Download or read book Robust Option Pricing written by Si Chen (S.M.) and published by . This book was released on 2009 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research aims to provide tractable approaches to price options using robust optimization. The pricing problem is reduced to a problem of identifying the replicating portfolio which minimizes the worst case arbitrage possible for a given uncertainty set on underlying asset returns. We construct corresponding uncertainty sets based on different levels of risk aversion of investors and make no assumption on specific probabilistic distributions of asset returns. The most significant benefits of our approach are (a) computational tractability illustrated by our ability to price multi-dimensional options and (b) modeling flexibility illustrated by our ability to model the "volatility smile". Specifically, we report extensive computational results that provide empirical evidence that the "implied volatility smile" that is observed in practice arises from different levels of risk aversion for different strikes. We are able to capture the phenomenon by appropriately finding the right risk-aversion as a function of the strike price. Besides European style options which have fixed exercising date, our method can also be adopted to price American style options which we can exercise early. We also show the applicability of this pricing method in the case of exotic and multi-dimensional options, in particular, we provide formulations to price Asian options, Lookback options and also Index options. These prices are compared with market prices, and we observe close matches when we use our formulations with appropriate uncertainty sets constructed based on market-implied risk aversion.
Download or read book Robust Option Pricing written by Peter M. DeMarzo and published by . This book was released on 2016 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We apply gradient strategy methods, developed in the literature on robust optimization, approachability and calibration, to develop new bounds for option prices. While this literature focuses on asymptotic performance, we provide a financial interpretation of these methods by demonstrating how the gradient strategies developed by Hannan and Blackwell to minimize asymptotic regret imply trading strategies that yield arbitrage-based bounds for option prices. These bounds are both new and robust in that they do not depend on the continuity of the stock price process, complete markets, or an assumed pricing kernel. Rather, they depend only on the realized quadratic variation of the stock price process, which can be measured and, more importantly, hedged in financial markets using existing securities. We then argue that the Hannanndash;Blackwell strategy is path dependent and therefore suboptimal with a finite horizon. We solve for the optimal path-independent strategy, and compare the bounds achieved with Black-Scholes.
Download or read book Robust Spread Option Pricing written by Ilya Kolpakov and published by . This book was released on 2014 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: I examine accuracy and robustness of European spread option pricing method of Hurd and Zhou (2010) for European spread options. This method approximates an indefinite bivariate integral by a sum over a uniform grid and the method's accuracy varies greatly depending on the choice of truncation bounds and the number of grid points. I find optimal parameters for a realistic sample of spread options and show that the pricing procedure can be made both faster and more robust by using a technique suggested in Andersen and Andreasen (2002), namely approximating the true distribution of log returns with a normal one and integrating the payoff transform against the difference of exact and approximating transforms.
Download or read book Robust Option Pricing with Characteristic Functions and the B Spline Order of Density Projection written by Justin Kirkby and published by . This book was released on 2016 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper extends and refines the method of option pricing by frame projection of risk-neutral densities to incorporate general B-splines, including the cubic basis, and general payoff structures. We introduce a coefficient stabilization method which substantially improves convergence for higher order splines. This stabilization has subsequently provided robust implementations for exotic option extensions of the method. After demonstrating the greater robustness of a fixed-width truncation rule over generally accepted cumulant based approaches, we devise a novel Hilbert transform based approach for the selection of truncated density supports, applicable to any density approximation method, which facilitates greater control over realized pricing errors. Robustness of B-spline frame projection is demonstrated by an extensive set of experiments which guide the selection of splines of various orders and subsequent parameter decisions. Finally, we provide formulas for digital and forward starting options.
