Implied Volatility and Option Pricing Models

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Title: Implied Volatility and Option Pricing Models
Author: Huang, Kun
Contributor: Svenska handelshögskolan, institutionen för finansiell ekonomi och ekonomisk statistik, finansiell ekonomi
Hanken School of Economics, Department of Finance and Statistics, Finance
Belongs to series: Economics and Society – 326
ISSN: 0424-7256 (printed)
2242-699X (PDF)
ISBN: 978-952-232-378-1 (printed)
978-952-232-379-8 (PDF)
Abstract: Since the stock market crash of October 1987, extensive research has been carried out on modelling implied volatility for option pricing. The three essays of this thesis investigate how to generate arbitrage-free and smile-consistent implied volatility using various option pricing models. The first essay studies the efficiency of the Vanna-Volga method in equity options markets. The Vanna-Volga method is commonly used in the FX options market to manage implied volatility surface and hedge against the movement of underlying asset prices. However, this method has not attracted much attention in other derivative markets. Apart from the Vanna-Volga method, the accuracy of two approximations of Vanna-Volga implied volatility are also examined. The compelling numerical results provide evidence to support the efficiency of the Vanna-Volga method and two approximations for building a smile-consistent implied volatility of the equity index option. The second essay studies the Heston (1993) model, which is the most successful stochastic volatility model, in a local volatility context. The hybrid model combines the advantages of the local volatility and stochastic volatility models, and minimizes their downsides by incorporating a leverage function which reflects the weights of local and stochastic volatility. The challenge for implementing the hybrid model is the computation of the leverage function. The study results convince us of the better performance of the hybrid model than the pure Heston model. In recent years, the negative interest rate has become a feature of financial markets. The negative interest rate spawns serious problems for financial modelling, particularly for option pricing and hedging in interest rate derivative markets. The benchmark model for pricing and hedging interest rate derivatives was Hagan's asymptotic expansion of implied volatility which is built under the SABR process. However, the weakness of Hagan's asymptotic expansion came to light in the case of negative interest rates. The third essay explores a different asymptotic formula of implied volatility under the SABR process, and the model was proposed in De Marco, Hillairet and Jacquire (2013). The numerical results show the accuracy of the model, particularly for large maturities and small strikes when the CEV component is close to zero and when the volatility of volatility is high.
Date: 2019-02-08
Subject: Option Pricing
Model Calibration
Arbitrage-free Implied Volatility
Stochastic Process
Stochastic Volatility
Local Volatility
Stochastic Local Volatility
Fourier-cosine series expansion

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