Pricing Long Term Options With Stochastic Volatility And Stochastic Interest Rates
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Pricing Long Term Options With Stochastic Volatility And Stochastic Interest Rates
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Author : Alexander van Haastrecht
language : en
Publisher:
Release Date : 2010
Pricing Long Term Options With Stochastic Volatility And Stochastic Interest Rates written by Alexander van Haastrecht and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Pricing And Hedging Long Term Options
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Author : Zhiwu Chen
language : en
Publisher:
Release Date : 2000
Pricing And Hedging Long Term Options written by Zhiwu Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
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.
Generic Pricing Of Fx Inflation And Stock Options Under Stochastic Interest Rates And Stochastic Volatility
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Author : Alexander van Haastrecht
language : en
Publisher:
Release Date : 2009
Generic Pricing Of Fx Inflation And Stock Options Under Stochastic Interest Rates And Stochastic Volatility written by Alexander van Haastrecht and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
We consider the pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility, for which we use a generic multi-currency framework. We allow for a general correlation structure between the drivers of the volatility, the inflation index, the domestic (nominal) and the foreign (real) rates. Having the flexibility to correlate the underlying FX/Inflation/Stock index with both stochastic volatility and stochastic interest rates yields a realistic model, which is of practical importance for the pricing and hedging of options with a long-term exposure. We derive explicit valuation formulas for various securities, such as vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. These vanilla derivatives can be valued in closed-form under Schobel and Zhu (1999) stochastic volatility, whereas we devise an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston (1993) model. Finally, we numerical investigate the quality of this approximation and consider a calibration example to FX market data.
Relative Pricing Of Options With Stochastic Volatility
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Author : Olivier Ledoit
language : en
Publisher:
Release Date : 1998
Relative Pricing Of Options With Stochastic Volatility written by Olivier Ledoit and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
This paper offers a new approach for pricing options on assets with stochastic volatility. We start by constructing the quot;surfacequot; of Black-Scholes implied volatilities for (readily observable) liquid, European call options with varying strike prices and maturities. Then, we show that the implied volatility of an at-the-money call option with time-to-maturity going tozero is equal to the underlying asset's instantaneous (stochastic) volatility. We then model the stochastic processes followed by the implied volatilities of options of all maturities and strike prices jointly with the stock price, and find a no-arbitrage condition that their drift must satisfy. Finally, we use the resulting arbitrage-free joint process for the stock price and its volatility to price other derivatives, such as standard but illiquid options as well as exotic options using numerical methods. The great advantage of our approach is that, when pricing these other derivatives, we are secure in the knowledge that the model values the hedging instruments - namely the stock and the simple, liquid options - consistently with the market. Our approach can easily be extended to allow for stochastic interest rates and a stochastic dividend yield, which may be particularly relevant to the pricing of currency and commodity options. We can also extend our model to price bond options when the term structure of interest rates has stochastic volatility.
A Model Incorporating Stochastic Volatility For Pricing Options On Interest Rate Caps
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Author : Vitor Cepelowicz
language : en
Publisher:
Release Date : 1994
A Model Incorporating Stochastic Volatility For Pricing Options On Interest Rate Caps written by Vitor Cepelowicz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Interest rate futures categories.
Index Option Pricing Models With Stochastic Volatility And Stochastic Interest Rates
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Author :
language : un
Publisher:
Release Date : 2000
Index Option Pricing Models With Stochastic Volatility And Stochastic Interest Rates written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Index Option Pricing Models With Stochastic Volatility And Stochastic Interest Rates
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Author : George J. Jiang
language : en
Publisher:
Release Date : 2013
Index Option Pricing Models With Stochastic Volatility And Stochastic Interest Rates written by George J. Jiang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
This paper specifies a multivariate stochastic volatility (SV) model for the Samp;P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric Samp;P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premium of stochastic volatility to gauge each model?s performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or quot;leverage effectquot; does help to explain the skewness of the volatility 'smile', allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino amp; Turnbull (1990), our empirical findings strongly suggest the existence of a non zero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information from the options market in pricing options. Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficient in modeling short-term kurtosis of asset returns, an SV model with fatter-tailed noise or jump component may have better explanatory power.
Index Option Pricing Models With Stochastic Volatility And Stochastic Interest Rates
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Author : George J. Jiang
language : en
Publisher:
Release Date : 2000
Index Option Pricing Models With Stochastic Volatility And Stochastic Interest Rates written by George J. Jiang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Pricing American Options Under Stochastic Volatility And Stochastic Interest Rates
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Author : Jannick B. G. Schreiner
language : en
Publisher:
Release Date : 2012
Pricing American Options Under Stochastic Volatility And Stochastic Interest Rates written by Jannick B. G. Schreiner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Option Pricing With Long Memory Stochastic Volatility Models
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Author : Zhigang Tong
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2013
Option Pricing With Long Memory Stochastic Volatility Models written by Zhigang Tong and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
It is now known that long memory stochastic volatility models can capture the well-documented evidence of volatility persistence. However, due to the complex structures of the long memory processes, the analytical formulas for option prices are not available yet. In this book, we propose two fractional continuous time stochastic volatility models which are built on the popular short memory stochastic volatility models. Using the tools from stochastic calculus, fractional calculus and Fourier transform, we derive the (approximate) analytical solutions for option prices. We also numerically study the effects of long memory on option prices. We show that the fractional integration parameter has the opposite effect to that of volatility of volatility parameter. We also find that long memory models can accommodate the short term options and the decay of volatility skew better than the corresponding short memory models. These findings would appeal to the researchers and practitioners in the areas of quantitative finance.