Highly efficient pricing of exotic derivatives under mean-reversion, jumps and stochastic volatility

The pricing of exotic derivatives continues to attract much attention from academics and practitioners alike. Despite the overwhelming interest, the task of finding a robust methodology that could derive closed-form solutions for exotic derivatives remains a difficult challenge. In addition, the level of sophistication is greatly enhanced when options are priced in a more realistic framework. This includes, but not limited to, utilising jump-diffusion models with mean-reversion, stochastic volatility, and/or stochastic jump intensity. More pertinently, these inclusions allow the resulting asset price process to capture the various empirical features, such as heavy tails and asymmetry, commonly observed in financial data. However, under such a framework, the density function governing the underlying asset price process is generally not available. This leads to a breakdown of the classical risk-neutral option valuation method via the discounted expectation of the final payoff. Furthermore, when an analytical expression for the option pricing formula becomes available, the solution is often complex and in semi closed-form. Hence, a substantial amount of computational time is required to obtain the value of the option, which may not satisfy the efficiency demanded in practice. Such drawbacks may be remedied by utilising numerical integration techniques to price options more efficiently in the Fourier domain instead, since the associated characteristic functions are more readily available. This thesis is concerned primarily with the efficient and accurate pricing of exotic derivatives under the aforementioned framework. We address the research opportunity by exploring the valuation of exotic options with numerical integration techniques once the associated characteristic functions are developed. In particular, we advocate the use of the novel Fourier-cosine (COS) expansions, and the more recent Shannon wavelet inverse Fourier technique (SWIFT). Once the option prices are obtained, the efficiency of the two techniques are benchmarked against the widely-acclaimed fast Fourier transform (FFT) method. More importantly, we perform extensive numerical experiments and error analyses to show that, under our proposed framework, not only is the COS and SWIFT methods more efficient, but are also highly accurate with exponential rate of error convergence. Finally, we conduct a set of sensitivity analyses to evaluate the models’ consistency and robustness under different market condition

Extreme Risk, Value-At-Risk And Expected Shortfall In The Gold Market

Extreme value theory (EVT) has been widely applied in fields such as hydrology and insurance. It is a tool used to reflect on probabilities associated with extreme, and thus rare, events. EVT is useful in modeling the impact of crashes or situations of extreme stress on investor portfolios. It describes the behavior of maxima or minima in a time series, i.e., tails of a distribution. In this paper, we propose the use of generalised Pareto distribution (GPD) to model extreme returns in the gold market. This method provides effective means of estimating tail risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). This is confirmed by various backtesting procedures. In particular, we utilize the Kupiec unconditional coverage test and the Christoffersen conditional coverage test for VaR backtesting, while the Bootstrap test is used for ES backtesting. The results indicate that GPD is superior to the traditional Gaussian and Student’s t models for VaR and ES estimations

Generalized Hyperbolic Distributions And Value-At-Risk Estimation For The South African Mining Index

South Africa is a cornucopia of mineral riches and the performance of its mining industry has significant impacts on the economy. Hence, an accurate distributional assumption of the underlying mining index returns is imperative for the forecasting and understanding of the financial market. In this paper, we propose three subclasses of the generalized hyperbolic distributions as appropriate models for the Johannesburg Stock Exchange (JSE) Mining Index returns. These models are shown to outperform the traditional assumption of normality and accommodate for a number of stylized features, such as excess kurtosis and volatility clustering, embedded within the financial data. The models are compared using the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC) and log-likelihoods. In addition, Value-at-Risk (VaR) estimation and backtesting were also performed to test the extreme tails. The various criteria utilized suggest the generalized hyperbolic (GH) skew Student’s t-distribution as the most robust model for the South African Mining Index returns

The Performance Of Linear Versus Non-Linear Models In Forecasting Returns On The Johannesburg Stock Exchange