Download or read book Robust Estimation of Shape Constrained State Price Density Surfaces written by Markus Ludwig and published by . This book was released on 2015 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to better capture empirical phenomena, research on option price and implied volatility modeling increasingly advocates the use of nonparametric methods over simple functional forms. This, however, comes at a price, since these methods require dense observations to yield sensible results. Calibration is therefore typically performed using time-series data. Ironically, the use of historical data in turn limits the accuracy with which current observations can be modeled. We propose a novel approach that enables the use of flexible functional forms using only a snapshot of option prices. Our estimators are genuinely conditional and generalize well beyond available data, all the while respecting theory-imposed shape constraints. We demonstrate the numerical stability and the pricing performance of our method by approximating arbitrage-free implied volatility, price, and state price density surfaces from S&P 500 options over a period of 12 years.
Download or read book Volatility Trading website written by Euan Sinclair and published by John Wiley & Sons. This book was released on 2008-06-23 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Volatility Trading, Sinclair offers you a quantitative model for measuring volatility in order to gain an edge in your everyday option trading endeavors. With an accessible, straightforward approach. He guides traders through the basics of option pricing, volatility measurement, hedging, money management, and trade evaluation. In addition, Sinclair explains the often-overlooked psychological aspects of trading, revealing both how behavioral psychology can create market conditions traders can take advantage of-and how it can lead them astray. Psychological biases, he asserts, are probably the drivers behind most sources of edge available to a volatility trader. Your goal, Sinclair explains, must be clearly defined and easily expressed-if you cannot explain it in one sentence, you probably aren't completely clear about what it is. The same applies to your statistical edge. If you do not know exactly what your edge is, you shouldn't trade. He shows how, in addition to the numerical evaluation of a potential trade, you should be able to identify and evaluate the reason why implied volatility is priced where it is, that is, why an edge exists. This means it is also necessary to be on top of recent news stories, sector trends, and behavioral psychology. Finally, Sinclair underscores why trades need to be sized correctly, which means that each trade is evaluated according to its projected return and risk in the overall context of your goals. As the author concludes, while we also need to pay attention to seemingly mundane things like having good execution software, a comfortable office, and getting enough sleep, it is knowledge that is the ultimate source of edge. So, all else being equal, the trader with the greater knowledge will be the more successful. This book, and its companion CD-ROM, will provide that knowledge. The CD-ROM includes spreadsheets designed to help you forecast volatility and evaluate trades together with simulation engines.
Download or read book Pricing no arbitrage bounds and robust hedging of installment options written by Mark Davis and published by . This book was released on 2002 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: An installment option is a European option in which the premium, instead of being paid up-front, is paid in a series of installments. If all installments are paid the holder receives the exercise value, but the holder has the right to terminate payments on any payment date, in which case the option lapses with no further payments on either side. We discuss pricing and risk management for these options, in particular the use of static hedges, and also study a continuous-time limit in which premium is paid at a certain rate per unit time.Key words: Option Pricing, Exotic Options, Stable Hedging, Replicating, Portfolios, No-arbitrage bounds.
Download or read book Robust Static Super Replication of Barrier Options written by Jan H. Maruhn and published by Walter de Gruyter. This book was released on 2009-07-14 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Static hedge portfolios for barrier options are very sensitive with respect to changes of the volatility surface. To prevent potentially significant hedging losses this book develops a static super-replication strategy with market-typical robustness against volatility, skew and liquidity risk as well as model errors. Empirical results and various numerical examples confirm that the static superhedge successfully eliminates the risk of a changing volatility surface. Combined with associated sub-replication strategies this leads to robust price bounds for barrier options which are also relevant in the context of dynamic hedging. The mathematical techniques used to prove appropriate existence, duality and convergence results range from financial mathematics, stochastic and semi-infinite optimization, convex analysis and partial differential equations to semidefinite programming.
