Enhanced Valuation of European Options Under Jump Processes and Innovative Characterization of Implied Volatility Smile

2011 ◽  
Author(s):  
Ludovic Dubrana
Keyword(s):  
Implied Volatility ◽  
Jump Processes ◽  
European Options ◽  
Volatility Smile

scholarly journals Patterns of 50 ETF Options Implied Volatility in China: On Implied Volatility Functions

2021 ◽  
Vol 24 (1) ◽  
pp. 135-145
Author(s):  
Pengshi Li ◽  
Yan Lin ◽  
Yuting Zhong
Keyword(s):  
Implied Volatility ◽  
Stock Exchange ◽  
Empirical Work ◽  
Ordinary Least Squares ◽  
Options Pricing ◽  
Options Market ◽  
European Options ◽  
Volatility Smile ◽  
Volatility Function ◽  
Better Than

The aim of this study is to examine the volatility smile based on the European options on Shanghai stock exchange 50 ETF. The data gives evidence of the existence of a well-known U-shaped implied volatility smile for the SSE 50 ETF options market in China. For those near-month options, the implied volatility smirk is also observed. And the implied volatility remains high for the short maturity and decreases as the maturity increases. The patterns of the implied volatility of SSE 50 ETF options indicate that in-the-money options and out-of-the-money options are more expensive relative to at-the-money options. This makes the use of at-the-money implied volatility for pricing out-of- or in-the-money options questionable. In order to investigate the implied volatility, the regression-based implied volatility functions model is considered employed to study the implied volatility in this study as this method is simple and easy to apply in practice. Several classical implied volatility functions are investigated in this paper to find whether some kind of implied volatility functions could lead to more accurate options pricing values. The potential determinants of implied volatility are the degree of moneyness and days left to expiration. The empirical work has been expressed by means of simple ordinary least squares framework. As the study shows, when valuing options, the results of using volatility functions are mixed. For far-month options, using at-the-money implied volatility performs better than other volatility functions in option valuation. For near-month options, the use of volatility functions can improve the valuation accuracy for deep in-the-money options or deep out-of-the-money options. However, no particular implied volatility function performs very well for options of all moneyness level and time to maturity.

scholarly journals Pricing and hedging Asian options under Levy processes and robust long-term investing with learning about stock returns

2021 ◽  
Author(s):  
Andrew Na
Keyword(s):  
Stock Returns ◽  
Implied Volatility ◽  
Calibration Method ◽  
Recursive Utility ◽  
Asian Options ◽  
Volatility Smile ◽  
Bivariate Model ◽  
Risky Assets ◽  
Fourier Cosine

In this work we propose a parametric model using the techniques of time-changed subordination that captures the implied volatility smile. We demonstrate that the Fourier-Cosine method can be used in a semi-static way to hedge for quadratic, VaR and AVaR risk. We also observe that investors looking to hedge VaR can simply hold the amount in a portfolio of mostly cash, whereas an investor hedging AVaR will need to hold more risky assets. We also extend ES risk to a robust framework. A conditional calibration method to calibrate the bivariate model is proposed. For a robust long-term investor who maximizes their recursive utility and learns about the stock returns, as the willingness to substitute over time increases, the equity demand decreases and consumption-wealth ratio increases. As the preference for robustness increases the demand for risk decreases. For a positive correlation, we observe that learning about returns encourages the investor to short the bond at all levels of u and vice versa

EQUILIBRIUM VALUATION OF CURRENCY OPTIONS UNDER A DISCONTINUOUS MODEL WITH CO-JUMPS

2020 ◽  
pp. 1-19
Author(s):  
Yu Xing ◽  
Yuhua Xu ◽  
Huawei Niu
Keyword(s):  
Implied Volatility ◽  
Option Price ◽  
Closed Form Solution ◽  
Continuous Model ◽  
Form Solution ◽  
Jump Processes ◽  
Currency Options ◽  
Currency Option ◽  
Jump Intensity ◽  
Discontinuous Model

Abstract In this paper, we study the equilibrium valuation for currency options in a setting of the two-country Lucas-type economy. Different from the continuous model in Bakshi and Chen [1], we propose a discontinuous model with jump processes. Empirical findings reveal that the jump components in each country's money supply can be decomposed into the simultaneous co-jump component and the country-specific jump component. Each of the jump components is modeled with a Poisson process whose jump intensity follows a mean reversion stochastic process. By solving a partial integro-differential equation (PIDE), we get a closed-form solution to the PIDE for a European call currency option. The numerical results show that the derived option pricing formula is efficient for practical use. Importantly, we find that the co-jump has a significant impact on option price and implied volatility.

Implied volatility smirk and future stock returns: evidence from the German market

2015 ◽  
Vol 41 (12) ◽  
pp. 1357-1379
Author(s):  
Di Mo ◽  
Neda Todorova ◽  
Rakesh Gupta
Keyword(s):  
High Frequency ◽  
Implied Volatility ◽  
Stock Index ◽  
High Frequency Data ◽  
Frequency Data ◽  
European Options ◽  
German Market ◽  
Content Type ◽  
The Relationship ◽  
Option Market

Purpose – The purpose of this paper is to investigate the relationship between option’s implied volatility smirk (IVS) and excess returns in the Germany’s leading stock index Deutscher-Aktien Index (DAX) 30. Design/methodology/approach – The study defines the IVS as the difference in implied volatility derived from out-of-the-money put options and at-the-money call options. This study employs the ordinary least square regression with Newey-West correction to analyse the relationship between IVS and excess DAX 30 index returns in Germany. Findings – The authors find that the German market adjusts information in an efficient way. Consequently, there is no information linkage between option volatility smirk and market index returns over the nine years sample period after considering the control variables, global financial crisis dummies, and the subsample test. Research limitations/implications – This study finds that the option market and the DAX 30 index are informationally efficient. Implications of the findings are that the investors cannot profit from the information contained in the IVS since the information is simultaneously incorporated into option prices and the stock index prices. The findings of this study are applicable to other markets with European options and for market participants who seek to exploit short-term market divergence from efficiency. Originality/value – The relationship between IVS and stock price changes has not been investigated sufficiently in academic literature. This study looks at this relationship in the context of European options using high-frequency transactions data. Prior studies look at this relationship for only American options using daily data. Pricing efficiency of the European option market using high-frequency data have not been studied in the prior literature. The authors find different results for the German market based on this high-frequency data set.

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