Author: Yannis TheodorakakosPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
On Alternative Option Pricing Models and the Effects of Modelling Volatility Within a Stochastic Context as Observed in FTSE-100 Index Options
Author: Yannis TheodorakakosAn Empirical Comparison of Alternative Stochastic Volatility Option Pricing Models
Author: Tiezhu GaoPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
In this thesis, I empirically compare the pricing performance of three classes of stochastic volatility option pricing models and the traditional Black-Scholes (1973) model in the pricing of S & P Canada 60 Index Options. The stochastic volatility models that I study are as follows: (1) the ad hoc Black and Scholes (1973) procedure that fits the implied volatility surface, (2) Madan et al.'s (1998) variance gamma model, and (3) Heston's (1993) continuous-time stochastic volatility model. I find that Heston's continuous-time stochastic volatility model outperforms the other models in terms of in-sample pricing and out-of-sample pricing. Second, the addition of the stochastic volatility term to the stochastic volatility model and variance gamma model does not resolve the "volatility smiles" effects, but it reduces the effects. Third, the Black-Scholes model performs adequately in pricing options, with the advantage of simplicity, although it suffers from the shortcoming of the "volatility smiles" effect. Finally, although it includes more parameters, the ad hoc Black and Scholes model does not perform as well as expected.
Application of Stochastic Volatility Models in Option Pricing
Author: Pascal DebusPublisher: GRIN Verlag
ISBN: 3656491941
Category : Business & Economics
Languages : de
Pages : 59
Book Description
Bachelorarbeit aus dem Jahr 2010 im Fachbereich BWL - Investition und Finanzierung, Note: 1,2, EBS Universität für Wirtschaft und Recht, Sprache: Deutsch, Abstract: The Black-Scholes (or Black-Scholes-Merton) Model has become the standard model for the pricing of options and can surely be seen as one of the main reasons for the growth of the derivative market after the model ́s introduction in 1973. As a consequence, the inventors of the model, Robert Merton, Myron Scholes, and without doubt also Fischer Black, if he had not died in 1995, were awarded the Nobel prize for economics in 1997. The model, however, makes some strict assumptions that must hold true for accurate pricing of an option. The most important one is constant volatility, whereas empirical evidence shows that volatility is heteroscedastic. This leads to increased mispricing of options especially in the case of out of the money options as well as to a phenomenon known as volatility smile. As a consequence, researchers introduced various approaches to expand the model by allowing the volatility to be non-constant and to follow a sto-chastic process. It is the objective of this thesis to investigate if the pricing accuracy of the Black-Scholes model can be significantly improved by applying a stochastic volatility model.
Empirical Performance of Option Pricing Models with Stochastic Local Volatility
Author: Greg OrosiPublisher:
ISBN:
Category :
Languages : en
Pages : 16
Book Description
We examine the empirical performance of several stochastic local volatility models that are the extensions of the Heston stochastic volatility model. Our results indicate that the stochastic volatility model with quadratic local volatility significantly outperforms the stochastic volatility model with CEV type local volatility. Moreover, we compare the performance of these models to several other benchmarks and find that the quadratic local volatility model compares well to the best performing option pricing models reported in the current literature for European-style S&P500 index options. Our results also indicate that the model with quadratic local volatility reproduces the characteristics of the implied volatility surface more accurately than the Heston model. Finally, we demonstrate that capturing the shape of the implied volatility surface is necessary to price binary options accurately.
