
Navision code MQFA
Publication date 27 Sep 2011
Size 155mm x 235mm
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Marcello Minenna

Marcello Minenna addressed by Risk magazine as the “quant enforcer” and the “quant regulator” is the Head of the Quantitative Analysis Unit at CONSOB (the Italian Securities and Exchange Commission) where he develops quantitative models for surveillance and supports the enforcement and regulatory units in their activities.

Marcello has been teaching in several Universities and holding courses for practitioners in the field of financial mathematics all around the world. He graduated at Bocconi University and received his PhD and MA in mathematics for finance from State University of Brescia and from Columbia University. He is the author of several publications including the bestselling Risk-book A Guide to Quantitative Finance.

Table of contents

About the Author




List of Figures

List of Tables

1 Introduction


2 The First Pillar: Price Unbundling and Probabilistic Scenarios

2.1 The risk-neutral density of a non-equity product

2.2 Price unbundling via the financial investment table

2.3 First pillar and non-elementary products

2.3.1 Increasing the detail of the financial investment table

2.3.2 The table of probabilistic scenarios

2.3.3 Methodology to build the table of probabilistic scenarios

2.3.4 Probabilistic scenarios for “non-equity exchange structures”

2.4 First pillar and elementary products

2.5 Closing remarks


3 The Second Pillar: Degree of Risk

3.1 Methodology to calibrate an optimal grid

3.2 The model for the automatic asset manager

3.3 The model to simulate the volatility

3.4 The predictive model for the volatility

3.4.1 The diffusion limit of the M-Garch(1,1)

3.4.2 Distributive properties and volatility prediction intervals

3.4.3 Estimation of the parameters

3.5 Management failures and the optimal grid

3.5.1 Definition of management failures and introduction to the calibration problem

3.5.2 Relation between relative widths and management failures

3.5.3 The optimal grid on the reduced space of volatilities [σ0, σn]

3.5.4 The optimal grid on the full space of volatilities [0, +∞[

3.6 Risk Classification

3.7 Detecting migrations

3.8 Closing remarks


4 The Third Pillar: Recommended Investment Time Horizon

4.1 The minimum time horizon for risk-target and benchmark products

4.1.1 The strong characterisation of the cost-recovery event

4.1.2 The weak characterisation of the cost-recovery event

4.1.3 The closed formula for the cumulative probability of the first-passage times The case of the standard Brownian motion The case of the arithmetic Brownian motion The case of the geometric Brownian motion The case of the geometric Brownian motion specific to the product

4.1.4 Asymptotic analysis

4.1.5 Sensitivity analysis First-order partial derivatives Limit representations of the first-order partial derivative with respect to the volatility Second-order partial derivatives

4.1.6 Existence and uniqueness of the minimum time horizon for local correct ordering

4.1.7 The function of the minimum times

4.1.8 Existence and uniqueness of the minimum time horizon for a global correct ordering

4.1.9 Switching to a discrete volatility setting

4.1.10 Extensions to more general dynamics for the process

4.1.11 Technical remarks

4.2 The recommended time horizon for return-target products

4.2.1 Illiquid products

4.2.2 Liquidity and liquidability

4.3 Closing remarks


5 Some Applications of the Risk-Based Approach

5.1 A risk-target product

5.2 A benchmark product

5.3 Return-target products: the case of a plain-vanilla bond with significant credit risk

5.4 Return-target products: the case of a VPPI product

5.5 Return-target products: the case of an index-linked certificate

5.6 Non-equity exchange structures: the case of a collar replacing a fixed-rate liability


6 Conclusions