Author: Tiezhu GaoPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
An Empirical Comparison of Alternative Stochastic Volatility Option Pricing Models
Author: Tiezhu GaoAn Empirical Comparison of Alternative Stochastic Volatility Models
Author: Michael BelledinAn Empirical Comparison of Alternative Option Pricing Models
Author: Ta-Peng WuPublisher:
ISBN:
Category : Options (Finance)
Languages : en
Pages : 298
Book Description
Empirical Performance of Alternative Option Pricing Models
Author: Zhiwu ChenPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Substantial progress has been made in extending the Black-Scholes model to incorporate such features as stochastic volatility, stochastic interest rates and jumps.On the empirical front, however, it is not yet known whether and by how much each generalized feature will improve option pricing and hedging performance. This paper fills this gap by first developing an implementable option model in closed form that allows volatility, interest rates and jumps to bestochastic and that is parsimonious in the number of parameters. The model includes many known ones as special cases. Delta-neutral and single-instrument minimum-variance hedging strategies are derived analytically. Using Samp;P 500 options, we examine a set of alternative models from three perspectives: (1) internal consistency of implied parameters/volatility with relevant time-series data, (2)out-of-sample pricing and (3) hedging performance. The models of focus include the benchmark Black-Scholes formula and the ones that respectively allow for (i) stochastic volatility, (ii) both stochastic volatility and stochastic interest rates, and (iii) stochastic volatility and jumps.Overall, incorporating both stochastic volatility and random jumps produces the best pricing performance and the most internally-consistent implied-volatility process. Its implied volatility does not quot;smilequot; across moneyness. But, for hedging, adding either jumps or stochastic interest rates does not seem to improve performance any further once stochastic volatility is taken into account.
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.
Empirical Performance Study of Alternative Option Pricing Models
Author: Sofiane AbouraPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The mispricing of the deep-in-the money and deep-out-the-money generated by the Black-Scholes (1973) model is now well documented in the literature. In this paper, we discuss different option valuation models on the basis of empirical tests carry out on the French option market. We examine methods that account for non-normal skewness and kurtosis, relax the martingale restriction, mix two log-normal distributions, and allows either for jump diffusion process or for stochastic volatility. We find that the use of a jump diffusion and stochastic volatility model performs as well as the inclusion of non normal skewness and kurtosis in terms of precision in the option valuation.Keywords : Implied Volatility, Stochastic Volatility Model, Jump Diffusion Model, Skewness, Kurtosis.
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.
Alternative Models of Stock Prices Dynamics
Author: Mikhail ChernovPublisher:
ISBN:
Category :
Languages : en
Pages : 38
Book Description
The purpose of this paper is to shed further light on the tensions that exist between the empirical fit of stochastic volatility (SV) models and their linkage to option pricing. A number of recent papers have investigated several specifications of one-factor SV diffusion models associated with option pricing models. The empirical failure of one-factor affine, Constant Elasticity of Variance (CEV), and one-factor log-linear SV models leaves us with two strategies to explore: (1) add a jump component to better fit the tail behavior or (2) add an additional (continuous path) factor where one factor controls the persistence in volatility and the second determines the tail behavior. Both have been partially pursued and our paper embarks on a more comprehensive examination which yields some rather surprising results. Adding a jump component to the basic Heston affine model is known to be a successful strategy as demonstrated by Andersen et al. (1999), Eraker et al. (1999), Chernov et al. (1999), and Pan (1999). Unfortunately, the presence of a jump component introduces quite a few unpleasant econometric issues. In addition, several financial issues, like hedging and risk factors become more complex. In this paper we show that a two-factor log-linear SV diffusion model (without jumps) appears to yield a remarkably good empirical fit. We estimate the model via the EMM procedure of Gallant and Tauchen (1996) which allows us to compare the non-nested log-linear SV diffusion with the affine jump specification. Obviously, there is one drawback to the log-linear SV models when it comes to pricing derivatives since no closed-form solutions are available. Against this cost weights the advantage of avoiding all the complexities involved with jump processes.
A Comparison of Stochastic Volatility Option Pricing Models
Author: Pricing and Hedging Long-Term Options
Author: Zhiwu ChenPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Recent empirical studies find that once an option pricing model has incorporated stochastic volatility, allowing interest rates to be stochastic does not improve pricing or hedging any further while adding random jumps to the modeling framework only helps the pricing of extremely short-term options but not the hedging performance. Given that only options of relatively short terms are used in existing studies, this paper addresses two related questions: Do long-term options contain different information than short-term options? If so, can long-term options better differentiate among alternative models? Our inquiry starts by first demonstrating analytically that differences among alternative models usually do not surface when applied to short term options, but do so when applied to long-term contracts. For instance, within a wide parameter range, the Arrow-Debreu state price densities implicit in different stochastic-volatility models coincide almost everywhere at the short horizon, but diverge at the long horizon. Using regular options (of less than a year to expiration) and LEAPS, both written on the Samp;P 500 index, we find that short- and long-term contracts indeed contain different information and impose distinct hurdles on any candidate option pricing model. While the data suggest that it is not as important to model stochastic interest rates or random jumps (beyond stochastic volatility) for pricing LEAPS, incorporating stochastic interest rates can nonetheless enhance hedging performance in certain cases involving long-term contracts.