Journal ArticleDOI
Dynamics of implied volatility surfaces
Rama Cont,José Da Fonseca +1 more
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In this paper, the authors use time series of option prices on the SP500 and FTSE indices to study the deformation of the implied volatility surface and show that it may be represented as a randomly fluctuating surface driven by a small number of orthogonal random factors.Abstract:
The prices of index options at a given date are usually represented via the corresponding implied volatility surface, presenting skew/smile features and term structure which several models have attempted to reproduce. However, the implied volatility surface also changes dynamically over time in a way that is not taken into account by current modelling approaches, giving rise to `Vega' risk in option portfolios. Using time series of option prices on the SP500 and FTSE indices, we study the deformation of this surface and show that it may be represented as a randomly fluctuating surface driven by a small number of orthogonal random factors. We identify and interpret the shape of each of these factors, study their dynamics and their correlation with the underlying index. Our approach is based on a Karhunen-Loeve decomposition of the daily variations of implied volatilities obtained from market data. A simple factor model compatible with the empirical observations is proposed. We illustrate how this ...read more
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Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes
Jing-Zhi Huang,Liuren Wu +1 more
TL;DR: In this paper, the authors present a unified framework that synthesizes the ongoing efforts to identify the "true" dynamics of the underlying return process by performing a specification analysis of option pricing models.
Journal ArticleDOI
Statistical arbitrage in the US equities market
Marco Avellaneda,Jeong Hyun Lee +1 more
TL;DR: In this article, the authors study model-driven statistical arbitrage in US equities using principal component analysis (PCA) or regressing stock returns on sector Exchange Traded Funds (ETFs).
Journal ArticleDOI
A Multifactor Volatility Heston Model
TL;DR: In this article, the authors model the volatility of a single risky asset using a multifactor (matrix) Wishart affine process, recently introduced in finance by Gourieroux and Sufana.
Journal ArticleDOI
A survey of functional principal component analysis
TL;DR: A review of functional principal component analysis, and its use in explanatory analysis, modeling and forecasting, and classification of functional data is provided in this article from both methodological and practical viewpoints.
Journal ArticleDOI
Non-parametric calibration of jump–diffusion option pricing models
Rama Cont,Peter Tankov +1 more
TL;DR: A non-parametric method for calibrating jump-diffusion models to a set of observed option prices is presented and it is shown via simulation tests that using the entropy penalty resolves the numerical instability of the calibration problem.
References
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Journal ArticleDOI
The Pricing of Options and Corporate Liabilities
Fischer Black,Myron S. Scholes +1 more
TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Journal ArticleDOI
Empirical Performance of Alternative Option Pricing Models
TL;DR: In this article, an option pricing model that allows volatility, interest rates and jumps to be stochastic is presented. But it is not known whether and by how much each generalization improves option pricing and hedging.
Book
Applied Nonparametric Regression
TL;DR: This chapter discusses smoothing in high Dimensions, Investigating multiple regression by additive models, and incorporating parametric components and alternatives.
Journal ArticleDOI
Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics
TL;DR: The authors construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive Ornstein-Uhlenbeck (OU) processes, and study these models in relation to financial data and theory.
Journal ArticleDOI
Implied Binomial Trees
TL;DR: In this article, a new method for inferring risk-neutral probabilities (or state-contingent prices) from the simultaneously observed prices of European options is developed. But this method requires the assumption that the underlying asset has a limited risk-free lognormal distribution.