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Author: Qiang Luo Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
In this paper, a closed-form analytical solution of option price under the Bi-Heston model is derived. Through empirical analysis, the advantages and disadvantages of the parametric pricing model are compared and analysed with those of the non-parametric model. The analysis shows that: (1) the parametric pricing model significantly outperforms the machine learning model in terms of in-sample pricing effects, while the Bi-Heston model slightly outperforms the Heston model. (2) In terms of out-of-sample pricing, the machine learning model is inferior to the parametric model for call options, while the Bi-Heston model is significantly better than the other two models for put options, and the other two models are similar. (3) In the robustness analysis of the three pricing models, the machine learning model shows strong instability, while the Bi-Heston model shows a more stable side.
Author: Qiang Luo Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
In this paper, a closed-form analytical solution of option price under the Bi-Heston model is derived. Through empirical analysis, the advantages and disadvantages of the parametric pricing model are compared and analysed with those of the non-parametric model. The analysis shows that: (1) the parametric pricing model significantly outperforms the machine learning model in terms of in-sample pricing effects, while the Bi-Heston model slightly outperforms the Heston model. (2) In terms of out-of-sample pricing, the machine learning model is inferior to the parametric model for call options, while the Bi-Heston model is significantly better than the other two models for put options, and the other two models are similar. (3) In the robustness analysis of the three pricing models, the machine learning model shows strong instability, while the Bi-Heston model shows a more stable side.
Author: Jianqing Fan Publisher: ISBN: Category : Languages : en Pages : 55
Book Description
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: Wolfgang Karl Härdle Publisher: Springer Science & Business Media ISBN: 364217146X Category : Mathematics Languages : en Pages : 317
Book Description
The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.
Author: Xiaoyi Chen Publisher: ISBN: Category : Hedging (Finance) Languages : en Pages : 108
Book Description
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: Cheng Few Lee Publisher: World Scientific ISBN: 9811202400 Category : Business & Economics Languages : en Pages : 5053
Book Description
This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.
Author: Daniel Alexandre Bloch Publisher: ISBN: Category : Languages : en Pages : 49
Book Description
An option pricing model is tied to its ability of capturing the dynamics of the underlying spot price process. Its misspecification will lead to pricing and hedging errors. Parametric pricing formula depends on the particular form of the dynamics of the underlying asset. For tractability reasons, some assumptions are made which are not consistent with the multifractal properties of market returns. On the other hand, non-parametric models such as neural networks use market data to estimate the implicit stochastic process driving the spot price and its relationship with contingent claims. When pricing multidimensional contingent claims, or even vanilla options with complex models, one must rely on numerical methods such as partial differential equations, numerical integration methods such as Fourier methods, or Monte Carlo simulations. Further, when calibrating financial models on market prices, a large number of model prices must be generated to fit the model parameters. Thus, one requires highly efficient computation methods which are fast and accurate. Neural networks with multiple hidden layers are universal interpolators with the ability of representing any smooth multidimentional function. As such, supervised learning is concerned with solving function estimation problems. The networks are decomposed into two separate phases, a training phase where the model is optimised off-line, and a testing phase where the model approximates the solution on-line. As a result, these methods can be used in finance in a fast and robust way for pricing exotic options as well as calibrating option prices in view of interpolating/extrapolating the volatility surface. They can also be used in risk management to fit options prices at the portfolio level in view of performing some credit risk analysis. We review some of the existing methods using neural networks for pricing market and model prices, present calibration, and introduce exotic option pricing. We discuss the feasibility of these methods, highlight problems, and propose alternative solutions.
Author: Tobias Herwig Publisher: Taylor & Francis ISBN: 9783540308379 Category : Business & Economics Languages : en Pages : 120
Book Description
The focus of this volume is on the development of new approaches for the market-conform valuation of newly issued derivatives. The first chapter presents a flexible approach to construct the binomial process of the underlying asset price by using a simultaneously backward and forward induction algorithm. This framework can be used to price and hedge a wide range of plain-vanilla and exotic options. In the second chapter this new approach is compared to existing models using a sample of plain-vanilla options, American call options and European Barrier options from two competing markets. In the third chapter new methods to value American-style options via Monte Carlo simulations in accordance with given market prices are discussed. After a short introduction to Monte Carlo methods, two new approaches are proposed. These new frameworks are illustrated via pricing examples for standard American put options.
Author: Michael J. Stutzer Publisher: ISBN: Category : Languages : en Pages :
Book Description
When used to price popular bond futures options, the Black model is subject to a moneyness bias similar to the Black-Scholes stock index option bias. It is shown that a suitably modified version of Stutzer's canonical stock option pricing model (Stutzer, J.Finance, 1996, 1633-52 ) also helps explain the former bias. This paper further extends the entropic approach to asset pricing theory and estimation developed in the aforementioned paper, in J.Econometrics, 1995, 367-97 and in Econometrica, 1997, 861-74.
Author: Qiang Luo
Author: Qiang Luo
Author: Jianqing Fan
Author: Ta-Peng Wu
Author: Wolfgang Karl Härdle
Author: Xiaoyi Chen
Author: Cheng Few Lee
Author: Wentao Yan
Author: Daniel Alexandre Bloch
Author: Tobias Herwig
Author: Michael J. Stutzer