Volatility Option Research Articles

Analytically pricing volatility options and capped/floored volatility swaps with nonlinear payoffs in discrete observation case under the Merton jump-diffusion model driven by a nonhomogeneous Poisson process

In this paper, we introduce novel analytical solutions for valuating volatility derivatives, including volatility options and capped/floored volatility swaps, employing discrete sampling within the framework of the Merton jump-diffusion model, which is driven by a nonhomogeneous Poisson process. The absence of a comprehensive understanding of the probability distribution characterizing the realized variance has historically impeded the development of a robust analytical valuation approach for such instruments. Through the application of the cumulative distribution function of the realized variance conditional on Poisson jumps, we have derived explicit expectations for the derivative payoffs articulated as functions of the extremum values of the square root of the realized variance. We delineate precise pricing structures for an array of instruments, encompassing variance and volatility swaps, variance and volatility options, and their respective capped and floored variations, alongside establishing put-call parity and relationships for capped and floored positions. Complementing the theoretical advancements, we substantiate the practical efficacy and precision of our solutions via Monte Carlo simulations, articulated through multiple numerical examples. Conclusively, our analysis extends to the quantification of jump impacts on the fair strike prices of volatility derivatives with nonlinear payoffs, facilitated by our analytic pricing expressions.

Deterministic modelling of implied volatility in cryptocurrency options with underlying multiple resolution momentum indicator and non-linear machine learning regression algorithm

Modeling implied volatility (IV) is important for option pricing, hedging, and risk management. Previous studies of deterministic implied volatility functions (DIVFs) propose two parameters, moneyness and time to maturity, to estimate implied volatility. Recent DIVF models have included factors such as a moving average ratio and relative bid-ask spread but fail to enhance modeling accuracy. The current study offers a generalized DIVF model by including a momentum indicator for the underlying asset using a relative strength index (RSI) covering multiple time resolutions as a factor, as momentum is often used by investors and speculators in their trading decisions, and in contrast to volatility, RSI can distinguish between bull and bear markets. To the best of our knowledge, prior studies have not included RSI as a predictive factor in modeling IV. Instead of using a simple linear regression as in previous studies, we use a machine learning regression algorithm, namely random forest, to model a nonlinear IV. Previous studies apply DVIF modeling to options on traditional financial assets, such as stock and foreign exchange markets. Here, we study options on the largest cryptocurrency, Bitcoin, which poses greater modeling challenges due to its extreme volatility and the fact that it is not as well studied as traditional financial assets. Recent Bitcoin option chain data were collected from a leading cryptocurrency option exchange over a four-month period for model development and validation. Our dataset includes short-maturity options with expiry in less than six days, as well as a full range of moneyness, both of which are often excluded in existing studies as prices for options with these characteristics are often highly volatile and pose challenges to model building. Our in-sample and out-sample results indicate that including our proposed momentum indicator significantly enhances the model’s accuracy in pricing options. The nonlinear machine learning random forest algorithm also performed better than a simple linear regression. Compared to prevailing option pricing models that employ stochastic variables, our DIVF model does not include stochastic factors but exhibits reasonably good performance. It is also easy to compute due to the availability of real-time RSIs. Our findings indicate our enhanced DIVF model offers significant improvements and may be an excellent alternative to existing option pricing models that are primarily stochastic in nature.

A novel term-structure-based Heston model for implied volatility surface

It remains a challenge for existing financial models to accurately capture the shapes of implied volatility (IV) of options with all maturities simultaneously. Inspired by Chen et al.’s empirical finding, ‘the shorter the option expiry, the higher the IV is’, we propose a novel and simple approach to solve this challenge, by introducing a term-structure-based correction (i.e. an exponential increase function of the options expiry) to the volatility of volatility (vol–vol) term of the classical Heston stochastic volatility model. We derive an approximate formula for the IV under the corrected model with the perturbation method and further apply the formula to predict the IVs of options written on the Shanghai Stock Exchange 50 ETF. Numerical experiments and empirical results show that the introduction of a term-structure-based correction function surely overcomes the deficiency of the classical Heston model in capturing the short-term IVs, thus improving notably its performance of IV forecasting.

