Generic Pricing Of Fx Inflation And Stock Options Under Stochastic Interest Rates And Stochastic Volatility
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Author | : Alexander van Haastrecht |
Publisher | : |
Total Pages | : 45 |
Release | : 2009 |
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Download Generic Pricing of FX, Inflation and Stock Options Under Stochastic Interest Rates and Stochastic Volatility Book in PDF, Epub and Kindle
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.
Author | : George J. Jiang |
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Total Pages | : 62 |
Release | : 1998 |
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Download Pricing Stock Options Under Stochastic Volatility and Stochastic Interest Rates with Efficient Method of Moments Estimation Book in PDF, Epub and Kindle
Author | : Alexander van Haastrecht |
Publisher | : |
Total Pages | : 28 |
Release | : 2011 |
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Download Pricing Long-Maturity Equity and FX Derivatives with Stochastic Interest Rates and Stochastic Volatility Book in PDF, Epub and Kindle
In this paper we extend the stochastic volatility model of Schouml;bel and Zhu (1999) by including stochastic interest rates. Furthermore we allow all driving model factors to be instantaneously correlated with each other, i.e. we allow for a correlation between the instantaneous interest rates, the volatilities and the underlying stock returns. By deriving the characteristic function of the log-asset price distribution, we are able to price European stock options in closed-form by Fourier inversion. Furthermore we present a Foreign Exchange generalization and show how the pricing of Forward-starting options like cliquets can be performed. Additionally we discuss the practical implementation of these new models.
Author | : Jannick B. G. Schreiner |
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Total Pages | : 71 |
Release | : 2012 |
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Download Pricing American Options Under Stochastic Volatility and Stochastic Interest Rates Book in PDF, Epub and Kindle
Author | : George J. Jiang |
Publisher | : |
Total Pages | : 48 |
Release | : 1999 |
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Download Pricing Stock Options Under Stochastic Volatility and Interest Rates with Efficient Method of Moments Estimation Book in PDF, Epub and Kindle
Author | : Alexey Medvedev |
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Total Pages | : 48 |
Release | : 2007 |
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Download Pricing American Options Under Stochastic Volatility and Stochastic Interest Rates Book in PDF, Epub and Kindle
Author | : Marc Sáez |
Publisher | : |
Total Pages | : 29 |
Release | : 1995 |
Genre | : Options (Finance) |
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Download Option Pricing Under Stochastic Volatility and Stochastic Interest Rate in the Spanish Case Book in PDF, Epub and Kindle
Author | : Marc Sáez i Zafra |
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Total Pages | : |
Release | : 1995 |
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Download Option Pricing Under Stochastic Volatility and Stochastic Interest Rate in the Spanish Case Book in PDF, Epub and Kindle
Author | : Olivier Ledoit |
Publisher | : |
Total Pages | : 11 |
Release | : 1998 |
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Download Relative Pricing of Options with Stochastic Volatility Book in PDF, Epub and Kindle
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.
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Total Pages | : |
Release | : 2000 |
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Download Index option pricing models with stochastic volatility and stochastic interest rates Book in PDF, Epub and Kindle