In this paper we provide a comprehensive comparison of the predictive accuracy of linear and non-linear models when forecasting financial returns, using a number of macroeconomic variables, on the Johannesburg Stock Exchange. We implement a range of linear specifications, Markov switching ARMA and Dynamic Regression models, and univariate models in which the conditional heteroskedasticity is captured by GARCH or EGARCH innovations. Our results indicate that Markov switching models provide the most significant in-sample fit. However, results for the stable portion of the out-of-sample period and the recent recovery period are mixed with both EGARCH-based linear models and 2-state Dynamic Regression models outperforming the alternatives. Over the market crisis period we find that the forecast performance of the nonlinear models is worse than that of the linear models, which suggests that the benefit of the nonlinear treatment of conditional volatility diminishes over this period

A Comparative Study On The Effects Of Market Crisis And Recessions On The Performance Of Defensive Sectors

Research has shown that the performance of defensive sectors is consistent during a recession. However, whether such consistency still holds during periods of market crisis, which is considered an economic anomaly, is not immediately obvious. This paper proposes a further investigation into the performance of defensive sectors during a market crisis, particularly on the Johannesburg Stock Exchange (JSE). It will investigate whether these defensive sectors retained their non-cyclical nature during the recent market crisis (01/12/2007 – 31/08/2009) by comparing their performance during the crisis to their performance in South Africa’s most recent recession (1/12/1996 – 31/08/1999). Our investigation is carried out by assessing the betas of these sectors across both periods of focus. It then adds to the assessment of the betas by comparing the variances of the defensive sectors in both periods to determine whether there is a statistically significant difference. Our study is unique in that it proposes to investigate with the different market capitalisations (large, medium, and small) across the defensive sectors. The results of this study give conclusive evidence that defensive sectors do indeed remain non-cyclical during a market crisis. We can therefore give recommendations on switching to defensive strategies with greater certainty of the performance of defensive sectors during this economic anomaly

Pneumothorax and mortality in the mechanically ventilated SARS patients: a prospective clinical study

INTRODUCTION: Pneumothorax often complicates the management of mechanically ventilated severe acute respiratory syndrome (SARS) patients in the isolation intensive care unit (ICU). We sought to determine whether pneumothoraces are induced by high ventilatory pressure or volume and if they are associated with mortality in mechanically ventilated SARS patients. METHODS: We conducted a prospective, clinical study. Forty-one mechanically ventilated SARS patients were included in our study. All SARS patients were sedated and received mechanical ventilation in the isolation ICU. RESULTS: The mechanically ventilated SARS patients were divided into two groups either with or without pneumothorax. Their demographic data, clinical characteristics, ventilatory variables such as positive end-expiratory pressure, peak inspiratory pressure, mean airway pressure, tidal volume, tidal volume per kilogram, respiratory rate and minute ventilation and the accumulated mortality rate at 30 days after mechanical ventilation were analyzed. There were no statistically significant differences in the pressures and volumes between the two groups, and the mortality was also similar between the groups. However, patients developing pneumothorax during mechanical ventilation frequently expressed higher respiratory rates on admission, and a lower PaO(2)/FiO(2 )ratio and higher PaCO(2 )level during hospitalization compared with those without pneumothorax. CONCLUSION: In our study, the SARS patients who suffered pneumothorax presented as more tachypnic on admission, and more pronounced hypoxemic and hypercapnic during hospitalization. These variables signaled a deterioration in respiratory function and could be indicators of developing pneumothorax during mechanical ventilation in the SARS patients. Meanwhile, meticulous respiratory therapy and monitoring were mandatory in these patients

Highly Efficient Shannon Wavelet-based Pricing of Power Options under the Double Exponential Jump Framework with Stochastic Jump Intensity and Volatility

