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| Author | : Matthew James Lorig |
| Publisher | : |
| Total Pages | : 187 |
| Release | : 2011 |
| Genre | : |
| ISBN | : 9781124885568 |
1J.-P. Fouque, G. Papanicolaou, and R. Sircar, Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, 2000.
| Author | : Jean-Pierre Fouque |
| Publisher | : |
| Total Pages | : 22 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of European and path-dependent options in a fast mean-reverting stochastic volatility setting. Our method is shown to be equivalent to those developed in Fouque, Papanicolaou, and Sircar (2000), but has the advantage of being able to price options for which the methods of Fouque et.al. are unsuitable. In particular, we are able to price double-barrier options. To our knowledge, this is the first time that double-barrier options have been priced in a stochastic volatility setting in which the Brownian motions driving the stock and volatility are correlated.
| Author | : Jean-Pierre Fouque |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for European option prices. The resulting pricing formulas are semi-analytic, in the sense that they can be expressed as integrals. Difficulties associated with the numerical evaluation of these integrals are discussed, and techniques for avoiding these difficulties are provided. Overall, it is shown that computational complexity for our model is comparable to the case of a pure Heston model, but our correction brings significant flexibility in terms of fitting to the implied volatility surface. This is illustrated numerically and with option data.
| Author | : Kin Keung Lai |
| Publisher | : Routledge |
| Total Pages | : 102 |
| Release | : 2013-09-11 |
| Genre | : Business & Economics |
| ISBN | : 1135006997 |
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 | : Jean-Pierre Fouque |
| Publisher | : Cambridge University Press |
| Total Pages | : 222 |
| Release | : 2000-07-03 |
| Genre | : Business & Economics |
| ISBN | : 9780521791632 |
This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.
| Author | : Henrik Andersson |
| Publisher | : |
| Total Pages | : 45 |
| Release | : 2002 |
| Genre | : |
| ISBN | : |
In this paper we derive a closed form approximation to a stochastic volatility option-pricing model and propose a variant of EGARCH for parameter estimation. The model thereby provides a consistent approach to the problem of option pricing and parameter estimation. Using Swedish stocks, the model provides a good fit to the heteroscedasticity prevalent in the time-series. The stochastic volatility model also prices options on the underlying stock more accurately than the traditional Black-Scholes formula. This result holds for both historic and implied volatility. A large part of the volatility smile that is observed for options of different maturity and exercise prices is thereby explained.
| Author | : Hoi Ying Wong |
| Publisher | : |
| Total Pages | : 25 |
| Release | : 2009 |
| Genre | : |
| ISBN | : |
Many underlying assets of option contracts, such as currencies, commodities, energy, temperature and even some stocks, exhibit both mean reversion and stochastic volatility. This paper investigates the valuation of options when the underlying asset follows a mean-reverting lognormal process with stochastic volatility. A closed-form solution is derived for European options by means of Fourier transform. The proposed model allows the option pricing formula to capture both the term structure of futures prices and the market implied volatility smile within a unified framework. A bivariate trinomial lattice approach is introduced to value path-dependent options with the proposed model. Numerical examples using European options, American options and barrier options demonstrate the use of the model and the quality of the numerical scheme.
| Author | : Evashun Pillay |
| Publisher | : |
| Total Pages | : 115 |
| Release | : 2009 |
| Genre | : Dissertations, Academic |
| ISBN | : |
| Author | : Alan L. Lewis |
| Publisher | : |
| Total Pages | : 372 |
| Release | : 2000 |
| Genre | : Business & Economics |
| ISBN | : |
| Author | : Greg Orosi |
| Publisher | : |
| Total Pages | : 16 |
| Release | : 2014 |
| Genre | : |
| ISBN | : |
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.
