By Sebastien Bossu, Peter Carr
In Advanced fairness Derivatives: Volatility and Correlation, Sébastien Bossu stories and explains the complicated recommendations used for pricing and hedging fairness unique derivatives. Designed for monetary modelers, choice investors and complex traders, the content material covers an important theoretical and sensible extensions of the Black-Scholes model.
Each bankruptcy contains a number of illustrations and a brief collection of difficulties, masking key issues similar to implied volatility floor versions, pricing with implied distributions, neighborhood volatility versions, volatility derivatives, correlation measures, correlation buying and selling, neighborhood correlation types and stochastic correlation.
The writer has a twin expert and educational history, making Advanced fairness Derivatives: Volatility and Correlation the suitable reference for quantitative researchers and mathematically savvy finance execs seeking to collect an in-depth knowing of fairness unique derivatives pricing and hedging.
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Extra resources for Advanced Equity Derivatives: Volatility and Correlation
Other option payoffs that depend on the history of the underlying asset price (such as Asian or barrier options) or have an early exercise feature (such as American options) require more sophisticated valuation methods and cannot be perfectly replicated with a static portfolio of vanilla options. In practice, only a finite number of strikes are available. While it is possible to overhedge convex payoffs with a finite portfolio of vanillas, exact replication cannot be achieved. FOCUS ON OVERHEDGING Exotic option traders often look at ways to overhedge a particular option payoff with a portfolio of vanillas, and price it accordingly.
CHAPTER 3 Implied Distributions Perhaps the favorite activity of quantitative analysts is to decode market data into information about the future upon which a trader can base his or her decisions. This is the purpose of the implied distribution that translates option prices into probabilities for the underlying stock or stock index to reach certain levels in the future. In this chapter, we derive the implied distribution and show how it may be exploited to price and hedge certain exotic payoffs.
2 Consequence for Hedge Ratios The smile does not mean that Black-Scholes is wrong and should be rejected. Practitioners typically price over-the-counter (OTC) vanilla options using Black-Scholes and an appropriate volatility interpolation or extrapolation scheme, for the simple reason that implied volatilities are derived from listed option prices in the first place. In other words, the fact that the Black-Scholes model may be faulty is fairly irrelevant for vanilla option pricing. However, the vanilla hedge ratios or Greeks are model-dependent and should be adjusted for the smile.
Advanced Equity Derivatives: Volatility and Correlation by Sebastien Bossu, Peter Carr