Total variation regularization analysis for inverse volatility option pricing problem

We investigate in this paper an inverse problem of recovering the space-dependent volatility in option pricing. To enhance precision across the domain, we transform the original problem into an inverse source problem of a bounded degenerate parabolic equation, utilizing linearization and variable substitution. Unlike classical methods, we apply a total variation regularization combined with a novel generalized finite integration technique. This approach accommodates volatility jumps in an overnight rate scenario. Leveraging an optimal control framework, we demonstrate that the inverse problem can be reformulated as an optimal control problem whose existence, necessary conditions, local uniqueness and stability for the minimizer of control functional are obtained. For numerical verification, we derive the Euler equation and design a discretization algorithm with generalized finite integration technique. Numerical examples showcase the robustness of our approach, highlighting advantages in accuracy and effectiveness over other strategies.

통화옵션과 국채선물이 원달러환율에 미치는 영향

In this study, the impact of currency options(volatility) and KTB futures prices on the USD/KRW exchange rate was divided into before and after COVID-19 and a comparative analysis was conducted using cross-sectional regression analysis and VECM. The analysis results are as follows. First, looking at the results of the regression analysis, the currency option market showed that only the one-year volatility of the currency option affected the USD/KRW exchange rate in all periods. However, both 3-year and 10-year KTB futures had no significant impact before COVID-19, but appeared to have a statistically significant impact on the exchange rate starting after COVID-19. Second, cointegration exists in all time series before and after COVID-19, and in particular, it can be seen that the cointegration correlation is stronger after COVID-19 than before. Third, the results of the VECM analysis showed that the influence of KTB futures had no significance before COVID-19, but became significant after COVID-19. Fourth, the results of the shock response analysis showed that the impact of shocks in the options market and KTB futures market on the USD/KRW exchange rate was greater after COVID-19 than before and had a long lasting effect. Fifth, the results of the variance decomposition of forecast errors for the USD/KRW exchange rate also showed that the influence on KTB futures increased more after COVID-19 than before. Understanding foreign exchange is very important not only for exports and imports, but also for international trade and global economic activities. In the future, we hope that more in-depth research on the foreign exchange market and international trade will continue.

Calibration of European option pricing model in uncertain environment: Valuation of uncertainty implied volatility

Uncertain differential equations have been widely used in modeling financial markets, and option pricing formulae have been obtained by employing these equations. However, according to the existing literature, the parameter estimation of the option pricing model driven by the uncertain differential equation has not been evaluated so far, and the parameters have been assumed to be arbitrary numbers for such problems. Based on the mentioned gap, this study presents an approach for parameter estimation of European option pricing model in the uncertain environment for the first time. For this purpose, some of the most common uncertain models are considered, and the corresponding empirical examples are presented. Since implied volatility as an instrument provides traders a range of prices that securities change among them, this study evaluates the implied volatility of the European option under the geometric Liu process for the first time. Empirical comparison for both in sample and out of sample dataset based on the uncertainty framework and Black–Scholes model demonstrates that the uncertain models are more accurate for evaluating the European option prices and the implied volatilities.

Forecasting implied volatilities of currency options with machine learning techniques and econometrics models

AbstractDeveloping an effective modeling framework to minimize foreign exchange (FX) risk is of vital importance for hedgers and traders in FX markets. In this study, we compare the ability of long short-term memory (LSTM) models to that of random forest and several time series models for forecasting EURUSD implied volatility across the volatility surface. As our literature study argues, there are only a few published papers on this subject. We find that the LSTM model is the best model for shorter option maturities, while the AR-GARCH model is superior when the maturities increase. We observe that the LSTM model is able to capture immense and immediate changes in implied volatility, which is important for hedging against significant shifts in FX rates.

Quality issues of implied volatilities of index and stock options in the OptionMetrics IvyDB database

AbstractFor stock and index options in the United States, OptionMetrics records prices at 3:59 p.m., not 4:00 p.m. as assumed in previous literature. The resulting 1‐min time discrepancy with closing share prices creates artificial variability in implied volatility spreads and strongly affects market‐wide spreads. It leads to particularly large distortions at the onset of the COVID‐19 pandemic. For index options in Europe, OptionMetrics data show large deviations from put‐call parity even though the original option prices match the parity exactly. Finally, the implied volatilities of stock options in Europe show clusters of exceptional deviations due to incorrect dividend information.

