Implied Volatility for European Options

2003 ◽  
pp. 197-266
Author(s):  
Srdjan Stojanovic
Keyword(s):  
Implied Volatility ◽  
European Options

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.

CURRENCY DERIVATIVES UNDER A MINIMAL MARKET MODEL WITH RANDOM SCALING

2005 ◽  
Vol 08 (08) ◽  
pp. 1157-1177 ◽  
Author(s):  
DAVID HEATH ◽  
ECKHARD PLATEN
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Market Model ◽  
European Options ◽  
Bessel Processes ◽  
Exchange Rate Dynamics ◽  
Volatility Model ◽  
Minimal Market Model ◽  
Implied Volatility Surfaces

This paper uses an alternative, parsimonious stochastic volatility model to describe the dynamics of a currency market for the pricing and hedging of derivatives. Time transformed squared Bessel processes are the basic driving factors of the minimal market model. The time transformation is characterized by a random scaling, which provides for realistic exchange rate dynamics. The pricing of standard European options is studied. In particular, it is shown that the model produces implied volatility surfaces that are typically observed in real markets.

scholarly journals Option pricing with random risk aversion

2022 ◽  
Author(s):  
Luiz Vitiello ◽  
Ser-Huang Poon
Keyword(s):  
Risk Aversion ◽  
Implied Volatility ◽  
Market Volatility ◽  
European Options ◽  
Parameter Change ◽  
Pricing Kernel ◽  
Underlying Asset ◽  
State Dependent ◽  
Low Levels ◽  
Aggregate Wealth

AbstractBased on a standard general equilibrium economy, we develop a framework for pricing European options where the risk aversion parameter is state dependent, and aggregate wealth and the underlying asset have a bivariate transformed-normal distribution. Our results show that the volatility and the skewness of the risk aversion parameter change the slope of the pricing kernel, and that, as the volatility of the risk aversion parameter increases, the (Black and Scholes) implied volatility shifts upwards but its shape remains the same, which implies that the volatility of the risk aversion parameter does not change the shape of the risk neutral distribution. Also, we demonstrate that the pricing kernel may become non-monotonic for high levels of volatility and low levels of skewness of the risk aversion parameter. An empirical example shows that the estimated volatility of the risk aversion parameter tends to be low in periods of high market volatility and vice-versa.

A closed-form approximation formula for pricing European options under a three-factor model

2021 ◽  
pp. 1-27
Author(s):  
Hye-mee Kil ◽  
Jeong-Hoon Kim
Keyword(s):  
Closed Form ◽  
Implied Volatility ◽  
Factor Model ◽  
Closed Form Solution ◽  
Form Solution ◽  
Approximation Formula ◽  
European Options ◽  
Implied Volatility Surface ◽  
Volatility Surface ◽  
Three Factor

Abstract The double-mean-reverting model, introduced by Gatheral [(2008). Consistent modeling of SPX and VIX options. In The Fifth World Congress of the Bachelier Finance Society London, July 18], is known to be a successful three-factor model that can be calibrated to both CBOE Volatility Index (VIX) and S&P 500 Index (SPX) options. However, the calibration of this model may be slow because there is no closed-form solution formula for European options. In this paper, we use a rescaled version of the model developed by Huh et al. [(2018). A scaled version of the double-mean-reverting model for VIX derivatives. Mathematics and Financial Economics 12: 495–515] and obtain explicitly a closed-form pricing formula for European option prices. Our formulas for the first and second-order approximations do not require any complicated calculation of integral. We demonstrate that a faster calibration result of the double-mean revering model is available and yet the practical implied volatility surface of SPX options can be produced. In particular, not only the usual convex behavior of the implied volatility surface but also the unusual concave down behavior as shown in the COVID-19 market can be captured by our formula.

scholarly journals ESTIMASI NILAI IMPLIED VOLATILITY MENGGUNAKAN SIMULASI MONTE CARLO

2018 ◽  
Vol 7 (3) ◽  
pp. 239
Author(s):  
MAKBUL MUFLIHUNALLAH ◽  
KOMANG DHARMAWAN ◽  
NI MADE ASIH
Keyword(s):  
Monte Carlo ◽  
Capital Market ◽  
Implied Volatility ◽  
Option Price ◽  
European Options ◽  
Price Variation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Alternative Investment ◽  
The Capital Market

Investing among investors is an exciting activity to gain profit in the financial world. The development of investment in the financial world affects the number of alternative investment instruments that can be offered to investors in the capital market. The management of instruments in finance depends on the accuracy of forecasting of variables for example volatility. Volatility is a statistic of the degree of price variation in one period to the next which is expressed by ?. Volatility values can be estimated using Implied Volatility. Implied Volatility is the volatility used in determining the price of European options obtained by equalizing the price of the theoretical options, the price obtained from the Black-Scholes model, with the option price in the market. In this research will discuss how to estimate Implied Volatility value using the option obtained from simulation with Monte Carlo.

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.

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