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.

Stock price distributions and news:evidence from index options

We estimate the shape of the distribution of stock prices using data from options on the underlying asset, and test whether this distribution is distorted in a systematic manner each time a particular news event occurs. In particular we look at the response of the FTSE100 index to market wide announcements of key macroeconomic indicators and policy variables. We show that the whole distribution of stock prices can be distorted on an event day. The shift in distributional shape happens whether the event is characterized as an announcement occurrence or as a measured surprise. We find that larger surprises have proportionately greater impact, and that higher moments are more sensitive to events however characterised.

The relationship between implied and realized volatility : evidence from the Australian stock index option market

This paper examines the relationship between the volatility implied in option prices and the subsequently realized volatility by using the S&P/ASX 200 index options (XJO) traded on the Australian Stock Exchange (ASX) during a period of 5 years. Unlike stock index options such as the S&P 100 index options in the US market, the S&P/ASX 200 index options are traded infrequently and in low volumes, and have a long maturity cycle. Thus an errors-in-variables problem for measurement of implied volatility is more likely to exist. After accounting for this problem by instrumental variable method, it is found that both call and put implied volatilities are superior to historical volatility in forecasting future realized volatility. Moreover, implied call volatility is nearly an unbiased forecast of future volatility.

The expiration day effect of indexoptions and index futures on the underlying shares

This paper studies the effect of the expiration day of index options and futures on the trading volume, variance and price of the underlying shares. The data consists of all trades for the underlying shares in the FOX-index for expiration days during the period October 1995 to the mid of yer 1999. The main results seem to support the findings of Kan 2001, i.e. no manipulation on a larger scale. However, some indication of manipulation could be found if certain characteristics are favorable. These characteristics include: a) a large quantity of outstanding futures or at/in the money options contracts, b) there exists shares with high index weight but fairly low trading volume. Lastly, there is some indication that manipulation might be more popular towards the end of the examined time period.

Finnish Short-Term Stock Returns

Functioning capital markets are a crucial part of a competitive economy since they provide the mechanisms to allocate resources. In order to be well functioning a capital market has to be efficient. Market efficiency is defined as a market where prices at any time fully reflect all available information. Basically, this means that abnormal returns cannot be predicted since they are dependent on future, presently unknown, information. The debate of market efficiency has been going on for several decades. Most academics today would probably agree that financial markets are reasonably efficient since virtually nobody has been able to achieve continuous abnormal positive returns. However, it is clear that a set of return anomalies exists, although they are apparently to small to enable substantial economic profit. Moreover, these anomalies can often be attributed to market design. The motivation for this work is to expand the knowledge of short-term trading patterns and to offer some explanations for these patterns. In the first essay the return pattern during the day is examined. On average stock prices move during two time periods of the day, namely, immediately after the opening and around the formal close of the market. Since stock prices, on average, move upwards these abnormal returns are generally positive and cause the distinct U-shape of intraday returns. In the second essay the results in the first essay are examined further. The return pattern around the former close is shown to partly be the result of manipulative action by market participants. In the third essay the focus is shifted towards trading patterns of the underlying stocks on days when index options and index futures on the stocks expire. Generally no expiration day effect was found. However, some indication of an expiration day effect was found when a large amount of open in- or at-the-money contracts existed. Also, the effects were likelier to be found for shares with high index-weight but fairly low trading volume. Last, in the forth essay the attention is turned to the behaviour of different tax clienteles around the dividend ex-day. Two groups of investors showed abnormal trading behaviour. Domestic non-financial investors, especially domestic companies, showed a dividend capturing behaviour, i.e. buying cum-dividend and selling ex-dividend shares. The opposite behaviour was found for foreign investors and domestic financial institutions. The effect was more notable for high yield, high volume stocks.

Modeling and Forecasting Implied Volatility: Implications for Trading, Pricing, and Risk Management

Modeling and forecasting of implied volatility (IV) is important to both practitioners and academics, especially in trading, pricing, hedging, and risk management activities, all of which require an accurate volatility. However, it has become challenging since the 1987 stock market crash, as implied volatilities (IVs) recovered from stock index options present two patterns: volatility smirk(skew) and volatility term-structure, if the two are examined at the same time, presents a rich implied volatility surface (IVS). This implies that the assumptions behind the Black-Scholes (1973) model do not hold empirically, as asset prices are mostly influenced by many underlying risk factors. This thesis, consists of four essays, is modeling and forecasting implied volatility in the presence of options markets’ empirical regularities. The first essay is modeling the dynamics IVS, it extends the Dumas, Fleming and Whaley (DFW) (1998) framework; for instance, using moneyness in the implied forward price and OTM put-call options on the FTSE100 index, a nonlinear optimization is used to estimate different models and thereby produce rich, smooth IVSs. Here, the constant-volatility model fails to explain the variations in the rich IVS. Next, it is found that three factors can explain about 69-88% of the variance in the IVS. Of this, on average, 56% is explained by the level factor, 15% by the term-structure factor, and the additional 7% by the jump-fear factor. The second essay proposes a quantile regression model for modeling contemporaneous asymmetric return-volatility relationship, which is the generalization of Hibbert et al. (2008) model. The results show strong negative asymmetric return-volatility relationship at various quantiles of IV distributions, it is monotonically increasing when moving from the median quantile to the uppermost quantile (i.e., 95%); therefore, OLS underestimates this relationship at upper quantiles. Additionally, the asymmetric relationship is more pronounced with the smirk (skew) adjusted volatility index measure in comparison to the old volatility index measure. Nonetheless, the volatility indices are ranked in terms of asymmetric volatility as follows: VIX, VSTOXX, VDAX, and VXN. The third essay examines the information content of the new-VDAX volatility index to forecast daily Value-at-Risk (VaR) estimates and compares its VaR forecasts with the forecasts of the Filtered Historical Simulation and RiskMetrics. All daily VaR models are then backtested from 1992-2009 using unconditional, independence, conditional coverage, and quadratic-score tests. It is found that the VDAX subsumes almost all information required for the volatility of daily VaR forecasts for a portfolio of the DAX30 index; implied-VaR models outperform all other VaR models. The fourth essay models the risk factors driving the swaption IVs. It is found that three factors can explain 94-97% of the variation in each of the EUR, USD, and GBP swaption IVs. There are significant linkages across factors, and bi-directional causality is at work between the factors implied by EUR and USD swaption IVs. Furthermore, the factors implied by EUR and USD IVs respond to each others’ shocks; however, surprisingly, GBP does not affect them. Second, the string market model calibration results show it can efficiently reproduce (or forecast) the volatility surface for each of the swaptions markets.

