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A Closed-Form Solution for the Global Quadratic Hedging of Options Under Geometric Gaussian Random Walks

A Closed-Form Solution for the Global Quadratic Hedging of Options Under Geometric Gaussian Random Walks
Author: Frédéric Godin
Publisher:
Total Pages:
Release: 2019
Genre:
ISBN:

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A closed-form solution is obtained for the discrete-time global quadratic hedging problem of Schweizer (1995) applied to vanilla European options under the geometric Gaussian random walk model for the underlying asset. The computation of coefficients embedded in the closed-form expression can be computed either directly or through a recursive algorithm.


Option Convergence Rate with Geometric Random Walks Approximations

Option Convergence Rate with Geometric Random Walks Approximations
Author: Guillaume Leduc
Publisher:
Total Pages:
Release: 2016
Genre:
ISBN:

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We describe a broad setting under which, for European options, if the underlying asset form a geometric random walk then, the error with respect to the Black-Scholes model converges to zero at a speed of 1/n for continuous payoffs functions, and at a speed of 1/√n for discontinuous payoffs functions.


American Options, the Method of Images and Closed Form Solutions

American Options, the Method of Images and Closed Form Solutions
Author: Gabriela Baumgartner
Publisher:
Total Pages: 29
Release: 2018
Genre:
ISBN:

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This paper considers solutions for a class of optimal stopping problems, maximising the expected product of a Wiener process and a positive decreasing scale function. The general approach to such problems involves a partial differential equation with movable boundary. The method of images is a useful tool for solving fixed-boundary PDE problems. We adapt this method to a sub-class of movable boundary problems. When the scale function in the original problem is a survival function of Generalised Pareto (GPD) type, we use a self-similarity property to reduce the PDE to an ODE. This ODE was widely studied in the 19th century, and the solution involves confluent hypergeometric functions. In cases of integer parameters, we give simpler closed form solutions involving the normal distribution function. The same approach also works when the Wiener process is reflected at zero.


A Profitable Modification to Global Quadratic Hedging

A Profitable Modification to Global Quadratic Hedging
Author: Maciej Augustyniak
Publisher:
Total Pages: 43
Release: 2019
Genre:
ISBN:

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Recent research has shown that global quadratic hedging, also known as variance-optimal hedging and mean-variance hedging, can significantly reduce the risk of hedging call and put options with long-term maturities (one year or more), such as Long-Term Equity AnticiPation Securities (LEAPS). We propose a modification to global quadratic hedging that is more profitable on average to the hedger without substantially increasing his downside hedging risk, if at all. We prove mathematically that the expected terminal hedging gain of our modified strategy is greater than that of the global quadratic hedging strategy. The performance of our strategy is evaluated under simulated return paths from GARCH and regime-switching models, and under empirical S&P 500 return paths.


Binomial Options Pricing Has No Closed-Form Solution

Binomial Options Pricing Has No Closed-Form Solution
Author: Evangelos Georgiadis
Publisher:
Total Pages: 5
Release: 2014
Genre:
ISBN:

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We set a lower bound on the complexity of options pricing formulae in the lattice metric by proving that no general explicit or closed form (hypergeometric) expression for pricing vanilla European call and put options exists when employing the binomial lattice approach. Our proof follows from Gosper's algorithm.


A Closed-Form Approach to Valuing Risk-Neutral Moments from Option Prices

A Closed-Form Approach to Valuing Risk-Neutral Moments from Option Prices
Author: Aristogenis Lazos
Publisher:
Total Pages: 36
Release: 2018
Genre:
ISBN:

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This paper develops closed-form solutions for the finite integrals in the volatility, cubic and quartic contracts in Bakshi, Kapadia and Madan (2003) which avoid discretization errors and do not involve interpolation and extrapolation. It compares the accuracy of the closed-form approach with the popular interpolation-extrapolation approach in the literature. Our results show that the closed-form approach provides more accurate estimates for skewness. This holds across different option pricing models and parameterization which have been shown to be favourable for the interpolation-extrapolation approach. Finally, our results show that the closed-form approach always extracts expectations consistent with the term structure of the volatility smirk whereas the interpolation-extrapolation approach fails several times.


Introduction to Econophysics

Introduction to Econophysics
Author: Rosario N. Mantegna
Publisher: Cambridge University Press
Total Pages: 164
Release: 1999-11-13
Genre: Business & Economics
ISBN: 1139431226

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This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.


A Non-Random Walk Down Wall Street

A Non-Random Walk Down Wall Street
Author: Andrew W. Lo
Publisher: Princeton University Press
Total Pages: 449
Release: 2011-11-14
Genre: Business & Economics
ISBN: 1400829097

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For over half a century, financial experts have regarded the movements of markets as a random walk--unpredictable meanderings akin to a drunkard's unsteady gait--and this hypothesis has become a cornerstone of modern financial economics and many investment strategies. Here Andrew W. Lo and A. Craig MacKinlay put the Random Walk Hypothesis to the test. In this volume, which elegantly integrates their most important articles, Lo and MacKinlay find that markets are not completely random after all, and that predictable components do exist in recent stock and bond returns. Their book provides a state-of-the-art account of the techniques for detecting predictabilities and evaluating their statistical and economic significance, and offers a tantalizing glimpse into the financial technologies of the future. The articles track the exciting course of Lo and MacKinlay's research on the predictability of stock prices from their early work on rejecting random walks in short-horizon returns to their analysis of long-term memory in stock market prices. A particular highlight is their now-famous inquiry into the pitfalls of "data-snooping biases" that have arisen from the widespread use of the same historical databases for discovering anomalies and developing seemingly profitable investment strategies. This book invites scholars to reconsider the Random Walk Hypothesis, and, by carefully documenting the presence of predictable components in the stock market, also directs investment professionals toward superior long-term investment returns through disciplined active investment management.


Monte Carlo Simulation and Finance

Monte Carlo Simulation and Finance
Author: Don L. McLeish
Publisher: John Wiley & Sons
Total Pages: 308
Release: 2011-09-13
Genre: Business & Economics
ISBN: 1118160940

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Monte Carlo methods have been used for decades in physics, engineering, statistics, and other fields. Monte Carlo Simulation and Finance explains the nuts and bolts of this essential technique used to value derivatives and other securities. Author and educator Don McLeish examines this fundamental process, and discusses important issues, including specialized problems in finance that Monte Carlo and Quasi-Monte Carlo methods can help solve and the different ways Monte Carlo methods can be improved upon. This state-of-the-art book on Monte Carlo simulation methods is ideal for finance professionals and students. Order your copy today.