The Empirical Performance of the Stochastic Volatility Model in Pricing FTSE-100 Index Options
Author: Krisda PhatcharoenThe Black-Scholes and Heston Models for Option Pricing
Author: Ziqun YePublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Stochastic volatility models on option pricing have received much study following the discovery of the non-at implied surface following the crash of the stock markets in 1987. The most widely used stochastic volatility model is introduced by Heston (1993) because of its ability to generate volatility satisfying the market observations, being non-negative and mean-reverting, and also providing a closed-form solution for the European options. However, little research has been done on Heston model used to price early-exercise options. This presumably is largely due to the absence of a closed-form solution and the increase in computational requirement that complicates the required calibration exercise. This thesis examines the performance of the Heston model versus the Black-Scholes model for the American Style equity option of Microsoft and the index option of S&P 100 index. We employ a finite difference method combined with a Projected Successive Over-relaxation method for pricing an American put option under the Black-Scholes model, while an Alternating Direction Implicit method is utilized to decompose a multi-dimensional partial differential equation into several one dimensional steps under the Heston model. For the calibration of the Heston model, we apply a two step procedure where in the first step we apply an indirect inference method to historical stock prices to estimate diffusion parameters under a probability measure and then use a least squares method to estimate the instantaneous volatility and the market risk premium which are used to switch from working under the probability measure to working under the risk-neutral measure. We find that option price is positively related with the value of the mean reverting speed and the long-term variance. It is not sensitive to the market price of risk and it is negatively related with the risk free rate and the volatility of volatility. By comparing the European put option and the American put option under the Heston model, we observe that their implied volatility generally follow similar patterns. However, there are still some interesting observations that can be made from the comparison of the two put options. First, for the out-of-the-money category, the American and European options have rather comparable implied volatilities with the American options' implied volatility being slightly bigger than the European options. While for the in-the-money category, the implied volatility of the European options is notably higher than the American options and its value exceeds the implied volatility of the American options. We also assess the performance of the Heston model by comparing its result with the result from the Black-Scholes model. We observe that overall the Heston model performs better than the Black-Scholes model. In particular, the Heston model has tendency of underpricing the in-the-money option and overpricing the out-of-the-money option. Whereas, the Black-Scholes model is inclined to underprice both the in-the-money option and the out-of-the-money option.b.
Applicability of Options Pricing Models
Author: Vipul Kumar SinghPublisher: LAP Lambert Academic Publishing
ISBN: 9783659392955
Category :
Languages : en
Pages : 188
Book Description
Rigorous efforts are being made since the four decades to root out the problem of pricing options with non-constant volatility. The suggested models can be positively categorized into deterministic volatility models and stochastic volatility models. In most of the cases of the previous researches on this issue have been tried with comparing and contrasting Black-Scholes model against the various models crafted by the researches. This book, in this way sounds unique because for the first time the various models of option pricing have directly been analyzed upon the live data of S&P CNX Nifty index options procured right from the market.This book is only a foundation stone which just gives a direction to proceed and find out innumerable opportunities to explore which will definitely be a better designed volatility model to forecast and predict a future course of investments by shielding and safeguarding it. Objective of this book is to postulate a reason why market prices display pricing biases and to examine whether an alternative framework of deterministic and stochastic models can whether give a price similar to those quoted in the market.
Are Classical Option Pricing Models Consistent with Observed Option Second-Order Moments? Evidence from High-Frequency Data
Author: Francesco AudrinoPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
As a means of validating an option pricing model, we compare the ex-post intra-day realized variance of options with the realized variance of the associated underlying asset that would be implied using assumptions as in the Black and Scholes (BS) model, the Heston and the Bates model. Based on data for the S&P 500 index, we find that the BS model is strongly directionally biased due to the presence of stochastic volatility. The Heston model reduces the mismatch in realized variance between the two markets, but deviations are still significant. With the exception of short-dated options, we achieve best approximations after controlling for the presence of jumps in the underlying dynamics. Finally, we provide evidence that, although heavily biased, the realized variance based on the BS model contains relevant predictive information that can be exploited when option high-frequency data is not available.
Volatility Surface and Term Structure
Author: Kin Keung LaiPublisher: Routledge
ISBN: 1135006989
Category : Business & Economics
Languages : en
Pages : 113
Book Description
This book provides different financial models based on options to predict underlying asset price and design the risk hedging strategies. Authors of the book have made theoretical innovation to these models to enable the models to be applicable to real market. The book also introduces risk management and hedging strategies based on different criterions. These strategies provide practical guide for real option trading. This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market. This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.
Author: Yueh-Neng Lin