Real Options Volatility Surface for Valuing Renewable Energy Projects

Real Options Volatility Surface for Valuing Renewable Energy Projects

The rough Hawkes Heston stochastic volatility model

AbstractWe study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes‐type process proportional to the intensity process of the jump component appearing in the dynamics of the spot variance itself and the log returns. The model belongs to the class of affine Volterra models. In particular, the Fourier‐Laplace transform of the log returns and the square of the volatility index can be computed explicitly in terms of solutions of deterministic Riccati‐Volterra equations, which can be efficiently approximated using a multi‐factor approximation technique. We calibrate a parsimonious specification of our model characterized by a power kernel and an exponential law for the jumps. We show that our parsimonious setup is able to simultaneously capture, with a high precision, the behavior of the implied volatility smile for both S&P 500 and VIX options. In particular, we observe that in our setting the usual shift in the implied volatility of VIX options is explained by a very low value of the power in the kernel. Our findings demonstrate the relevance, under an affine framework, of rough volatility and self‐exciting jumps in order to capture the joint evolution of the S&P 500 and VIX.

The Impact of the Russo-Ukrainian War on the Risk and Return of TAIEX

Abstract This study examines the impact of the Russia-Ukraine war (RUW) on the dynamic of TAIEX options' risk-return profile. Since the outbreak of the war on February 24, 2022, global economic sanctions have disrupted the world economy. Soaring energy and food prices and supply shortages have suppressed global economic growth, leading to rising inflation. Financial markets have reacted to the shocks caused by this war, thus intensifying the volatility of options markets. This study utilizes Hsu's (2013) option return models to investigate the impacts of how the war influences the TAIEX options' risk-return profile, including PDFs, profitability, and expected returns. The contributions of this paper are two-fold: It is the first paper on the (RUW) on the options markets; additionally, we demonstrate theoretically and empirically that the normality assumption of simple arithmetic returns is acceptable, making the Hsu's (2013) option return models more robust. The results indicate that the war has significantly affected and altered the PDFs of option returns, expected option returns, and volatility after the war. However, both theoretically and empirically shows that, despite the challenges posed by the war, put options trading during this period has been profitable. Keywords: Russo-Ukrainian War, TAIEX options, Option return model, Risk/Return Profile.

Simultaneous Calibration of European Option Volatility and Fractional Order under the Time Fractional Vasicek Model

In this paper, we recover the European option volatility function σ(t) of the underlying asset and the fractional order α of the time fractional derivatives under the time fractional Vasicek model. To address the ill-posed nature of the inverse problem, we employ Tikhonov regularization. The Alternating Direction Multiplier Method (ADMM) is utilized for the simultaneous recovery of the parameter α and the volatility function σ(t). In addition, the existence of a solution to the minimization problem has been demonstrated. Finally, the effectiveness of the proposed approach is verified through numerical simulation and empirical analysis.

A study of the correlation between volatility and risk diversification control in options and futures markets

A study of the correlation between volatility and risk diversification control in options and futures markets

Sensitivity Analysis Based on Portfolio Option Models Using Tesla and Nio as Examples

The electric vehicle (EV) industry is undergoing a significant transformation, driven by environmental concerns, advancements in battery technology, and changing consumer preferences. Companies like Tesla and China's NIO are at the forefront of this revolution, showcasing the global potential of EVs. This study undertook a sensitivity analysis of these two leading EV manufacturers, Tesla and NIO, to understand the dynamics of their stock prices and implications for investment strategies. Data was meticulously collected from various financial databases to capture daily stock prices, which were then used to compute monthly returns. The study also delved into options, focusing on the strike prices and volatility of Tesla and NIO options. Using a combination of stock prices, strike prices, and volatility, the intrinsic and time value of these options were analyzed. The research employed a composite option model to describe the price variation of an option, considering factors like asset price volatility, risk-free rate, and dividend yield. The findings revealed that stock prices and option prices exhibited certain sensitivities to market variables. For instance, Tesla's option prices showed an upward trend with rising stock prices, while NIO's option prices displayed varied responses to stock price changes. The study underscores the importance of understanding these sensitivities for informed investment decisions in the evolving EV market.

The Dynamic Informativeness of Scheduled News

We propose a method to identify the informativeness of a future scheduled announcement at the daily level, exploiting the discontinuity it creates in the term structure of option volatility. We implement the strategy in a panel data model to estimate the relation between prior signals and the future announcement. This method allows us to separate substitutes from complements, it can isolate multiple signals within the same quarter, and it can condition on the timing and signal characteristics. We find that analyst forecasts substitute earnings announcement information and that recommendations do not provide extra information on top of forecasts. Moreover, our evidence suggests that insiders sell to avoid uncertainty when the announcement is far away but pull forward earnings information when they trade one month before. This paper was accepted by Eric So, accounting. Funding: This publication is part of the project “Eliciting the properties of private signals” (with project number VI.Veni.201E.029 of the research program VENI SGW, which is (partly) financed by the Dutch Research Council (NWO). Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.4970 .

