Parametric And Non Parametric Option Hedging And Estimation Based On Hedging Error Minimization
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| Author | : Xiaoyi Chen |
| Publisher | : |
| Total Pages | : 108 |
| Release | : 2020 |
| Genre | : Hedging (Finance) |
| ISBN | : |
Over the past few decades, option pricing accuracy has always been a standard criterion in gauging the performance of model parameter estimates. However, as a primary concern for option market makers, option hedging activity receives much less attention than pricing. Since option hedging strives to eliminate risks of market makers' portfolio positions in practice, it might be a more sensible measure in evaluating model estimates. In the first part of this thesis, a parameter estimation procedure based on minimizing the risks accumulated over the lifetime of an option is proposed. More specifically, a loss function which involves option pricing and hedging strategies is first defined to evaluate the cumulative hedging error(CHE). Then, after a simulation study assuming the Black-Scholes(BS) model for stock dynamics and option prices, an estimation method based on minimizing CHE is compared with maximum likelihood estimation(MLE) and implied estimation under three different model settings: the Black-Scholes model, the Merton jump diffusion, and the Heston stochastic volatility model. This comparison is conducted using an empirical study consisting of multiple datasets of individual stocks and options spanning 2011-2014 with the back-testing procedure. The second part of this thesis tries to mitigate the model-dependent feature of the first part, allowing flexible smoothing spline estimates for the option pricing curves. There are shape constraints induced by the arbitrage-free conditions of pricing options. Therefore, the form of the smoothing spline is carefully chosen to satisfy the constraints. In addition, certain transformation to the inputs of the pricing curve is performed to reduce dimensions. Under such strict constraints, we propose an option pricing curve which is composed of a weighted average between the Black-Scholes pricing function and a constrained cubic spline function. The resulting pricing and hedging strategies generated by the weighted curve estimator are then used to evaluate the previously defined cumulative hedging error(CHE). The back-testing results show that in general, smaller cumulative hedging error for real equity market data is achieved by the proposed hedging error minimization method, compared with traditional estimation methods.
| Author | : Panagiōtēs Ch Andreou |
| Publisher | : |
| Total Pages | : 261 |
| Release | : 2008 |
| Genre | : Hedging (Finance) |
| ISBN | : |
| Author | : Toby Daglish |
| Publisher | : |
| Total Pages | : |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
This article investigates the extent to which options on the Australian Stock Price Index can be explained by parametric and nonparametric option pricing techniques. In particular, comparisons are made of out-of-sample option pricing performance and hedging performance. The dataset differs from many of those used previously in the empirical options pricing literature in that it consists of American options. In addition, a broader spectrum of techniques are considered: a spline-based nonparametric technique is considered in addition to the standard kernel techniques, while the performance of a Heston stochastic volatility model is also considered. Although some evidence is found of superior performance by nonparametric techniques for in-sample pricing, the parametric methods exhibit a markedly better ability to explain future prices and show superior hedging performance.
| Author | : Andrew P. Carverhill |
| Publisher | : |
| Total Pages | : 17 |
| Release | : 2003 |
| Genre | : |
| ISBN | : |
Since its introduction in 1973, the Black-Scholes model has found increasingly more resistance in application. In order to use Black-Scholes to price any option, one needs to know the implied volatility surface. The existence of such surface is an evidence of misspecification of the model. In this case, the problem is with the assumption of a geometric Brownian motion for the stock price process. There is strong empirical evidence that stocks do not follow such process. However, no agreement has been reached on what is the best distribution to use.Neural Network approaches the problem very differently. Essentially, a Neural Network is a non-parametric estimation technique. It does not make any distributional assumption regarding the underlying variable. Instead, it puts up a formula with a set of unknown parameters and let the optimization routine search for the parameters best fitted to the desired results. Hutchinson-Lo-Poggio (1994) showed that it is indeed possible to use a Neural Network to price Samp;P futures options. In this paper, we will continue with this line of research. Specifically, we will examine the best way to set up and train a Neural Network for option pricing and hedging. We will also investigate if a Neural Network could produce better hedging parameters than the standard option pricing model. We use Samp;P futures options data covering the period 1990-2000.
