FORECASTS AND IMPLICATIONS USING VIX OPTIONS

This study examines the Chicago Board Option Exchange (CBOE) Volatility Index (VIX) which is the implied volatility calculated from short-term option prices on the Standards & Poor’s 500 stock index (S&P 500). Findings suggest VIX overestimates average volatility by approximately 3% but explains 55% of S&P 500’s proceeding month’s volatility. The implied volatility (IV) from options on the VIX add additional explanatory power for the S&P’s 500 proceeding kurtosis values (a measure of tail risk). The VIX option’s volatility smirks did not add additional explanatory power for explaining the S&P 500 volatility or kurtosis. A simple trading rule based on buying the S&P 500 whether the VIX, IV from the options on the VIX, and the VIX option’s volatility smirk decline over the preceding month results in an additional 0.96% return in the following month. However, this only occurs approximately 10% of the time and does not outperform a simple buy-and-hold strategy as the strategy has the investor out of the market the majority of the time

Currency option pricing with Wishart process

AbstractIt has been well-documented that foreign exchange rates exhibit both mean reversion and stochastic volatility. In addition to these, recent empirical evidence shows a stochastic skew of implied volatility surface from currency option data, which means that the slope of implied volatility curve of a given maturity is stochastically time varying. This paper develops a currency option pricing model which accommodates for this phenomena. The proposed model postulates that the log-currency value follows a mean reverting process with stochastic volatility driven by Wishart process under risk-neutral measure. Pricing formula for European currency option is derived in terms of Fourier Transform. Benchmarking against the Monte Carlo simulation, our numerical examples reveal that the pricing formula is accurate and remarkably efficient. The proposed model is also generalized to include jumps. The ability of the our model on capturing stochastic skew is illustrated through a numerical example

On the calibration of the 3/2 model

A

Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity

Firstly, we present a more general and realistic double-exponential jump model with stochastic volatility, interest rate, and jump intensity. Using Feynman-Kac formula, we obtain a partial integrodifferential equation (PIDE), with respect to the moment generating function of log underlying asset price, which exists an affine solution. Then, we employ the fast Fourier Transform (FFT) method to obtain the approximate numerical solution of a power option which is conveniently designed with different risks or prices. Finally, we find the FFT method to compute that our option price has better stability, higher accuracy, and faster speed, compared to Monte Carlo approach

Wavelet-based option pricing: An empirical study

In this paper, we adopt a wavelet-based option valuation model and empirically compare the pricing and forecasting performance of this model with that of the stochastic volatility model with jumps and the spline method. Both the in-sample valuation and out-of-sample forecasting accuracy are examined using daily index options in the UK, Germany, and Hong Kong from January 2009 to December 2012. Our results show that the wavelet-based model compares favorably with the other two models and that it provides an excellent alternative for valuing option prices. Its superior performance comes from the powerful ability of the wavelet method in approximating the risk-neutral moment-generating functions

Highly Efficient Shannon Wavelet-based Pricing of Power Options under the Double Exponential Jump Framework with Stochastic Jump Intensity and Volatility

We propose a highly efficient and accurate valuation method for exotic-style options based on the novel Shannon wavelet inverse Fourier technique (SWIFT). Specifically, we derive an efficient pricing methods for power options under a more realistic double exponential jump model with stochastic volatility and jump intensity. Inclusion of such innovations may accommodate for the various stylised facts observed in the prices of financial assets, and admits a more realistic pricing framework as a result. Following the derivation of our SWIFT pricing method for power options, we perform extensive numerical experiments to analyse both the method's accuracy and efficiency. In addition, we investigate the sensitivities in the resulting prices, as well as the inherent errors, to changes in the underlying market conditions. Our numerical results demonstrate that the SWIFT method is not only more efficient when benchmarked to its close competitors, such as the Fourier- cosine (COS) and the widely-acclaimed fast-Fourier transform (FFT) methods, but it is also robust across a range of different market conditions exhibiting exponential error convergence

Option pricing under the double exponential jump‐diffusion model with stochastic volatility and interest rate

This paper proposes an efficient option pricing model that incorporates stochastic interest rate (SIR), stochastic volatility (SV), and double exponential jump into the jump‐diffusion settings. The model comprehensively considers the leptokurtosis and heteroscedasticity of the underlying asset’s returns, rare events, and an SIR. Using the model, we deduce the pricing characteristic function and pricing formula of a European option. Then, we develop the Markov chain Monte Carlo method with latent variable to solve the problem of parameter estimation under the double exponential jump‐diffusion model with SIR and SV. For verification purposes, we conduct time efficiency analysis, goodness of fit analysis, and jump/drift term analysis of the proposed model. In addition, we compare the pricing accuracy of the proposed model with those of the Black–Scholes and the Kou (2002) models. The empirical results show that the proposed option pricing model has high time efficiency, and the goodness of fit and pricing accuracy are significantly higher than those of the other two models

