Quantitative Finance - Back to Basic Principles

Cover

Half-Title

Title

Copyright

Dedication

Contents

List of Figures

List of Tables

Foreword I

Foreword II

Acknowledgments

1 FinancialModeling

Introduction

2 AboutModeling

A Philosophy ofmodeling

B An example from physics and some applications in finance

3 From Black & Scholes to SmileModeling

A Study of derivatives under theBlack&Scholesmodel

Methodology

The search for convexity

Vanilla European option

Numerical application

Price scenarios

Delta gamma scenarios:

European binary option

Price Scenario

Delta and gamma scenarios

American binary option

Numerical application

Price scenario

Delta and gamma scenarios

Barrier option

Price scenario

Delta and gamma scenarios

Asian option

Numerical application

Price scenario

Delta and gamma scenarios

When is it possible to useBlack&Scholes

B Study of classical Smilemodels

Black&Scholesmodel

Termstructure Black&Scholes

MonteCarlo simulation

Terminal smilemodel

Replicationapproach (an almostmodel-free approach)

MonteCarlo simulation (direct approach)

MonteCarlo simulation (fastmethod)

Classic example

Separable local volatility

Termstructure of parametric slices

Dupire/Derman&Kani local volatilitymodel

Stochastic volatilitymodel

C Models, advanced characteristics and statistical features

Local volatilitymodel

Stochastic volatilitymodel

4 What is the Fair Value in the Presence of the Smile?

A What is the value corresponding to the cost of hedge?

TheDelta spot ladder for two barrier options

The vega volatility ladder

The vega spot ladder

Conclusion

5 Mono Underlying Risk Exploration

Dividends

Models: discrete dividends

Models: cash amount dividendmodel

Models: proportional dividendmodel

Models:mixed dividendmodel

Models: dividend toxicity index

Statistical observations on dividends

Interest ratemodeling

Models:why dowe need stochastic interest rates?

Models: simple hybridmodel

Models: statistics and fair pricing

Forward skewmodeling

The local volatilitymodel is not enough

Local volatility calibration

Alpha stable process

Truncated alpha stable invariants

Local volatility truncated alpha stable process

6 A General Pricing Formula

7 Multi-Asset Case

A Study of derivatives under the multi-dimensional Black & Scholes

Methodology

PCAfor PnL explanation

Eigenvalue decomposition for symmetric operators

Stochastic application

Profit and loss explanation

The source of the parameters

Basket option

Worst of option (wo: call)

Best of option(Bo: put)

Other options (Best of call andworst of put)

Model calibrationusing fixed-point algorithm

Model estimation using an envelope approach

Conclusion

8 Discounting and General Value Adjustment Techniques

Full and symmetric collateral agreement

Perfect collateralization

Applications

Repomarket

Optimal posting of collateral

Partial collateralization

Asymmetric collateralization

9 Investment Algorithms

What is a good strategy?

Asimple strategy

Reverse the time

Avoidthis datawhen learning

Strategies are assets

Multi-asset strategy construction

Signal detection

Predictionmodel

Riskminimization

10 Building Monitoring Signals

A Fat-tail toxicity index

B Volatility signals

Nature of the returns

The dynamic of the returns

Signal definition.

Asset and strategies cartography

Assetmanagement

C Correlation signals

Simple basketmodel

Estimating correlation level

Implied correlation skew

Multi-dimensional stochastic volatility

Local correlationmodel

General Conclusion

Solutions

Bibliography

Index