An Accurate Pricing Formula for Vanilla Options in a Cash Dividend Framework with Linear Algorithmic Complexity PDF Download
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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: 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: 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: 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: Valeriy V. Ryabchenko
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Our second study considered a regression approach to pricing European options in an incomplete market. The algorithm replicates an option by a portfolio consisting of the underlying security and a risk-free bond. We apply linear regression framework and quadratic programming with linear constraints (input = sample paths of underlying security; output = table of option prices as a function of time and price of the underlying security). We populate the model with historical prices of the underlying security (possibly massaged to the present volatility) or with Monte Carlo simulated prices. Risk neutral processes or probabilities are not needed in this framework.
Author: Espen Gaarder Haug
Publisher: Professional Finance & Investment
ISBN:
Category : Business & Economics
Languages : en
Pages : 586
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Book Description
Accompanying CD-ROM contains ... "all pricing formulas, with VBA code and ready-to-use Excel spreadsheets and 3D charts for Greeks (or Option Sensitivities)."--Jacket.
Author: Espen Gaardner Haug
Publisher: McGraw Hill Professional
ISBN: 9780071395892
Category : Business & Economics
Languages : en
Pages : 268
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Book Description
When pricing options in todayÕs fast-action markets, you need quick access to precise facts and market-tested information. The Complete Guide to Options Pricing Formulas is the only authoritative, comprehensive reference to make the necessary set of option pricing tools available in one place. This invaluable reference work, which includes valuable software and ready-to-use programming code to enhance your understanding of the options pricing models discussed and their practical implementations, also gives you a complete listing of key options formulas, all in a dictionary format for ease of use; commentary from derivatives expert and author Espen Gaarder Haug that explains key points in the most important and useful formulas; practitioner-oriented formulas, and highlights of the latest options pricing research from major institutions worldwide; and much more! Invaluable for both experienced users and those learning how to use the tools of valuation, The Complete Guide to Options Pricing Formulas is the first and only book to place all of the research and information you need at your fingertips with precise directions on maximizing its real-world value.
Author: Miquel Montero
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in which some of the properties volatility and dividend policy of the underlying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because most relevant facts usually entail sharp predictable consequences. The effect of this potential risk on perpetual American vanilla options is remarkable: the very equation that will determine the fair price depends on the solution to be found. Sound results are found under the optics both of finance and physics. In particular, a parallelism among the overall outcome of this problem and a phase transition is established.
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.
Author: Jiri Kamiel Hoogland
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 10
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Book Description
Author: Hans Buehler
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This article shows how to incorporate cash dividends and credit risk into equity derivatives pricing and risk management. In essence, we show that in an arbitrage-free model the stock price process upon default must have the form S(t) = { F(t) - D(t) } X(t) D(t) ] where X is a local martingale with X(0)=1, the curve F represents the "risky" forward and D is the floor imposed on the stock price process in the form of appropriately discounted future dividends. We show that the method presented is the only such method which is consistent with the assumption of cash dividends and simple credit risk. We discuss the implications for implied volatility, no-arbitrage conditions and we derive a version of Dupire's formula which handles cash dividend and credit risk properly. We discuss pricing and risk management of European options, PDE methods and in quite some detail variance swaps and related derivatives such as gamma swaps, conditional variance swaps and corridor variance swaps. Indeed, to the our best if our knowledge, this is the first article which shows the correct handling of cash dividends when pricing variance swaps. The present version 1.31 has been updated after several comments from readers.
