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Principles of Financial Engineering, 3rd Edition by Elsevier Science

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Chapter 16

Correlation as an Asset Class and the Smile

In this chapter, we deal with correlation trading and more advanced aspects of volatility trading. First, we explain how dispersion trades and correlation swaps can be used to generate correlation exposure. Then we discuss the pricing and synthetic replication of correlation swaps. We introduce dirac functions and show their usefulness in analyzing the dependence of the option price on the volatility of the underlying around the strike price. We use Tanaka’s formula to show how option prices can be related to gamma gains. The Breeden–Litzenberger theorem is shown to link risk-adjusted probabilities to arbitrage-free option prices. We use the dirac delta function to prove the theorem. The volatility ...

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