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Über dieses Buch

The series of recent financial crises have thrown open the world of quantitative finance and financial modeling. This book brings together proven and new methodologies from finance, physics and engineering, along with years of industry and academic experience to provide a cookbook of models for dealing with the challenges of today's markets.

Inhaltsverzeichnis

Frontmatter

1. Financial Modeling

At the time of writing, the term model has been widely overused and misused. The US subprime financial crisis in 2008 and 2009 and its subsequent impacts on the rest of the economy have prompted some journalists and magazines to launch unfair attacks on ‘quants’ that is the designers of models.
Adil Reghai

2. About Modeling

Using the term ‘philosophy’ implies problems or questions with ambiguous answers. Regarding derivatives, the question that first spring to mind is the following:
Why do we need a modeling philosophy for financial products and particularly derivatives?
Adil Reghai

3. From Black & Scholes to the emergence of Smile Modeling

This step is crucial, as it is the first step in our incremental approach. Indeed, thanks to a relatively simple model, Black & Scholes (despite all its flaws), we are able to understand our position, the risks involved today and tomorrow, and what to put in place to perform effective hedging.
Adil Reghai

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

Until now, we have studied a few products using simple models. To build the fair value, we need to fully understand the way to hedge. We shall describe the fair value from the point of view of an investment bank, that is from the sell side. In particular, the hedging portfolio immunizes the book against spot and volatility movements.
Adil Reghai

5. Mono Underlying Risk Exploration

We have seen how to analyze the smile risk. We have learnt how to decompose this risk in a photography risk (fitting the initial smile) and a dynamic risk (capturing elements of its dynamic). Not all products need full exposure to the smile and its dynamic. This question is answered via a progressive approach in which we start by exploring the gamma map. We also compute the smile toxicity index to know if a model extension is necessary. In the most complex case, where the gamma map shows changes of exposure and the presence of an important smile toxicity index, we need to figure out the right mixing weight, the right blending factor issued from a statistical study of the volatility dynamic in the market. We developed a large set of models and approaches for which we have full access, analytically or semianalytically, to their properties.
Adil Reghai

6. A General Pricing Formula

When we collect all the axis of risk for a general mono underlying product, we need to take into account all the previous effects according to their contribution to the price and hitherto the cost of hedge.
Adil Reghai

7. Multi-Asset Case

Correlation plays a tremendous role when pricing and hedging multi-asset derivative products. It is also a fundamental element in asset allocation.
Adil Reghai

8. Discounting and General Value Adjustment Techniques

The collapse of Lehman has acted as a sharp reminder that financial modeling is about modeling PnL treasury shift. Indeed, holding financial products with Lehman as a counterparty can create a loss if our exposure is positive to Lehman at the time of default. This situation has created the need to follow the CVA (credit value adjustment — a measure of counterparty risk). How much should I adjust my price to reflect the possibility of my counterparty defaulting? There is also a symmetrical notion that is the DVA (debit value adjustment) which constitutes the answer to the damage my own default can create for my counterparties.
Adil Reghai

9. Investment Algorithms

An algorithm comprises a finite number of steps to accomplish a task. Algorithms are found everywhere nowadays, and thanks to the internet, Google and Amazon for example, they have simplified our lives.
Adil Reghai

10. Building Monitoring Signals

In the pricing section, we have seen the importance of fat tail for the forward skew modeling and especially for Crash put options. The alpha process can be very useful to design a very good indicator to detect the beginning of large movements or alternatively to detect large movements.
Adil Reghai

General Conclusion

Quantitative pricing and investment are art forms which can profit from the exact sciences. These sciences are more than two hundred years old and show us the path to take as well as differences with the financial world. Financial equations can evolve with regulation and social behavior. However, central limit theorems establish some statistical attractors which are important invariants that should be captured. We present a methodology that combines statistical invariants with classical pricing models. We also show how martingale models, usually designed for pricing, can be used to assess the quality of an investment strategy. We define measurable quantities, that we call toxicity indices, which allow us to rank financial products and investment strategies.
Adil Reghai

Backmatter

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