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A Volatility Of Volatility Expansion Of The Option Prices In The Sabr Stochastic Volatility Model
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Book Synopsis A Volatility-of-Volatility Expansion of the Option Prices in the SABR Stochastic Volatility Model by : Olesya V. Grishchenko
Download or read book A Volatility-of-Volatility Expansion of the Option Prices in the SABR Stochastic Volatility Model written by Olesya V. Grishchenko and published by . This book was released on 2014 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Asymptotic Expansion Formula for Up-and-Out Barrier Option Price Under Stochastic Volatility Model by : Takashi Kato
Download or read book An Asymptotic Expansion Formula for Up-and-Out Barrier Option Price Under Stochastic Volatility Model written by Takashi Kato and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate the validity of our approximation method through numerical examples.
Book Synopsis The Asymptotic Expansion Formula of Implied Volatility for Dynamic SABR Model and FX Hybrid Model by : Yasufumi Osajima
Download or read book The Asymptotic Expansion Formula of Implied Volatility for Dynamic SABR Model and FX Hybrid Model written by Yasufumi Osajima and published by . This book was released on 2007 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author considers SABR model which is a two factor stochastic volatility model and gives an asymptotic expansion formula of implied volatilities for this model. His approach is based on infinite dimensional analysis on the Malliavin calculus and large deviation.Furthermore, he applies the approach to a foreign exchange model where interest rates and the FX volatilities are stochastic and gives an asymptotic expansion formula of implied volatilities of foreign exchange options.
Book Synopsis Hyperbolic Normal Stochastic Volatility Model by : Jaehyuk Choi
Download or read book Hyperbolic Normal Stochastic Volatility Model written by Jaehyuk Choi and published by . This book was released on 2019 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR) model. Using two generalized Bougerol's identities in the literature, the study shows that our model has a closed-form Monte-Carlo simulation scheme and that the transition probability for one special case follows Johnson's SU distribution -- a popular heavy-tailed distribution originally proposed without stochastic process. It is argued that the SU distribution serves as an analytically superior alternative to the normal SABR model because the two distributions are empirically similar.
Book Synopsis Option Valuation Under Stochastic Volatility by : Alan L. Lewis
Download or read book Option Valuation Under Stochastic Volatility written by Alan L. Lewis and published by . This book was released on 2000 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Preliminary View of Calculating Call Option Prices Utilizing Stochastic Volatility Models by : Karl Shen
Download or read book A Preliminary View of Calculating Call Option Prices Utilizing Stochastic Volatility Models written by Karl Shen and published by . This book was released on 2009 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: We will begin with a review of key financial topics and outline many of the crucial ideas utilized in the latter half of the paper. Formal notation for important variables will also be established. Then, a derivation of the Black-Scholes equation will lead to a discussion of its shortcomings, and the introduction of stochastic volatility models. Chapter 2 will focus on a variation of the CIR Model using stock price in the volatility driving process, and its behavior to a greater degree. The key area of discussion will be to approximate a hedging function for European call option prices by Taylor Expansion. We will apply this estimation to real data, and analyze the behavior of the price correction. Then make conclusions about whether stock price has any positive effects on the model.
Book Synopsis A Weak Approximation with Malliavin Weights for Local Stochastic Volatility Model by : Toshihiro Yamada
Download or read book A Weak Approximation with Malliavin Weights for Local Stochastic Volatility Model written by Toshihiro Yamada and published by . This book was released on 2017 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a new efficient and practical weak approximation for option price under local stochastic volatility model as marginal expectation of stochastic differential equation, using iterative asymptotic expansion with Malliavin weights. The explicit Malliavin weights for SABR model are shown. Numerical experiments confirm the validity of our discretization with a few time steps.
Book Synopsis A Simple New Formula for Options with Stochastic Volatility by : Steven L. Heston
Download or read book A Simple New Formula for Options with Stochastic Volatility written by Steven L. Heston and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper shows a relationship between bond pricing models and option pricing models with stochastic volatility. It exploits this relationship to find a new stochastic volatility model with a closed-form solution for European option prices. The model allows nonzero correlation between volatility and spot asset returns. When the correlation is unity the model contains the Black-Scholes [1973] model and Cox's [1975] constant elasticity of variance model as special cases. The option formula preserves the Black-Scholes property that changes in volatility are equivalent to changes in option expiration.
Author :Antoine Petrus Cornelius van der Ploeg Publisher :Rozenberg Publishers ISBN 13 :9051705778 Total Pages :358 pages Book Rating :4.0/5 (517 download)
Book Synopsis Stochastic volatility and the pricing of financial derivatives by : Antoine Petrus Cornelius van der Ploeg
Download or read book Stochastic volatility and the pricing of financial derivatives written by Antoine Petrus Cornelius van der Ploeg and published by Rozenberg Publishers. This book was released on 2006 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pricing Via Quantization in Stochastic Volatility Models by : Giorgia Callegaro
Download or read book Pricing Via Quantization in Stochastic Volatility Models written by Giorgia Callegaro and published by . This book was released on 2015 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we apply a new methodology based on quantization to price options in stochastic volatility models. This method can be applied to any model for which an Euler scheme is available for the underlying process and it allows for pricing vanillas, as well as exotics, thanks to the knowledge of the transition probabilities for the discretized stock process. We apply the methodology to some celebrated stochastic volatility models, including the Stein and Stein (1991) model and the SABR model introduced in Hagan and Woodward (2002). A numerical exercise shows that the pricing of vanillas turns out to be accurate; in addition, when applied to some exotics like equity-volatility options, the quantization-based method overperforms by far the Monte Carlo simulation.