Download or read book Robust Spectral Methods for Solving Option Pricing Problems written by and published by . This book was released on 2012 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the invention of the classical Black-Scholes formula to price the financial derivatives, a number of mathematical models have been proposed by numerous researchers in this direction. Many of these models are in general very complex, thus closed form analytical solutions are rarely obtainable. In view of this, we present a class of efficient spectral methods to numerically solve several mathematical models of pricing options. We begin with solving European options. Then we move to solve their American counterparts which involve a free boundary and therefore normally difficult to price by other conventional numerical methods. We obtain very promising results for the above two types of options and therefore we extend this approach to solve some more difficult problems for pricing options, viz., jump-diffusion models and local volatility models. The numerical methods involve solving partial differential equations, partial integro-differential equations and associated complementary problems which are used to model the financial derivatives. In order to retain their exponential accuracy, we discuss the necessary modification of the spectral methods. Finally, we present several comparative numerical results showing the superiority of our spectral methods.
Download or read book Nonlinear Option Pricing written by Julien Guyon and published by CRC Press. This book was released on 2013-12-19 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Tools to Solve Your Option Pricing Problems For nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research—including Risk magazine’s 2013 Quant of the Year—Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods. Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numerical implementation. Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs. The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + bλ technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.
Download or read book Robust High Precision Option Pricing by Fourier Transforms written by Leif B. G. Andersen and published by . This book was released on 2018 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: While the idea of pricing options by Fourier methods has been around for more than two decades, the numerical evaluation of the necessary semi-infinite Fourier style integrals remains a challenging problem. Existing methods in the literature frequently lack robustness, and in practice often result in disappointing precision, especially when the integrands become oscillatory or poorly dampened. In this paper we propose two new methods to evaluate these integrals, both relying on double-exponential quadrature. In the first, we use a carefully constructed contour deformation to dampen out Fourier oscillations in the integrand, followed by an application of either automatic or fixed-size double exponential quadrature. In the second, we use a node-placement trick by T. Ooura to ensure that the integrand decays double-exponentially at all node points, even in the presence of oscillations. While both methods are generally applicable, for concreteness we mostly frame our development in the context of the popular (and tricky) Heston stochastic volatility model. As demonstrated by tests on hundred thousands of challenging model and option parameter configurations, our two schemes are efficient, accurate, and robust, and significantly outperform standard methods. For instance, in a challenging bulk test our recommended scheme is on average about 10 orders of magnitude more precise than standard adaptive Gauss-Lobatto quadrature, and is also far more robust.
Download or read book A New Fast and Robust Technique for Pricing and Hedging Asia Options written by Georgios Vasileiou Dalakouras and published by . This book was released on 2004 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient pricing algorithms for exotic derivatives written by Roger Lord and published by Rozenberg Publishers. This book was released on 2008 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A new fast and robust technique for pricing and hedging Asian options written by Georgios Vasileiou Dalakouras and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Robust Hedging of the Lookback Option written by David G. Hobson and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this article is to find bounds on the prices of exotic derivatives, and in particular the lookback option, in terms of the (market) prices of call options. This is achieved without making explicit assumptions about the dynamics of the price process of the underlying asset, but rather by inferring information about the potential distribution of asset prices from the call prices. Thus the bounds we obtain and the associated hedging strategies are model independent. The appeal and significance of the hedging strategies arises from their universality and robustness to model mis-specification.
Download or read book Options written by Stewart Dimont Hodges and published by Manchester University Press. This book was released on 1990 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vinzenz Bronzin s Option Pricing Models written by Wolfgang Hafner and published by Springer Science & Business Media. This book was released on 2009-11-18 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1908, Vinzenz Bronzin, a professor of mathematics at the Accademia di Commercio e Nautica in Trieste, published a booklet in German entitled Theorie der Prämiengeschäfte (Theory of Premium Contracts) which is an old type of option contract. Almost like Bachelier’s now famous dissertation (1900), the work seems to have been forgotten shortly after it was published. However, almost every element of modern option pricing can be found in Bronzin’s book. He derives option prices for an illustrative set of distributions, including the Normal. - This volume includes a reprint of the original German text, a translation, as well as an appreciation of Bronzin's work from various perspectives (economics, history of finance, sociology, economic history) including some details about the professional life and circumstances of the author. The book brings Bronzin's early work to light again and adds an almost forgotten piece of research to the theory of option pricing.
