Pricing Index Options with Stochastic Volatility

The objective of this paper is to investigate the pricing accuracy under stochastic volatility where the volatility follows a square root process. The theoretical prices are compared with market price data (the German DAX index options market) by using two different techniques of parameter estimation, the method of moments and implicit estimation by inversion. Standard Black & Scholes pricing is used as a benchmark. The results indicate that the stochastic volatility model with parameters estimated by inversion using the available prices on the preceding day, is the most accurate pricing method of the three in this study and can be considered satisfactory. However, as the same model with parameters estimated using a rolling window (the method of moments) proved to be inferior to the benchmark, the importance of stable and correct estimation of the parameters is evident.

Stochastic volatility jump-diffusions for European equity index dynamics

Major research on equity index dynamics has investigated only US indices (usually the S&P 500) and has provided contradictory results. In this paper a clarification and extension of that previous research is given. We find that European equity indices have quite different dynamics from the S&P 500. Each of the European indices considered may be satisfactorily modelled using either an affine model with price and volatility jumps or a GARCH volatility process without jumps. The S&P 500 dynamics are much more difficult to capture in a jump-diffusion framework.

Predicting stock index volatility: can market volume help?

This paper explores a number of statistical models for predicting the daily stock return volatility of an aggregate of all stocks traded on the NYSE. An application of linear and non-linear Granger causality tests highlights evidence of bidirectional causality, although the relationship is stronger from volatility to volume than the other way around. The out-of-sample forecasting performance of various linear, GARCH, EGARCH, GJR and neural network models of volatility are evaluated and compared. The models are also augmented by the addition of a measure of lagged volume to form more general ex-ante forecasting models. The results indicate that augmenting models of volatility with measures of lagged volume leads only to very modest improvements, if any, in forecasting performance.

Price discovery and volatility spillovers in index futures markets: Some evidence from Mexico

This paper investigates the hypotheses that the recently established Mexican stock index futures market effectively serves the price discovery function, and that the introduction of futures trading has provoked volatility in the underlying spot market. We test both hypotheses simultaneously with daily data from Mexico in the context of a modified EGARCH model that also incorporates possible cointegration between the futures and spot markets. The evidence supports both hypotheses, suggesting that the futures market in Mexico is a useful price discovery vehicle, although futures trading has also been a source of instability for the spot market. Several managerial implications are derived and discussed. (C) 2004 Elsevier B.V. All rights reserved.

Developing a rural land investment performance index for New Zealand

Agricultural production is one of the major industries in New Zealand and accounts for over 60% of all export trade. The farming industry comprises 70,000 entities ranging in size from small individual run farms to large corporate operations. The reliance of the New Zealand economy to the international rural sector has seen considerable volatility in the rural land markets over the past four decades, with significant shifts in rural land prices based on location, land use and underlying international rural commodity prices. With the increasing attention being paid to the rural sector, especially in relation to food production and bio-fuels, there has been an increasing corporate interest in rural land ownership in relatively low subsidised agricultural producing countries such as New Zealand and Australia. A factor that has limited this participation of institutional investors previously has been a lack of reliable and up-to-date investment performance data for this asset class. This paper is the initial starting phase in the development of a New Zealand South Island rural land investment performance index and covers the period 1990-2007. The research in this paper analyses all rural sales transactions in the South Island and develops a capital return index for rural property based on major rural property land use. Additional work on this index will cover both total return performance and geographic location.

Correlations and volatility spillovers across commodity and stock markets: Linking energies, food, and gold

This paper employs a VAR-GARCH model to investigate the return links and volatility transmission between the S&P 500 and commodity price indices for energy, food, gold and beverages over the turbulent period from 2000 to 2011. Understanding the price behavior of commodity prices and the volatility transmission mechanism between these markets and the stock exchanges are crucial for each participant, including governments, traders, portfolio managers, consumers, and producers. For return and volatility spillover, the results show significant transmission among the S&P 500 and commodity markets. The past shocks and volatility of the S&P 500 strongly influenced the oil and gold markets. This study finds that the highest conditional correlations are between the S&P 500 and gold index and the S&P 500 and WTI index. We also analyze the optimal weights and hedge ratios for commodities/S&P 500 portfolio holdings using the estimates for each index. Overall, our findings illustrate several important implications for portfolio hedgers for making optimal portfolio allocations, engaging in risk management and forecasting future volatility in equity and commodity markets. © 2013 Elsevier B.V.

Estimating the parameters of stochastic volatility models using option price data

This article describes a maximum likelihood method for estimating the parameters of the standard square-root stochastic volatility model and a variant of the model that includes jumps in equity prices. The model is fitted to data on the S&P 500 Index and the prices of vanilla options written on the index, for the period 1990 to 2011. The method is able to estimate both the parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options), including the volatility and jump risk premia. The estimation is implemented using a particle filter whose efficacy is demonstrated under simulation. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using graphics processing units (GPUs). The empirical results indicate that the parameters of the models are reliably estimated and consistent with values reported in previous work. In particular, both the volatility risk premium and the jump risk premium are found to be significant.