Forecasting and pricing powers of option-implied tree models: Tranquil and volatile market conditions

The aims of this paper are twofold. First, to investigate the accuracy of different option-implied trees in pricing European options in order to assess the power of implied trees in replicating the market information. Second, to compare deterministic volatility implied trees and stochastic implied volatility models (Bakshi et al. (2003)) in assessing the forecasting power of implied moments on subsequently realised moments, and ascertaining the existence, magnitude and sign of variance, skewness, and kurtosis risk-premia. The analysis is carried out using the Italian daily market data covering the period 2005-2014. This enables us to contrast the pricing performance of implied trees and to assess the magnitude and sign of risk premia in both a tranquil and a turmoil period. The findings are as follows. First, the pricing performance of the Enhanced Derman and Kani (EDK, Moriggia et al. 2009) model is superior to that of the Rubinstein (1994) model. This superiority is stronger especially in the high volatility period due to a better estimation of the left tail of the distribution describing bad market conditions. Second, the Bakshi et al. (2003) formula is the most accurate for forecasting skewness and kurtosis, while for variance it yields upwardly biased forecasts. All models agree on the signs of the risk premia: negative for variance and kurtosis, and positive for skewness, but differ in magnitude. Overall, the results suggest that selling (buying) variance and kurtosis (skewness) is profitable in both high and low volatility periods

Esscher transform of option pricing on a mean-reverting asset with GARCH.

Gao, Fei.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (leaves 52-53).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Option Pricing with GARCH --- p.1Chapter 1.2 --- Mean Reversion in GARCH --- p.3Chapter 1.3 --- Thesis Setting --- p.4Chapter 2 --- Literature Review --- p.5Chapter 2.1 --- GARCH Model --- p.5Chapter 2.2 --- Locally Risk-Neutral Valuation --- p.8Chapter 2.3 --- Conditional Esscher Transform --- p.9Chapter 3 --- The Model --- p.12Chapter 3.1 --- The Mean-Reverting GARCH Model --- p.12Chapter 3.2 --- The Characteristic Functions --- p.15Chapter 3.3 --- Identification of Pricing Measures --- p.21Chapter 3.3.1 --- Conditional Esscher Transform --- p.21Chapter 3.3.2 --- Our Proposed Change of Measure --- p.25Chapter 4 --- Option Pricing --- p.30Chapter 4.1 --- Fast Fourier Transform --- p.30Chapter 4.2 --- Option on Futures : --- p.32Chapter 4.3 --- Numerical Analysis --- p.35Chapter 5 --- Empirical Analysis - Application to the crude oil market --- p.37Chapter 5.1 --- Description of data --- p.37Chapter 5.2 --- Estimation --- p.38Chapter 5.3 --- Comparisons --- p.40Chapter 6 --- Summary and Future work --- p.42Chapter 7 --- Appendix --- p.43Bibliography --- p.5

Mean-reverting assets with mean-reverting volatility.

Lo, Yu Wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 66-70).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 2 --- Literature Review --- p.8Chapter 2.1 --- Mean-reverting Model --- p.8Chapter 2.2 --- Volatility Smile --- p.11Chapter 2.3 --- Stochastic Volatility Model --- p.13Chapter 2.4 --- Multiscale Stochastic Volatility Model --- p.15Chapter 3 --- The Heston Stochastic Volatility --- p.17Chapter 3.1 --- The Model --- p.17Chapter 3.1.1 --- The Characteristic Function --- p.18Chapter 3.2 --- European Option Pricing --- p.24Chapter 3.2.1 --- Plain Vanilla Options --- p.25Chapter 3.2.2 --- Implied Volatility --- p.28Chapter 3.2.3 --- Other Payoff Functions --- p.30Chapter 3.3 --- Trinomial Tree: Exotic Option Pricing --- p.31Chapter 3.3.1 --- Sub-tree for the volatility --- p.33Chapter 3.3.2 --- Sub-tree for the asset --- p.34Chapter 3.3.3 --- Non-zero Correlation --- p.37Chapter 3.3.4 --- Calibration to Future prices --- p.38Chapter 3.3.5 --- Numerical Examples --- p.39Chapter 4 --- Multiscale Stochastic Volatility --- p.42Chapter 4.1 --- Model Settings --- p.42Chapter 4.2 --- Pricing --- p.44Chapter 4.3 --- Simulation studies --- p.54Chapter 5 --- Conclusion --- p.59Appendix --- p.61Chapter A --- Verifications --- p.61Chapter A.l --- Proof of Lemma 3.1.1 --- p.61Chapter B --- Black-Scholes Greeks --- p.64Bibliography --- p.6