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Implied Volatility Functions

Implied Volatility Functions
Author: Bernard Dumas
Publisher:
Total Pages: 34
Release: 1996
Genre: Options (Finance)
ISBN:
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Abstract: Black and Scholes (1973) implied volatilities tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black-Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset's return is a deterministic function of the asset price and time and develop the deterministic volatility function (DVF) option valuation model, which has the potential of fitting the observed cross-section of option prices exactly. Using a sample of S & P 500 index options during the period June 1988 through December 1993, we evaluate the economic significance of the implied deterministic volatility function by examining the predictive and hedging performance of the DV option valuation model. We find that its performance is worse than that of an ad hoc Black-Scholes model with variable implied volatilities.

Implied Volatility Functions

Implied Volatility Functions
Author: Joshua V. Rosenberg
Publisher:
Total Pages: 21
Release: 2008
Genre:
ISBN:
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Dumas, Fleming, Whaley (DFW, 1998) find that option models based on deterministic volatility functions (DVF) perform poorly because the estimated volatility function is unstable over time. DFW provide evidence that the DVF changes significantly on a weekly basis. This paper proposes a new class of dynamic implied volatility function models (DIVF). This classof models separates a time-invariant implied volatility function from the stochastic state variables that drive changes in the individual implied volatilities. The dynamics of the state variables are modeled explicitly. This framework facilitates consistent pricing and hedging with time-variation in the implied volatility function (IVF). In tests conducted using the full history of Samp;P500 futures option prices, the DIVF model is found to substantially improve pricing performance compared to static implied volatility function models and benchmark pricing models such as Black and Scholes (1973).

Implied Volatility Functions

Implied Volatility Functions
Author: Joshua Rosenberg
Publisher:
Total Pages: 14
Release: 1999
Genre: Options (Finance)
ISBN:
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Implied Volatility Functions

Implied Volatility Functions
Author: Veli-Matti Ahoranta
Publisher: LAP Lambert Academic Publishing
Total Pages: 72
Release: 2010-12
Genre:
ISBN: 9783843382328
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Evidences that there are volatility smiles and smirks in various financial markets suggest that Black and Scholes (1973) valuation formula is not completely valid. This thesis investigates implied volatility patterns and -functions on Finnish warrant market. The intention of the thesis is to find answers to the three following questions: what is the form of the volatility structure in Finnish warrant markets? Does there exist a better method to estimate volatilities than basic Black-Scholes constant volatility model? In case that there exist a superior method to estimate volatilities, is the method constantly best with every level of moneyness and time to expiration? To find answers to these questions a sample data is gathered from the year 2006 and then it is analysed by using statistical measurements. The analysis provides interesting findings about the existence of volatility structures in Finnish markets and it provides interesting insights to the Finnish warrant markets

Principles of Financial Engineering

Principles of Financial Engineering
Author: Robert Kosowski
Publisher: Academic Press
Total Pages: 893
Release: 2014-11-26
Genre: Business & Economics
ISBN: 0123870070
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Principles of Financial Engineering, Third Edition, is a highly acclaimed text on the fast-paced and complex subject of financial engineering. This updated edition describes the "engineering" elements of financial engineering instead of the mathematics underlying it. It shows how to use financial tools to accomplish a goal rather than describing the tools themselves. It lays emphasis on the engineering aspects of derivatives (how to create them) rather than their pricing (how they act) in relation to other instruments, the financial markets, and financial market practices. This volume explains ways to create financial tools and how the tools work together to achieve specific goals. Applications are illustrated using real-world examples. It presents three new chapters on financial engineering in topics ranging from commodity markets to financial engineering applications in hedge fund strategies, correlation swaps, structural models of default, capital structure arbitrage, contingent convertibles, and how to incorporate counterparty risk into derivatives pricing. Poised midway between intuition, actual events, and financial mathematics, this book can be used to solve problems in risk management, taxation, regulation, and above all, pricing. A solutions manual enhances the text by presenting additional cases and solutions to exercises. This latest edition of Principles of Financial Engineering is ideal for financial engineers, quantitative analysts in banks and investment houses, and other financial industry professionals. It is also highly recommended to graduate students in financial engineering and financial mathematics programs. The Third Edition presents three new chapters on financial engineering in commodity markets, financial engineering applications in hedge fund strategies, correlation swaps, structural models of default, capital structure arbitrage, contingent convertibles and how to incorporate counterparty risk into derivatives pricing, among other topics Additions, clarifications, and illustrations throughout the volume show these instruments at work instead of explaining how they should act The solutions manual enhances the text by presenting additional cases and solutions to exercises

The Volatility Sneer

The Volatility Sneer
Author: D. Clive Thompson
Publisher:
Total Pages: 64
Release: 1997
Genre:
ISBN:
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Heath, Jarrow and Morton Implied Volatility Functions and Conditional Heteroskedasticity Models

Heath, Jarrow and Morton Implied Volatility Functions and Conditional Heteroskedasticity Models
Author: Kaushik I. Amin
Publisher:
Total Pages:
Release: 1998
Genre:
ISBN:
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We evaluate various popular models of interest rate volatility and the Heath-Jarrow-Morton (HJM) approach to value interest rate derivatives by studying the information content and the forecast ability of HJM implied volatility in the Eurodollar futures options market. Implied volatility corresponding to the Ho-Lee, Courtadon, Cox-Ingersoll-Ross, Vasicek, and a linear proportional volatility model are examined within the HJM framework. The exercise compares these implied volatilities to a number of historical volatility benchmarks based on the GARCH model, the Glosten-Jagannathan-Runkle model, and several hybrid models combining the Cox-Ingersoll-Ross and Courtadon spot rate models and the GARCH and GJR approaches to model interest rate volatility. Our results show that there is a strong interaction effect between return shocks and the level of the interest rates in the volatility dynamics that none of the existing HJM volatility models and none of the GARCH type models can fully capture. Specifically, the impact of a shock to interest rate volatility is higher under a high interest rate than a low interest rate. The importance of implied volatility from the Ho-Lee, Courtadon, and Cox-Ingersoll-Ross models is significantly reduced after a term capturing the interaction effect is added to the volatility specification. The importance of implied volatility from the linear proportional and the Vasicek models is reduced but they can still explain a reasonably large portion of the time-variation in volatility.