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Quantitative Finance by Matt Davison

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Chapter 32

Incomplete Markets

32.1 CHAPTER SUMMARY

In this chapter, some simple models that discuss the issue of how to extend the models of this chapter when options cannot be perfectly hedged are discussed. After a short introduction in Section 32.2, we devote Section 32.3 to examining a one-period trinomial tree model, which has “more uncertainty” than can be hedged. Although the perfect hedge of the binomial world is now broken, a great deal of hedging can still be done. Because of this, not just any price is possible, no matter the risk preferences of buyers and sellers. We follow this to produce intervals within the option the price can lie without producing an arbitrage. After introducing a concept known as Föllmer–Schweitzer or minimum ...

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