Essays on the Modeling and Prediction of Volatility and Higher Moments of Stock Returns (summary section only)

One of the most fundamental and widely accepted ideas in finance is that investors are compensated through higher returns for taking on non-diversifiable risk. Hence the quantification, modeling and prediction of risk have been, and still are one of the most prolific research areas in financial economics. It was recognized early on that there are predictable patterns in the variance of speculative prices. Later research has shown that there may also be systematic variation in the skewness and kurtosis of financial returns. Lacking in the literature so far, is an out-of-sample forecast evaluation of the potential benefits of these new more complicated models with time-varying higher moments. Such an evaluation is the topic of this dissertation. Essay 1 investigates the forecast performance of the GARCH (1,1) model when estimated with 9 different error distributions on Standard and Poor’s 500 Index Future returns. By utilizing the theory of realized variance to construct an appropriate ex post measure of variance from intra-day data it is shown that allowing for a leptokurtic error distribution leads to significant improvements in variance forecasts compared to using the normal distribution. This result holds for daily, weekly as well as monthly forecast horizons. It is also found that allowing for skewness and time variation in the higher moments of the distribution does not further improve forecasts. In Essay 2, by using 20 years of daily Standard and Poor 500 index returns, it is found that density forecasts are much improved by allowing for constant excess kurtosis but not improved by allowing for skewness. By allowing the kurtosis and skewness to be time varying the density forecasts are not further improved but on the contrary made slightly worse. In Essay 3 a new model incorporating conditional variance, skewness and kurtosis based on the Normal Inverse Gaussian (NIG) distribution is proposed. The new model and two previously used NIG models are evaluated by their Value at Risk (VaR) forecasts on a long series of daily Standard and Poor’s 500 returns. The results show that only the new model produces satisfactory VaR forecasts for both 1% and 5% VaR Taken together the results of the thesis show that kurtosis appears not to exhibit predictable time variation, whereas there is found some predictability in the skewness. However, the dynamic properties of the skewness are not completely captured by any of the models.

Three Essays on the Volatility of Finnish Stock Returns (summary section only)

First, in Essay 1, we test whether it is possible to forecast Finnish Options Index return volatility by examining the out-of-sample predictive ability of several common volatility models with alternative well-known methods; and find additional evidence for the predictability of volatility and for the superiority of the more complicated models over the simpler ones. Secondly, in Essay 2, the aggregated volatility of stocks listed on the Helsinki Stock Exchange is decomposed into a market, industry-and firm-level component, and it is found that firm-level (i.e., idiosyncratic) volatility has increased in time, is more substantial than the two former, predicts GDP growth, moves countercyclically and as well as the other components is persistent. Thirdly, in Essay 3, we are among the first in the literature to seek for firm-specific determinants of idiosyncratic volatility in a multivariate setting, and find for the cross-section of stocks listed on the Helsinki Stock Exchange that industrial focus, trading volume, and block ownership, are positively associated with idiosyncratic volatility estimates––obtained from both the CAPM and the Fama and French three-factor model with local and international benchmark portfolios––whereas a negative relation holds between firm age as well as size and idiosyncratic volatility.

Evaluating the Predictability of the Volatility Smile Using Return Distributions

In this paper, we examine the predictability of observed volatility smiles in three major European index options markets, utilising the historical return distributions of the respective underlying assets. The analysis involves an application of the Black (1976) pricing model adjusted in accordance with the Jarrow-Rudd methodology as proposed in 1982. Thereby we adjust the expected future returns for the third and fourth central moments as these represent deviations from normality in the distributions of observed returns. Thus, they are considered one possible explanation to the existence of the smile. The obtained results indicate that the inclusion of the higher moments in the pricing model to some extent reduces the volatility smile, compared with the unadjusted Black-76 model. However, as the smile is partly a function of supply, demand, and liquidity, and as such intricate to model, this modification does not appear sufficient to fully capture the characteristics of the smile.

Examining and Modeling the Dynamics of the Volatility Surface

The objective of this paper is to investigate and model the characteristics of the prevailing volatility smiles and surfaces on the DAX- and ESX-index options markets. Continuing on the trend of Implied Volatility Functions, the Standardized Log-Moneyness model is introduced and fitted to historical data. The model replaces the constant volatility parameter of the Black & Scholes pricing model with a matrix of volatilities with respect to moneyness and maturity and is tested out-of-sample. Considering the dynamics, the results show support for the hypotheses put forward in this study, implying that the smile increases in magnitude when maturity and ATM volatility decreases and that there is a negative/positive correlation between a change in the underlying asset/time to maturity and implied ATM volatility. Further, the Standardized Log-Moneyness model indicates an improvement to pricing accuracy compared to previous Implied Volatility Function models, however indicating that the parameters of the models are to be re-estimated continuously for the models to fully capture the changing dynamics of the volatility smiles.

Volatility Smile Dynamics in Scenario Analysis

The objective of this paper is to suggest a method that accounts for the impact of the volatility smile dynamics when performing scenario analysis for a portfolio consisting of vanilla options. As the volatility smile is documented to change at least with the level of implied at-the-money volatility, a suitable model is here included in the calculation process of the simulated market scenarios. By constructing simple portfolios of index options and comparing the ex ante risk exposure measured using different pricing methods to realized market values, ex post, the improvements of the incorporation of the model are monitored. The analyzed examples in the study generate results that statistically support that the most accurate scenarios are those calculated using the model accounting for the dynamics of the smile. Thus, we show that the differences emanating from the volatility smile are apparent and should be accounted for and that the methodology presented herein is one suitable alternative for doing so.