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Author: Fabien Le Floc'h
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
There is no exact closed form formula for pricing of European options with discrete cash dividends under the model where the underlying asset price follows a piecewise lognormal process with jumps at dividend ex-dates. This paper presents alternative expansions based on the technique of Etore and Gobet, leading to more robust first, second and third order expansions accross the range of strikes and the range of dividend dates.
Author: Fabien Le Floc'h
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
There is no exact closed form formula for pricing of European options with discrete cash dividends under the model where the underlying asset price follows a piecewise lognormal process with jumps at dividend ex-dates. This paper presents alternative expansions based on the technique of Etore and Gobet, leading to more robust first, second and third order expansions accross the range of strikes and the range of dividend dates.
Author: Pierre Etore
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
In the context of an asset paying affine-type discrete dividends, we present closed analytical approximations for the pricing of European vanilla options in the Black-Scholes model with time-dependent parameters. They are obtained using a stochastic Taylor expansion around a shifted lognormal proxy model. The final formulae are respectively first, second and third order approximations w.r.t. the fixed part of the dividends. Using Cameron-Martin transformations, we provide explicit representations of the correction terms as Greeks in the Black-Scholes model. The use of Malliavin calculus enables us to provide tight error estimates for our approximations. Numerical experiments show that the current approach yields very accurate results, in particular compared to known approximations of [BGS03,VW09], and quicker than the iterated integration procedure of [HHL03] or than the binomial tree method of [VN06].
Author: Timothy Klassen
Publisher:
ISBN:
Category :
Languages : en
Pages : 28
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Book Description
The pricing of vanilla options on underliers with cash dividends is a surprisingly contentious and active research subject, for both European or American exercise style. Neither on the listed options side (calls and puts) nor on the flow/structured side of longer-term vanillas or light exotics are market participants in agreement on what model to use, nor on what an efficient practical implementation of the chosen model would be. The modeling problem boils down to the question of what a proper generalization of the Black-Scholes model to the case of cash dividends is, i.e. what should replace simple geometric Brownian motion (GBM).We discuss this question with the aim of taking a first step towards a rationalization and normalization of the equity volatility market. We compare the two main classes of models in use, namely the "spot model" (piecewise GBM) and several "hybrid models" (shifted GBM). We are interested in consistency, simplicity, speed, and generality (covering all traded vanilla options, dividend and borrow rate assumptions, as well as easy modeling of business time, events, term-structure, credit, light exotics, etc). We also discuss the calibration problems that market participants face in some detail.We show that: (i) all hybrid models are closely related on a mathematical level -- despite qualitatively different financial properties -- with simple and accurate relationships between calibrated parameters (borrow costs and volatilities) for both European and American options with cash dividends; (ii) all hybrid models allow accurate and very fast pricing of vanilla options using fine-tuned tree methods; (iii) some hybrid models have essentially all the desired properties outlined above; in particular, we describe a hybrid model closely related to the spot model, motivated by the spot-strike adjustment idea of Bos and Vandermark.
Author: Gilles Boya
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
The aim of this article is to provide a fast and efficient formula to price vanilla options in presence of cash dividends. Bos & Vandermark have provided a simple and intuitive formula but not really accurate for long maturities or for strikes far from the money. Many authors have proposed some accurate formula but with a polynomial (quadratic for Henry-Labordère) algorithmic complexity in the number of dividends. In this article we derive a formula whose accuracy is equivalent to that of Henry-Labordère but with a linear algorithmic complexity, preserving the call-put parity and the continuity of the vanilla price at each ex-dividend dates.
Author: Ashok N. Vasvani
Publisher:
ISBN:
Category :
Languages : en
Pages : 110
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Book Description
Author: Romain Bompis
Publisher:
ISBN:
Category :
Languages : en
Pages : 277
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Book Description
Author: Mario Dell'Era
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We want to discuss the option pricing in stochastic volatility market models, in which we consider a generic function B (vt) for the drift of the volatility process. It is our intention to choose any equivalent martingale measure, such that, the drift of the volatility process, with respect to the new measure, is zero. This technique is possible when the Girsanov theorem is satisfied, since the stochastic volatility models are incomplete markets, thus one has to choose an arbitrary risk price of volatility. In all these cases we are able to compute in approximate way the price of Vanilla options in a closed-form. To the name a few, we can think of the popular Heston model, in which the solution is known in the literature, up to an inverse Fourier transform.
Author: 方媛
Publisher:
ISBN:
Category : Options (Finance)
Languages : en
Pages : 164
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Book Description
Author: Fabrice D. Rouah
Publisher: John Wiley & Sons
ISBN: 1118429206
Category : Business & Economics
Languages : en
Pages : 456
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Book Description
This comprehensive guide offers traders, quants, and students the tools and techniques for using advanced models for pricing options. The accompanying website includes data files, such as options prices, stock prices, or index prices, as well as all of the codes needed to use the option and volatility models described in the book. Praise for Option Pricing Models & Volatility Using Excel-VBA "Excel is already a great pedagogical tool for teaching option valuation and risk management. But the VBA routines in this book elevate Excel to an industrial-strength financial engineering toolbox. I have no doubt that it will become hugely successful as a reference for option traders and risk managers." —Peter Christoffersen, Associate Professor of Finance, Desautels Faculty of Management, McGill University "This book is filled with methodology and techniques on how to implement option pricing and volatility models in VBA. The book takes an in-depth look into how to implement the Heston and Heston and Nandi models and includes an entire chapter on parameter estimation, but this is just the tip of the iceberg. Everyone interested in derivatives should have this book in their personal library." —Espen Gaarder Haug, option trader, philosopher, and author of Derivatives Models on Models "I am impressed. This is an important book because it is the first book to cover the modern generation of option models, including stochastic volatility and GARCH." —Steven L. Heston, Assistant Professor of Finance, R.H. Smith School of Business, University of Maryland
Author: Lishang Jiang
Publisher: World Scientific
ISBN: 9812563695
Category : Science
Languages : en
Pages : 344
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Book Description
From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.
