Pricing Long-term Options with Stochastic Volatility and Stochastic Interest Rates PDF Download
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Author: Alexander van Haastrecht
Publisher:
ISBN: 9789085705208
Category :
Languages : en
Pages : 231
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Book Description
Author: Alexander van Haastrecht
Publisher:
ISBN: 9789085705208
Category :
Languages : en
Pages : 231
Get Book Here
Book Description
Author: Zhiwu Chen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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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.
Author: Olivier Ledoit
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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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.
Author:
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ISBN:
Category :
Languages : un
Pages :
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Author: Jannick B. G. Schreiner
Publisher:
ISBN:
Category :
Languages : en
Pages : 71
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Author: George J. Jiang
Publisher:
ISBN:
Category :
Languages : en
Pages : 39
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Author: George J. Jiang
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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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.
Author: Alexander van Haastrecht
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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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: Vitor Cepelowicz
Publisher:
ISBN:
Category : Interest rate futures
Languages : en
Pages : 214
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Author: Marc Sáez
Publisher:
ISBN:
Category : Options (Finance)
Languages : en
Pages : 29
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