Quanto Implied Volatility Smile
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Quanto Implied Volatility Smile
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Author : Alessandro Cesarini
language : en
Publisher:
Release Date : 2014
Quanto Implied Volatility Smile written by Alessandro Cesarini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
We propose a numerical procedure, addressed as copula integration method, to calculate quanto implied volatility adjustments. The method consists in a direct integration of the quanto vanilla payoff, using the bivariate terminal probability distribution of the asset and the relevant foreign exchange rate. The bivariate terminal distribution is obtained by coupling the marginal distributions of the two underlyings by means of a Gaussian copula. The asset and the foreign exchange rate marginal distributions are directly inferred from the corresponding Black-Scholes market volatility smiles. In order to obtain well defined marginal distributions, we propose an extrapolation method for the standard implied volatility outside the quoted region, which does not allow arbitrage opportunities. The validity of the copula integration method is established by comparing its predictions to exact results for quanto option prices, obtained by numerical computations in two realistic test cases, in which the dynamics of the assets is driven by a local volatility and a Heston stochastic volatility model.
Deconstructing The Volatility Smile
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Author : Romano Trabalzini
language : en
Publisher:
Release Date : 2014
Deconstructing The Volatility Smile written by Romano Trabalzini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
This paper investigates the relationship between the implied volatility smile and the underlying joint density of two quantities characterizing the stochastic volatility process - namely the mean integrated variance, $ frac{1}{T} int_0^T sigma_s^2ds$, and the stochastic integral $ int_0^T sigma_s dW_{s}^{ sigma}$. A simple form of this joint density is proposed which, when fit to the zero correlation smile and a single non-zero correlation smile, will then generate to good agreement the smile for an arbitrarily chosen correlation. Further, the method complements and extends the work of cite{carr_lee_robust} and cite{friz_gatheral} to non-zero correlation. In doing so, it allows for the study of volatility derivatives in the quanto case which is particularly relevant in the foreign exchange markets.
Quanto Pricing With Copulas
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Author : Michael N. Bennett
language : en
Publisher:
Release Date : 2003
Quanto Pricing With Copulas written by Michael N. Bennett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
We study the practical problem of pricing a particular multi-asset option, a quanto FX option. The Black model, which corresponds to a jointly lognormal distribution of asset prices at expiry, is inconsistent with the implied volatility smile for each of the three relevant currency pairs. We demonstrate a practical methodology for constructing a model for the joint distribution that is calibrated to all relevant implied volatilities. The margins of this distribution are determined separately in an initial stage. To calibrate the joint distribution to the implied volatility smile on the remaining FX rate, we perturb the dependence structure associated with the Black model (the Normal copula) in order to influence the tail dependence characteristics of the resulting joint distribution.We calibrate our model to a number of real-life scenarios corresponding to several maturities and currency set-ups. We find that a well-known ad-hoc adjustment to the Black pricing formula often gives lower quanto call prices than those calculated under our transformed copula model. The relative difference in quanto prices with strikes furthest away from at-the-money is occasionally large (10-15%).
Information Behind The Implied Volatility Smile
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Author : Michele A. Kreisler
language : en
Publisher:
Release Date : 1996
Information Behind The Implied Volatility Smile written by Michele A. Kreisler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
The Volatility Smile
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Author : Emanuel Derman
language : en
Publisher:
Release Date : 2016
The Volatility Smile written by Emanuel Derman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Finance categories.
"The Volatility Smile: An Introduction for Students and Practitioners The Black-Scholes-Merton options 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"--
Modeling The Implied Volatility Smile
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Author : Kim Sundkvist
language : en
Publisher:
Release Date : 2000
Modeling The Implied Volatility Smile written by Kim Sundkvist and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
The Impact Of Computational Error On The Volatility Smile
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Author : Don M. Chance
language : en
Publisher:
Release Date : 2013
The Impact Of Computational Error On The Volatility Smile written by Don M. Chance and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
It is well-known that the market prices of options produce implied volatilities that inexplicably vary by exercise price in a pattern often referred to as the volatility smile. This paper shows that not only do market prices produce volatility smiles, but so do model prices. This result occurs because of root finding algorithms, tolerance assumptions, numerical precisions, and quotation finiteness. Moreover, some assumptions result in patterns that resemble the smirks, and skews sometimes observed in market data. Consistent with empirical observations, the effects are greater the shorter the expiration. Elimination of these patterns is virtually impossible on a practical level, and even second-best results can be obtained only if options are traded with quadruple precision pricing and machine precision tolerance is assumed. We conclude that while alternative explanations for the smile can be true, prices generated under perfect conditions cannot even eliminate these smile, smirk, and skew patterns.
Smile In Motion
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Author : Martin Wallmeier
language : en
Publisher:
Release Date : 2012
Smile In Motion written by Martin Wallmeier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
The Slope Of The Smile And The Comovement Of Volatility And Returns
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Author : Anthony Neuberger
language : en
Publisher:
Release Date : 2009
The Slope Of The Smile And The Comovement Of Volatility And Returns written by Anthony Neuberger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
The slope of the implied volatility smile reflects the correlation between volatility shocks and returns. By defining the slope as the difference between two implied variances, the relationship between the slope, and the correlation between volatility and returns can be derived formally in a way that is essentially model free. More specifically, the slope is the price of a swap contract where the floating leg is the covariation between returns on the underlying asset and changes in its volatility. The term structure of the slope carries information about the correlation between returns and future volatility. The results are analogous to the finding that the model free implied variance is equal to the expected realized variance under the pricing measure.
On The Implied Volatility Layers Under The Future Risk Free Rate Uncertainty
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Author : Lin-Yee Hin
language : en
Publisher:
Release Date : 2014
On The Implied Volatility Layers Under The Future Risk Free Rate Uncertainty written by Lin-Yee Hin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
This paper suggests a method of estimation of the implied volatility smile uncertainty of the observed options prices due to future risk-free rate uncertainty. The purpose is to quantify the range of uncertainty under different scenarios.We consider the setting where both the implied volatility and the risk free rate are calculated jointly from the observed option prices. Due to the cumulative risk-free rate uncertainty, the corresponding system of equations is underdetermined, leading to uncertainty in the volatility surface.We estimate the size of implied volatility layers between the surfaces representing the upper and lower bounds for the implied volatilities for the future risk-free rate uncertainty, defined by current Libor rate and the size of fluctuation estimated from the historical data.