We propose a highly efficient and accurate valuation method for exotic-style options based on the novel Shannon wavelet inverse Fourier technique (SWIFT). Specifically, we derive an efficient pricing methods for power options under a more realistic double exponential jump model with stochastic volatility and jump intensity. Inclusion of such innovations may accommodate for the various stylised facts observed in the prices of financial assets, and admits a more realistic pricing framework as a result. Following the derivation of our SWIFT pricing method for power options, we perform extensive numerical experiments to analyse both the method's accuracy and efficiency. In addition, we investigate the sensitivities in the resulting prices, as well as the inherent errors, to changes in the underlying market conditions. Our numerical results demonstrate that the SWIFT method is not only more efficient when benchmarked to its close competitors, such as the Fourier- cosine (COS) and the widely-acclaimed fast-Fourier transform (FFT) methods, but it is also robust across a range of different market conditions exhibiting exponential error convergence

Anti-Inflammatory Activities of Cinnamomum cassia Constituents In Vitro and In Vivo

We have investigated the anti-inflammatory effects of Cinnamomum cassia constituents (cinnamic aldehyde, cinnamic alcohol, cinnamic acid, and coumarin) using lipopolysaccharide (LPS)-stimulated mouse macrophage (RAW264.7) and carrageenan (Carr)-induced mouse paw edema model. When RAW264.7 macrophages were treated with cinnamic aldehyde together with LPS, a significant concentration-dependent inhibition of nitric oxide (NO), tumor necrosis factor (TNF-α), and prostaglandin E2 (PGE2) levels productions were detected. Western blotting revealed that cinnamic aldehyde blocked protein expression of inducible nitric oxide synthase (iNOS), cyclooxygenase-2 (COX-2), nuclear transcription factor kappa B (NF-κB), and IκBα, significantly. In the anti-inflammatory test, cinnamic aldehyde decreased the paw edema after Carr administration, and increased the activities of catalase (CAT), superoxide dismutase (SOD), and glutathione peroxidase (GPx) in the paw tissue. We also demonstrated cinnamic aldehyde attenuated the malondialdehyde (MDA) level and myeloperoxidase (MPO) activity in the edema paw after Carr injection. Cinnamic aldehyde decreased the NO, TNF-α, and PGE2 levels on the serum level after Carr injection. Western blotting revealed that cinnamic aldehyde decreased Carr-induced iNOS, COX-2, and NF-κB expressions in the edema paw. These findings demonstrated that cinnamic aldehyde has excellent anti-inflammatory activities and thus has great potential to be used as a source for natural health products

Hispolon Protects against Acute Liver Damage in the Rat by Inhibiting Lipid Peroxidation, Proinflammatory Cytokine, and Oxidative Stress and Downregulating the Expressions of iNOS, COX-2, and MMP-9

The hepatoprotective potential of hispolon against carbon tetrachloride (CCl4)-induced liver damage was evaluated in preventive models in rats. Male rats were intraperitoneally treated with hispolon or silymarin once daily for 7 consecutive days. One hour after the final hispolon or silymarin treatment, the rats were injected with CCl4. Administration with hispolon or silymarin significantly decreased the alanine aminotransferase (ALT) and aspartate aminotransferase (AST) levels in serum and increased the activities of superoxide dismutase (SOD), catalase, glutathione peroxidase (GPx), and glutathione (GSH) content and decreased the malondialdehyde (MDA) content in liver compared with CCl4-treated group. Liver histopathology also showed that hispolon reduced the incidence of liver lesions induced by CCl4. In addition, hispolon decreased nitric oxide (NO) production and tumor necrosis factor (TNF-α), inducible NO synthase (iNOS) and cyclooxygenase-2 (COX-2) activation in CCl4-treated rats. We also examined the involvement of matrix metalloproteinase (MMP)-9 in the development of CCl4-induced liver damage in rats. Hispolon inhibited the expression of MMP-9 protein, indicating that MMP-9 played an important role in the development of CCl4-induced rat liver damage. Therefore, we speculate that hispolon protects rats from liver damage through their prophylactic redox balancing ability and anti-inflammation capacity