[PDF] Retrieving Risk Neutral Moments And Expected Quadratic Variation From Option Prices eBook

Author : Leonidas Rompolis
Publisher :
Page : 68 pages
File Size : 36,45 MB
Release : 2017
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ISBN :

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This paper derives exact formulas for retrieving risk neutral moments of future payoffs of any order from generic European-style option prices. It also provides an exact formula for retrieving the expected quadratic variation of the stock market implied by European option prices, which nowadays is used as an estimate of the implied volatility, and a formula approximating the jump component of this measure of variation. To implement the above formulas to discrete sets of option prices, the paper suggests a numerical procedure and provides upper bounds of its approximation errors. The performance of this procedure is evaluated through a simulation and an empirical exercise. Both of these exercises clearly indicate that the suggested numerical procedure can provide accurate estimates of the risk neutral moments, over different horizons ahead. These can be in turn employed to obtain accurate estimates of risk neutral densities and calculate option prices, efficiently, in a model-free manner. The paper also shows that, in contrast to the prevailing view, ignoring the jump component of the underlying asset can lead to seriously biased estimates of the new volatility index suggested by the Chicago Board Options Exchange (CBOE).

Author : Yisong S. Tian
Publisher :
Page : pages
File Size : 39,27 MB
Release : 2019
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ISBN :

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There has been a surge in the use of option-implied moments (e.g., volatility, skewness and kurtosis) in various empirical applications such as volatility forecasting, variance risk premium, empirical asset pricing, and portfolio selection. One potential obstacle in such applications is the requirement of European option prices in the estimation of these moments. In this paper, we develop a simple, accurate method for extracting risk-neutral density and its moments from American option prices. A key advantage of our approach is that a single implied binomial tree is constructed to fit all American option prices, utilizing the full information set in the entire options market. Since American options are more commonly traded than European options, our methodology expands the scope of research on option-implied density and moments to a much wider class of underlying assets (e.g., equity and futures options).

Author : Aristogenis Lazos
Publisher :
Page : 36 pages
File Size : 45,4 MB
Release : 2018
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ISBN :

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This paper develops closed-form solutions for the finite integrals in the volatility, cubic and quartic contracts in Bakshi, Kapadia and Madan (2003) which avoid discretization errors and do not involve interpolation and extrapolation. It compares the accuracy of the closed-form approach with the popular interpolation-extrapolation approach in the literature. Our results show that the closed-form approach provides more accurate estimates for skewness. This holds across different option pricing models and parameterization which have been shown to be favourable for the interpolation-extrapolation approach. Finally, our results show that the closed-form approach always extracts expectations consistent with the term structure of the volatility smirk whereas the interpolation-extrapolation approach fails several times.

Author : James Huang
Publisher :
Page : 32 pages
File Size : 34,74 MB
Release : 2009
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ISBN :

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In this paper we raise a question on the theoretical foundation of option implied risk neutral density. We prove that given any number of options, there exist numerous risk neutral densities which are piecewise constant, have only two values, either an lower bound or an upper bound on the true risk neutral density, and price all these options correctly. We also prove that given any number of options, there exist numerous risk neutral densities consistent with the prices of all these options whose first derivatives are piecewise constant and have only two values, either an lower bound or an upper bound on the true risk neutral density's first derivative. Similar results are proved with respect to the true risk neutral density's higher order derivatives. These results show how large errors we can make when extracting RNDs from option prices.

Author : Nassim Nicholas Taleb
Publisher : John Wiley & Sons
Page : 536 pages
File Size : 24,6 MB
Release : 1997-01-14
Category : Business & Economics
ISBN : 9780471152804

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Destined to become a market classic, Dynamic Hedging is the only practical reference in exotic options hedgingand arbitrage for professional traders and money managers Watch the professionals. From central banks to brokerages to multinationals, institutional investors are flocking to a new generation of exotic and complex options contracts and derivatives. But the promise of ever larger profits also creates the potential for catastrophic trading losses. Now more than ever, the key to trading derivatives lies in implementing preventive risk management techniques that plan for and avoid these appalling downturns. Unlike other books that offer risk management for corporate treasurers, Dynamic Hedging targets the real-world needs of professional traders and money managers. Written by a leading options trader and derivatives risk advisor to global banks and exchanges, this book provides a practical, real-world methodology for monitoring and managing all the risks associated with portfolio management. Nassim Nicholas Taleb is the founder of Empirica Capital LLC, a hedge fund operator, and a fellow at the Courant Institute of Mathematical Sciences of New York University. He has held a variety of senior derivative trading positions in New York and London and worked as an independent floor trader in Chicago. Dr. Taleb was inducted in February 2001 in the Derivatives Strategy Hall of Fame. He received an MBA from the Wharton School and a Ph.D. from University Paris-Dauphine.