Arbitrage Free Prediction Of The Implied Volatility Smile
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Arbitrage Free Prediction Of The Implied Volatility Smile
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Author : Petros Dellaportas
language : en
Publisher:
Release Date : 2014
Arbitrage Free Prediction Of The Implied Volatility Smile written by Petros Dellaportas 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 gives an arbitrage-free prediction for future prices of an arbitrary co-terminal set of options with a given maturity, based on the observed time series of these option prices. The statistical analysis of such a multi-dimensional time series of option prices corresponding to n strikes (with n large, e.g. n ≥ 40) and the same maturity, is a difficult task due to the fact that option prices at any moment in time satisfy non-linear and non-explicit no-arbitrage restrictions. Hence any n-dimensional time series model also has to satisfy these implicit restrictions at each time step, a condition that is impossible to meet since the model innovations can take arbitrary values. We solve this problem for any n ∈ N in the context of Foreign Exchange (FX) by first encoding the option prices at each time step in terms of the parameters of the corresponding risk-neutral measure and then performing the time series analysis in the parameter space. The option price predictions are obtained from the predicted risk neutral measure by effectively integrating it against the corresponding option payoffs. The non-linear transformation between option prices and the risk-neutral parameters applied here is not arbitrary: it is the standard mapping used by market makers in the FX option markets (the SABR parameterisation) and is given explicitly in closed form. Our method is not restricted to the FX asset class nor does it depend on the type of parameterisation used. Statistical analysis of FX market data illustrates that our arbitrage-free predictions outperform the naive random walk forecasts, suggesting a potential for building management strategies for portfolios of derivative products, akin to the ones widely used in the underlying equity and futures markets.
Forecasting Implied Volatility Smile Surface Via Deep Learning And Attention Mechanism
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Author : Shengli Chen
language : en
Publisher:
Release Date : 2020
Forecasting Implied Volatility Smile Surface Via Deep Learning And Attention Mechanism written by Shengli Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
The implied volatility smile surface is the basis of option pricing, and the dynamic evolution of the option volatility smile surface is difficult to predict. In this paper, attention mechanism is introduced into LSTM, and a volatility surface prediction method combining deep learning and attention mechanism is pioneeringly established. LSTM's forgetting gate makes it have strong generalization ability, and its feedback structure enables it to characterize the long memory of financial volatility. The application of attention mechanism in LSTM networks can significantly enhance the ability of LSTM networks to select input features. This paper considers the discrete points of the implied volatility smile surface as an overall prediction target, extracts the daily, weekly, and monthly option implied volatility as input features and establishes a set of LSTM-Attention deep learning systems. Using the dropout mechanism in training reduces the risk of over-fitting. For the prediction results, we use arbitrage-free smoothing to form the final implied volatility smile surface. This article uses the S&P 500 option market to conduct an empirical study. The research shows that the error curve of the LSTM-attention prediction system converges, and the prediction of the implied volatility surface is more accurate than other predicting system. According to the implied volatility surface of the 3-year rolling forecast, the BS formula is used to pricing the option contract, and then a time spread strategy and a butterfly spread strategy are constructed respectively. The experimental results show that the two strategies constructed using the predicted implied volatility surfaces have higher returns and sharp ratios than that the volatility surfaces are not predicted. This paper confirms that the use of AI to predict the implied volatility surface has theoretical and economic value. The research method provides a new reference for option pricing and strategy.
Arbitrage Free Smoothing Of The Implied Volatility Surface
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Author : Matthias R. Fengler
language : en
Publisher:
Release Date : 2005
Arbitrage Free Smoothing Of The Implied Volatility Surface written by Matthias R. Fengler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Smile Arbitrage
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Author : Alaa El Din Hammam
language : en
Publisher:
Release Date : 2009
Smile Arbitrage written by Alaa El Din Hammam 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 thesis studies the implied volatility, how it is recognized, modeled, and the ways used by practitioners in order to benefit from an arbitrage opportunity when compared to the realized volatility. Prediction power of implied volatility is examined and findings of previous studies are supported, that it has the best prediction power of all existing volatility models. When regressed on implied volatility, realized volatility shows a high beta of 0.88, which contradicts previous studies that found lower betas. Moment swaps are discussed and the ways to use them in the context of volatility trading, the payoff of variance swaps shows a significant negative variance premium which supports previous findings. An algorithm to find a fair value of a structured product aiming to profit from skew arbitrage is presented and the trade is found to be profitable in some circumstances. Different suggestions to implement moment swaps in the context of portfolio optimization are discussed.