Book Synopsis A General Formula for Option Prices in a Stochastic Volatility Model by : Stephen Chin
Download or read book A General Formula for Option Prices in a Stochastic Volatility Model written by Stephen Chin and published by . This book was released on 2009 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Implied Volatility at the Second Order with Application to the SABR Model by : Louis Paulot
Download or read book Asymptotic Implied Volatility at the Second Order with Application to the SABR Model written by Louis Paulot and published by . This book was released on 2016 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion. Furthermore, the first correction in the heat kernel expansion gives the second order correction for implied volatility, which we also give exactly at all strikes. As an application, we compute this asymptotic expansion at order 2 for the SABR model.
Book Synopsis Explicit Implied Volatilities for Multifactor Local-Stochastic Volatility Models by : Matthew Lorig
Download or read book Explicit Implied Volatilities for Multifactor Local-Stochastic Volatility Models written by Matthew Lorig and published by . This book was released on 2014 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do they require numerical integration. To illustrate the accuracy and versatility of our method, we implement it under five different model dynamics: CEV local volatility, quadratic local volatility, Heston stochastic volatility, 3/2 stochastic volatility, and SABR local-stochastic volatility.
Book Synopsis Series Expansion of the SABR Joint Density by : Qi Wu
Download or read book Series Expansion of the SABR Joint Density written by Qi Wu and published by . This book was released on 2015 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: Under the SABR stochastic volatility model, pricing and hedging contracts that are sensitive to forward smile risk (e.g., forward starting options, barrier options) require the joint transition density.In this paper, we address this problem by providing closed-form representations, asymptotically, of the joint transition density. Specifically, we construct an expansion of the joint density through a hierarchy of parabolic equations after applying total volatility-of-volatility scaling and a near-Gaussian coordinate transformation. We then established an existence result to characterize the truncation error and provide explicit joint density formulas for the first three orders. Our approach inherits the same spirit of a small total volatility-of-volatility assumption as in in the original SABR analysis. Our results for the joint transition density serve as a basis for managing forward smile risk. Through numerical experiments, we illustrate the accuracy of our expansion in terms of joint density, marginal density, probability mass and implied volatilities for European call options.
Book Synopsis A General Asymptotic Implied Volatility for Stochastic Volatility Models by : Pierre Henry-Labordere
Download or read book A General Asymptotic Implied Volatility for Stochastic Volatility Models written by Pierre Henry-Labordere and published by . This book was released on 2005 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we derive a general asymptotic implied volatility at the first-order for any stochastic volatility model using the heat kernel expansion on a Riemann manifold endowed with an Abelian connection. This formula is particularly useful for the calibration procedure. As an application, we obtain an asymptotic smile for a SABR model with a mean-reversion term, called lambda-SABR, corresponding in our geometric framework to the Poincare hyperbolic plane. When the lambda-SABR model degenerates into the SABR-model, we show that our asymptotic implied volatility is a better approximation than the classical Hagan-al expression. Furthermore, in order to show the strength of this geometric framework, we give an exact solution of the SABR model with beta=0 or 1. In a next paper, we will show how our method can be applied in other contexts such as the derivation of an asymptotic implied volatility for a Libor market model with a stochastic volatility.
Book Synopsis SABR and SABR LIBOR Market Models in Practice by : Christian Crispoldi
Download or read book SABR and SABR LIBOR Market Models in Practice written by Christian Crispoldi and published by Springer. This book was released on 2016-04-29 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest rate traders have been using the SABR model to price vanilla products for more than a decade. However this model suffers however from a severe limitation: its inability to value exotic products. A term structure model à la LIBOR Market Model (LMM) is often employed to value these more complex derivatives, however the LMM is unable to capture the volatility smile. A joint SABR LIBOR Market Model is the natural evolution towards a consistent pricing of vanilla and exotic products. Knowledge of these models is essential to all aspiring interest rate quants, traders and risk managers, as well an understanding of their failings and alternatives. SABR and SABR Libor Market Models in Practice is an accessible guide to modern interest rate modelling. Rather than covering an array of models which are seldom used in practice, it focuses on the SABR model, the market standard for vanilla products, the LIBOR Market Model, the most commonly used model for exotic products and the extended SABR LIBOR Market Model. The book takes a hands-on approach, demonstrating simply how to implement and work with these models in a market setting. It bridges the gap between the understanding of the models from a conceptual and mathematical perspective and the actual implementation by supplementing the interest rate theory with modelling specific, practical code examples written in Python.
Book Synopsis Empirical Performance of Option Pricing Models with Stochastic Local Volatility by : Greg Orosi
Download or read book Empirical Performance of Option Pricing Models with Stochastic Local Volatility written by Greg Orosi and published by . This book was released on 2014 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine the empirical performance of several stochastic local volatility models that are the extensions of the Heston stochastic volatility model. Our results indicate that the stochastic volatility model with quadratic local volatility significantly outperforms the stochastic volatility model with CEV type local volatility. Moreover, we compare the performance of these models to several other benchmarks and find that the quadratic local volatility model compares well to the best performing option pricing models reported in the current literature for European-style S&P500 index options. Our results also indicate that the model with quadratic local volatility reproduces the characteristics of the implied volatility surface more accurately than the Heston model. Finally, we demonstrate that capturing the shape of the implied volatility surface is necessary to price binary options accurately.