| Author | : Jianqing Fan |
| Publisher | : |
| Total Pages | : 55 |
| Release | : 2009 |
| Genre | : |
| ISBN | : |
Parametric option pricing models are largely used in Finance. These models capture several features of asset price dynamics. However, their pricing performance can be significantly enhanced when they are combined with nonparametric learning approaches that learn and correct empirically the pricing errors. In this paper, we propose a new nonparametric method for pricing derivatives assets. Our method relies on the state price distribution instead of the state price density because the former is easier to estimate nonparametrically than the latter. A parametric model is used as an initial estimate of the state price distribution. Then the pricing errors induced by the parametric model are fitted nonparametrically. This model-guided method estimates the state price distribution nonparametrically and is called Automatic Correction of Errors (ACE). The method is easy to implement and can be combined with any model-based pricing formula to correct the systematic biases of pricing errors. We also develop a nonparametric test based on the generalized likelihood ratio to document the efficacy of the ACE method. Empirical studies based on Samp;P 500 index options show that our method outperforms several competing pricing models in terms of predictive and hedging abilities.
| Author | : Godfrey Smith |
| Publisher | : |
| Total Pages | : 15 |
| Release | : 2013 |
| Genre | : |
| ISBN | : |
We test the accuracy and hedging performance of the deltas given by a range of nonparametric measure changes. The nonparametric models accurately estimate deltas across a number of asset price dynamics. The optimal nonparametric measure change displays superior estimation bias, which depends on how the models capture the stylised features of the dynamics, moneyness, and time-to-expiry. Differences in estimation error appear negligible. The optimal measure change produces superior static hedging outcomes compared to the Black-Scholes model. Differences in dynamic hedging outcomes are negligible.
| Author | : Jussi Klemelä |
| Publisher | : John Wiley & Sons |
| Total Pages | : 849 |
| Release | : 2018-02-28 |
| Genre | : Mathematics |
| ISBN | : 1119409128 |
An Introduction to Machine Learning in Finance, With Mathematical Background, Data Visualization, and R Nonparametric function estimation is an important part of machine learning, which is becoming increasingly important in quantitative finance. Nonparametric Finance provides graduate students and finance professionals with a foundation in nonparametric function estimation and the underlying mathematics. Combining practical applications, mathematically rigorous presentation, and statistical data analysis into a single volume, this book presents detailed instruction in discrete chapters that allow readers to dip in as needed without reading from beginning to end. Coverage includes statistical finance, risk management, portfolio management, and securities pricing to provide a practical knowledge base, and the introductory chapter introduces basic finance concepts for readers with a strictly mathematical background. Economic significance is emphasized over statistical significance throughout, and R code is provided to help readers reproduce the research, computations, and figures being discussed. Strong graphical content clarifies the methods and demonstrates essential visualization techniques, while deep mathematical and statistical insight backs up practical applications. Written for the leading edge of finance, Nonparametric Finance: • Introduces basic statistical finance concepts, including univariate and multivariate data analysis, time series analysis, and prediction • Provides risk management guidance through volatility prediction, quantiles, and value-at-risk • Examines portfolio theory, performance measurement, Markowitz portfolios, dynamic portfolio selection, and more • Discusses fundamental theorems of asset pricing, Black-Scholes pricing and hedging, quadratic pricing and hedging, option portfolios, interest rate derivatives, and other asset pricing principles • Provides supplementary R code and numerous graphics to reinforce complex content Nonparametric function estimation has received little attention in the context of risk management and option pricing, despite its useful applications and benefits. This book provides the essential background and practical knowledge needed to take full advantage of these little-used methods, and turn them into real-world advantage. Jussi Klemelä, PhD, is Adjunct Professor at the University of Oulu. His research interests include nonparametric function estimation, density estimation, and data visualization. He is the author of Smoothing of Multivariate Data: Density Estimation and Visualization and Multivariate Nonparametric Regression and Visualization: With R and Applications to Finance.
