The Volatility Smile: An Introduction for Students and Practitioners (Wiley Finance)

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9781118959169: The Volatility Smile: An Introduction for Students and Practitioners (Wiley Finance)
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The Volatility Smile The Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Topics covered include: * The principles of valuation * Static and dynamic replication * The Black-Scholes-Merton model * Hedging strategies * Transaction costs * The behavior of the volatility smile * Implied distributions * Local volatility models * Stochastic volatility models * Jump-diffusion models The first half of the book, Chapters 1 through 13, can serve as a standalone textbook for a course on option valuation and the Black-Scholes-Merton model, presenting the principles of financial modeling, several derivations of the model, and a detailed discussion of how it is used in practice. The second half focuses on the behavior of the volatility smile, and, in conjunction with the first half, can be used for as the basis for a more advanced course.

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The Black-Scholes-Merton option model was the greatest innovation of twentieth century finance, and remains the most widely applied theory in all of finance. Nevertheless, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatility against strike will typically display a curve or smile, which the model cannot explain.

Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new ideas and models that try to reconcile theory with markets. Beginning with the principles of financial valuation, The Volatility Smile presents a unique and unified treatment of the Black-Scholes-Merton option model and the more advanced models that have replaced it. Celebrated author, quant, and co-originator of the local volatility model Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and the consequences of different assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Key features:

  • The principles of valuation
  • The Black-Scholes-Merton model
  • Hedging strategies and transaction costs
  • The behavior of the volatility smile
  • Static and dynamic replication of standard and exotic options
  • New models: their origin, implementation, and consequences
  • Local volatility
  • Stochastic volatility
  • Jump-diffusion

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