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.

Three essays on asset pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lvy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.

Three Essays on Asset Pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lévy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.

A stochastic dynamic programming approach for pricing options on stock-index futures

The aim of this thesis is to price options on equity index futures with an application to standard options on S&P 500 futures traded on the Chicago Mercantile Exchange. Our methodology is based on stochastic dynamic programming, which can accommodate European as well as American options. The model accommodates dividends from the underlying asset. It also captures the optimal exercise strategy and the fair value of the option. This approach is an alternative to available numerical pricing methods such as binomial trees, finite differences, and ad-hoc numerical approximation techniques. Our numerical and empirical investigations demonstrate convergence, robustness, and efficiency. We use this methodology to value exchange-listed options. The European option premiums thus obtained are compared to Black's closed-form formula. They are accurate to four digits. The American option premiums also have a similar level of accuracy compared to premiums obtained using finite differences and binomial trees with a large number of time steps. The proposed model accounts for deterministic, seasonally varying dividend yield. In pricing futures options, we discover that what matters is the sum of the dividend yields over the life of the futures contract and not their distribution.

Reported consumption of takeaway food and its contribution to socioeconomic inequalities in body mass index

The aim of this study was to examine whether takeaway food consumption mediated (explained) the association between socioeconomic position and body mass index (BMI). A postal-survey was conducted among 1500 randomly selected adults aged between 25 and 64 years in Brisbane, Australia during 2009 (response rate 63.7%, N=903). BMI was calculated using self-reported weight and height. Participants reported usual takeaway food consumption, and these takeaway items were categorised into "healthy" and "less healthy" choices. Socioeconomic position was ascertained by education, household income, and occupation. The mean BMI was 27.1kg/m(2) for men and 25.7kg/m(2) for women. Among men, none of the socioeconomic measures were associated with BMI. In contrast, women with diploma/vocational education (β=2.12) and high school only (β=2.60), and those who were white-collar (β=1.55) and blue-collar employees (β=2.83) had significantly greater BMI compared with their more advantaged counterparts. However, household income was not associated with BMI. Among women, the consumption of "less healthy" takeaway food mediated BMI differences between the least and most educated, and between those employed in blue collar occupations and their higher status counterparts. Decreasing the consumption of "less healthy" takeaway options may reduce socioeconomic inequalities in overweight and obesity among women but not men.

A comparison of treatment options for management of end stage kidney disease in elderly patients : a systematic review

Background Chronic kidney disease is a global public health problem of increasing prevalence. There are five stages of kidney disease, with Stage 5 indicating end stage kidney disease (ESKD) requiring dialysis or death will eventually occur. Over the last two decades there have been increasing numbers of people commencing dialysis. A majority of this increase has occurred in the population of people who are 65 years and over. With the older population it is difficult to determine at times whether dialysis will provide any benefit over non-dialysis management. The poor prognosis for the population over 65 years raises issues around management of ESKD in this population. It is therefore important to review any research that has been undertaken in this area which compares outcomes of the older ESKD population who have commenced dialysis with those who have received non-dialysis management. Objective The primary objective was to assess the effect of dialysis compared with non-dialysis management for the population of 65 years and over with ESKD. Inclusion criteria Types of participants This review considered studies that included participants who were 65 years and older. These participants needed to have been diagnosed with ESKD for greater than three months and also be either receiving renal replacement therapy (RRT) (hemodialysis [HD] or peritoneal dialysis [PD]) or non-dialysis management. The settings for the studies included the home, self-care centre, satellite centre, hospital, hospice or nursing home. Types of intervention(s)/phenomena of interest This review considered studies where the intervention was RRT (HD or PD) for the participants with ESKD. There was no restriction on frequency of RRT or length of time the participant received RRT. The comparator was participants who were not undergoing RRT. Types of studies This review considered both experimental and epidemiological study designs including randomized controlled trials, non-randomized controlled trials, quasi-experimental, before and after studies, prospective and retrospective cohort studies, case control studies and analytical cross sectional studies. This review also considered descriptive epidemiological study designs including case series, individual case reports and descriptive cross sectional studies for inclusion. This review included any of the following primary and secondary outcome measures: •Primary outcome – survival measures •Secondary outcomes – functional performance score (e.g. Karnofsky Performance score) •Symptoms and severity of end stage kidney disease •Hospital admissions •Health related quality of life (e.g. KDQOL, SF36 and HRQOL) •Comorbidities (e.g. Charlson Comorbidity index).