Building Arbitrage Free Implied Volatility
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Author : Hadrien De March
language : en
Publisher:
Release Date : 2019
Building Arbitrage Free Implied Volatility written by Hadrien De March and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
We consider the classical problem of building an arbitrage-free implied volatility surface from bid-ask quotes. We design a fast numerical procedure, for which we prove the convergence, based on the Sinkhorn algorithm that has been recently used to solve efficiently (martingale) optimal transport problems.
Machine Learning In Insurance
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Author : Jens Perch Nielsen
language : en
Publisher: MDPI
Release Date : 2020-12-02
Machine Learning In Insurance written by Jens Perch Nielsen and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-02 with Business & Economics categories.
Machine learning is a relatively new field, without a unanimous definition. In many ways, actuaries have been machine learners. In both pricing and reserving, but also more recently in capital modelling, actuaries have combined statistical methodology with a deep understanding of the problem at hand and how any solution may affect the company and its customers. One aspect that has, perhaps, not been so well developed among actuaries is validation. Discussions among actuaries’ “preferred methods” were often without solid scientific arguments, including validation of the case at hand. Through this collection, we aim to promote a good practice of machine learning in insurance, considering the following three key issues: a) who is the client, or sponsor, or otherwise interested real-life target of the study? b) The reason for working with a particular data set and a clarification of the available extra knowledge, that we also call prior knowledge, besides the data set alone. c) A mathematical statistical argument for the validation procedure.
Analytically Tractable Stochastic Stock Price Models
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Author : Archil Gulisashvili
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-04
Analytically Tractable Stochastic Stock Price Models written by Archil Gulisashvili and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-04 with Mathematics categories.
Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochastic process. For instance, in the Hull-White model the volatility process is a geometric Brownian motion, the Stein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the Heston model a Cox-Ingersoll-Ross process governs the behavior of the volatility. One of the author's main goals is to provide sharp asymptotic formulas with error estimates for distribution densities of stock prices, option pricing functions, and implied volatilities in various stochastic volatility models. The author also establishes sharp asymptotic formulas for the implied volatility at extreme strikes in general stochastic stock price models. The present volume is addressed to researchers and graduate students working in the area of financial mathematics, analysis, or probability theory. The reader is expected to be familiar with elements of classical analysis, stochastic analysis and probability theory.
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.
Construction Of Arbitrage Free Implied Trees
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Author : Tobias Herwig
language : en
Publisher:
Release Date : 2005
Construction Of Arbitrage Free Implied Trees written by Tobias Herwig and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
In this paper we propose a new approach to identify the binomial process of the underlying asset price by using a simultaneous backward and forward induction algorithm. The model prices perfectly fit the strike and the term structure of the volatility smile given by traded benchmark options. The resulting implied binomial tree is semi-recombining and arbitrage-free. The model can be used to price and hedge a wide range of plain-vanilla and exotic options. Furthermore, the model allows to construct arbitrage-free multinomial trees.
De Arbitraging With A Weak Smile
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Author : Babak Mahdavi-Damghani
language : en
Publisher:
Release Date : 2014
De Arbitraging With A Weak Smile written by Babak Mahdavi-Damghani 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.
The aim of this article is to address the methodology behind de-arbitraging a realistic volatility surface and stressing it without adding arbitrages. We derive from basic principles the constraints which the changes on the strike and the tenor axis must satisfy in order to make a volatility surface arbitrage-free. The two most influential parameterized versions of the volatility surface will then be discussed, along with their origin and their limitations. Furthermore, this review will address the issues of finding the closest arbitrage-free volatility surface through the gSVI method, a more realistic parameterized version of the volatility surface applicable to the FX, commodities, and equities markets. Finally, using examples, the methodology behind coherently stressing this arbitrage-free volatility surface will be looked at, in order to capture and isolate the risk associated with higher-order Greeks like the Vanna or the Vomma.