Oil Price Uncertainty and IPOs

We examine the impact of oil price uncertainty on IPO volume in the oil and gas sector. By using the implied volatility of oil options, a forward-looking uncertainty measure, we identify the effect of uncertainty on the going-public decision. Oil price uncertainty exhibits a strong negative relation to IPO volume. A one standard deviation decrease in the implied volatility results in a 29% increase in the number of quarterly IPOs. The effect is concentrated among the price-sensitive upstream producers. We further report that uncertainty positively impacts the IPO withdrawal decision and increases the value of postponing the offering.

Investment Behavior of Foreign Institutional Investors and Implied Volatility Dynamics: An Empirical Study on the Indian Equity Derivatives Market

The aim of this study is to examine the association between the capital flows of foreign institutional investors (FIIs) in the equity derivatives market in India and the implied volatility of options. Previous studies on FIIs and realized volatility in the equity market provide the basis for this study. Covering a period of ten years (2012–2021), this study established the importance of FII capital flows in explaining the implied volatility of options. The Granger causality test confirms the unidirectional flow of causality between FII and implied volatility (VIX) in the Indian stock market. The vector autoregression model developed in the study confirms the dynamic relationship between implied volatility and the investment behavior of foreign institutional investors (FIIs). The outcome of this study will help options traders to understand the mispricing of options because of FII’s buying pressure on implied volatility. The results will also help policymakers understand how institutional investors influence option pricing so that appropriate decisions can be made.

On the Implied Volatility of Asian Options Under Stochastic Volatility Models

In this paper, we study the short-time behaviour of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black–Scholes model with a general stochastic volatility process. Using techniques of the Malliavin calculus developed in Alòs, García-Lorite, and Muguruza [2022. On Smile Properties of Volatility Derivatives: Understanding the VIX Skew. SIAM Journal on Financial Mathematics. 13(1): 32–69. https://doi.org/10.1137/19M1269981], we give sufficient conditions on the stochastic volatility in order to compute the level of the implied volatility of the option when the maturity converges to zero. Then, we find a short maturity asymptotic formula for the skew slope of the implied volatility that depends on the correlation between prices and volatilities and the Hurst parameter of the volatility model. We apply our general results to the SABR and fractional Bergomi models, and provide numerical simulations that confirm the accurateness of the asymptotic formulas.

Beware of Extreme Investor Sentiments! Indian Evidence on the Performance of Neuro-specific Options Volatility Trading Strategies on the Facets of COVID-19

This study investigates the dynamic relationship between noise trader sentiment and excessive volatility in the Indian financial market during the COVID-19 outbreak. It proposes novel options trading strategies to ensure profitability in times of irrational exuberance and to satisfy diverse investment requirements of volatility traders, which arise from the varying levels of stimulating neurotransmitters, namely dopamine and serotonin in the human body. Empirical results show that the incremental information content of sentiment measures is vital in forecasting future volatility and the proposed options trading strategies effectively accomplish the neuro-specific intentions of the traders during extreme volatility in the Indian equity market. JEL Codes: G12, G13

Exploring the Impact of COVID-19 on Financial Derivatives Markets

Currently, financial derivatives are important financial instruments. Financial derivatives can provide investors with the opportunity to hedge, speculate, and arbitrage. But due to the impact of COVID-19. The performance of financial derivatives has changed dramatically compared to the pre-epidemic period. This dissertation focuses on the performance of three major financial derivatives which include futures, options, and credit under COVID-19. The phenotypes of these three major financial derivatives are analyzed separately. In this paper, we examine the extensive literature to demonstrate the changes in financial derivatives during COVID-19. By collecting a large amount of data about financial derivatives during the COVID-19 period and before. And the data are quantitatively analyzed to show the specific performance of financial derivatives under COVID-19. The study found that there is a huge variation in the performance of these three financial derivatives in COVID-19. For futures, foreign performance futures can bring a negative impact on financial markets. As for domestic, the performance is different during the emergency resistance period and the normalized resistance period. The performance of the emergency resistance period is significantly less than the normalized resistance period. For options, the volatile market sentiment and panic caused by recurring epidemics affect investors' judgment, which leads to changes in the implied volatility of options and affects the price of options. For swap specify its basic means of operation in an epidemic state and the basic types.