| Author | : Cira Perna |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 212 |
| Release | : 2007-12-12 |
| Genre | : Business & Economics |
| ISBN | : 8847007046 |
The interaction between mathematicians and statisticians reveals to be an effective approach to the analysis of insurance and financial problems, in particular in an operative perspective. The Maf2006 conference, held at the University of Salerno in 2006, had precisely this purpose and the collection published here gathers some of the papers presented at the conference and successively worked out to this aim. They cover a wide variety of subjects in insurance and financial fields.
| Author | : Jussi Klemelä |
| Publisher | : John Wiley & Sons |
| Total Pages | : 681 |
| Release | : 2018-03-13 |
| Genre | : Mathematics |
| ISBN | : 1119409101 |
An Introduction to Machine Learning in Finance, With Mathematical Background, Data Visualization, and R Nonparametric function estimation is an important part of machine learning, which is becoming increasingly important in quantitative finance. Nonparametric Finance provides graduate students and finance professionals with a foundation in nonparametric function estimation and the underlying mathematics. Combining practical applications, mathematically rigorous presentation, and statistical data analysis into a single volume, this book presents detailed instruction in discrete chapters that allow readers to dip in as needed without reading from beginning to end. Coverage includes statistical finance, risk management, portfolio management, and securities pricing to provide a practical knowledge base, and the introductory chapter introduces basic finance concepts for readers with a strictly mathematical background. Economic significance is emphasized over statistical significance throughout, and R code is provided to help readers reproduce the research, computations, and figures being discussed. Strong graphical content clarifies the methods and demonstrates essential visualization techniques, while deep mathematical and statistical insight backs up practical applications. Written for the leading edge of finance, Nonparametric Finance: • Introduces basic statistical finance concepts, including univariate and multivariate data analysis, time series analysis, and prediction • Provides risk management guidance through volatility prediction, quantiles, and value-at-risk • Examines portfolio theory, performance measurement, Markowitz portfolios, dynamic portfolio selection, and more • Discusses fundamental theorems of asset pricing, Black-Scholes pricing and hedging, quadratic pricing and hedging, option portfolios, interest rate derivatives, and other asset pricing principles • Provides supplementary R code and numerous graphics to reinforce complex content Nonparametric function estimation has received little attention in the context of risk management and option pricing, despite its useful applications and benefits. This book provides the essential background and practical knowledge needed to take full advantage of these little-used methods, and turn them into real-world advantage. Jussi Klemelä, PhD, is Adjunct Professor at the University of Oulu. His research interests include nonparametric function estimation, density estimation, and data visualization. He is the author of Smoothing of Multivariate Data: Density Estimation and Visualization and Multivariate Nonparametric Regression and Visualization: With R and Applications to Finance.
| Author | : Dan Chen |
| Publisher | : |
| Total Pages | : |
| Release | : 2011 |
| Genre | : |
| ISBN | : |
The thesis focuses on valuation and hedging problems when the market is incomplete. The first essay considers the quadratic hedging strategy. We propose a generalized quadratic hedging strategy which can balance a short-term risk (additional cost) with a long-term risk (hedging errors). The traditional quadratic hedging strategies, i.e. self-financing strategy and risk-minimization strategy, can be seen as special cases of the generalized quadratic hedging strategy. This is applied to the insurance derivatives market. The second essay compares parametric and nonparametric measure-changing techniques. The essay discusses three pricing approaches: pricing via Esscher measure, via calibration and via nonparametric risk-neutral density; and empirically compares the performance of the three approaches in the metal futures markets. The last essay establishes the concept of stochastic volatility of volatility and proposes several estimation methods.
