- 190 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
About this book
Model-free Hedging: A Martingale Optimal Transport Viewpoint focuses on the computation of model-independent bounds for exotic options consistent with market prices of liquid instruments such as Vanilla options. The author gives an overview of Martingale Optimal Transport, highlighting the differences between the optimal transport and its martingale counterpart. This topic is then discussed in the context of mathematical finance.
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Chapter 1
Pricing and hedging without tears
Abstract Let us denote FT an European payoff depending on the value ST of an asset at T. The main questions, that we will focus on, are
(A) At which price should we sell this option? Is there a unique price?
(B) After having sold this option, what should we do in order to reduce (i.e., hedge) our potential losses?
By working on a discrete-time setting, we will try to answer these two questions without relying on knowledge of stochastic analysis, but by using classical tools in optimization and in probability. In particular, we will formulate the problem of pricing and hedging of derivative products as some linear, quadratic and convex optimization problems. This consists in minimizing an utility function written on the profit and loss wealth value of a delta-hedged portfolio. In particular, we will insist on convex duality from which risk-neutral models emerge as dual variables. This convex (linear) duality will appear naturally in the next chapter and will be a key tool when we will discuss (M)OT. We will also highlight the model-dependence of our approach.
1.1 An insurance viewpoint
Let us assume that we have sold an option (at t = 0) at the price C. An option, with payoff FT, gives the right to the holder to exercise the payoff at a maturity T. Its gain at T is FT. For exampl...
Table of contents
- Cover
- Title Page
- Series Page
- Copyright Page
- Table of Contents
- Preface
- 1 Pricing and hedging without tears
- 2 Martingale optimal transport
- 3 Model-independent options
- 4 Continuous-time MOT and Skorokhod embedding
- References
- Index
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Yes, you can access Model-free Hedging by Pierre Henry-Labordere in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.