Pricing derivatives with stochastic volatility

This Ph.D. thesis contains 4 essays in mathematical finance with a focus on pricing Asian option (Chapter 4), pricing futures and futures option (Chapter 5 and Chapter 6) and time dependent volatility in futures option (Chapter 7). In Chapter 4, the applicability of the Albrecher et al.(2005)'s comonotonicity approach was investigated in the context of various benchmark models for equities and com- modities. Instead of classical Levy models as in Albrecher et al.(2005), the focus is the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and the Schwartz (1997) two-factor model. It is shown that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by-product delivers super-hedging strategies which can be easily implemented. In Chapter 5, two types of three-factor models were studied to give the value of com- modities futures contracts, which allow volatility to be stochastic. Both these two models have closed-form solutions for futures contracts price. However, it is shown that Model 2 is better than Model 1 theoretically and also performs very well empiri- cally. Moreover, Model 2 can easily be implemented in practice. In comparison to the Schwartz (1997) two-factor model, it is shown that Model 2 has its unique advantages; hence, it is also a good choice to price the value of commodity futures contracts. Fur- thermore, if these two models are used at the same time, a more accurate price for commodity futures contracts can be obtained in most situations. In Chapter 6, the applicability of the asymptotic approach developed in Fouque et al.(2000b) was investigated for pricing commodity futures options in a Schwartz (1997) multi-factor model, featuring both stochastic convenience yield and stochastic volatility. It is shown that the zero-order term in the expansion coincides with the Schwartz (1997) two-factor term, with averaged volatility, and an explicit expression for the first-order correction term is provided. With empirical data from the natural gas futures market, it is also demonstrated that a significantly better calibration can be achieved by using the correction term as compared to the standard Schwartz (1997) two-factor expression, at virtually no extra effort. In Chapter 7, a new pricing formula is derived for futures options in the Schwartz (1997) two-factor model with time dependent spot volatility. The pricing formula can also be used to find the result of the time dependent spot volatility with futures options prices in the market. Furthermore, the limitations of the method that is used to find the time dependent spot volatility will be explained, and it is also shown how to make sure of its accuracy.

Econometric models in foreign exchange market

According to the significance of the econometric models in foreign exchange market, the purpose of this research is to give a closer examination on some important issues in this area. The research covers exchange rate pass-through into import prices, liquidity risk and expected returns in the currency market, and the common risk factors in currency markets. Firstly, with the significant of the exchange rate pass-through in financial economics, the first empirical chapter studies on the degree of exchange rate pass-through into import in emerging economies and developed countries in panel evidences for comparison covering the time period of 1970-2009. The pooled mean group estimation (PMGE) is used for the estimation to investigate the short run coefficients and error variance. In general, the results present that the import prices are affected positively, though incompletely, by the exchange rate. Secondly, the following study addresses the question whether there is a relationship between cross-sectional differences in foreign exchange returns and the sensitivities of the returns to fluctuations in liquidity, known as liquidity beta, by using a unique dataset of weekly order flow. Finally, the last study is in keeping with the study of Lustig, Roussanov and Verdelhan (2011), which shows that the large co-movement among exchange rates of different currencies can explain a risk-based view of exchange rate determination. The exploration on identifying a slope factor in exchange rate changes is brought up. The study initially constructs monthly portfolios of currencies, which are sorted on the basis of their forward discounts. The lowest interest rate currencies are contained in the first portfolio and the highest interest rate currencies are in the last. The results performs that portfolios with higher forward discounts incline to contain higher real interest rates in overall by considering the first portfolio and the last portfolio though the fluctuation occurs.

The regulation of AMP-activated protein kinase by vascular endothelial growth factor

The function of the vascular endothelium is to maintain vascular homeostasis, by providing an anti-thrombotic, anti-inflammatory and vasodilatory interface between circulating blood and the vessel wall, meanwhile facilitating the selective passage of blood components such as signaling molecules and immune cells. Dysfunction of the vascular endothelium is implicated in a number of pathological states including atherosclerosis and hypertension, and is thought to precede atherogenesis by a number of years. Vascular endothelial growth factor A (VEGF) is a crucial mitogenic signaling molecule, not only essential for embryonic development, but also in the adult for regulating both physiological and pathological angiogenesis. Previous studies by our laboratory have demonstrated that VEGF-A activates AMP-activated protein kinase (AMPK), the downstream component of a signaling cascade important in the regulation of whole body and cellular energy status. Furthermore, studies in our laboratory have indicated that AMPK is essential for VEGF-A-stimulated vascular endothelial cell proliferation. AMPK activation typically stimulates anabolic processes and inhibits catabolic processes including cell proliferation, with the ultimate aim of redressing energy imbalance, and as such is an attractive therapeutic target for the treatment of obesity, metabolic syndromes, and type 2 diabetes. Metabolic diseases are associated with adverse cardiovascular outcomes and AMPK activation is reported to have beneficial effects on the vascular endothelium. The mechanism by which VEGF-A stimulates AMPK, and the functional consequences of VEGF-A-stimulated AMPK activation remain uncertain. The present study therefore aimed to identify the specific mechanism(s) by which VEGF-A regulates the activity of AMPK in endothelial cells, and how this might differ from the activation of AMPK by other agents. Furthermore, the role of AMPK in the pro-proliferative actions of VEGF-A was further examined. Human aortic and umbilical vein endothelial cells were therefore used as a model system to characterise the specific effect(s) of VEGF-A stimulation on AMPK activation. The present study reports that AMPK α1 containing AMPK complexes account for the vast majority of both basal and VEGF-A-stimulated AMPK activity. Furthermore, AMPK α1 is localized to the endoplasmic reticulum when sub-confluent, but translocated to the Golgi apparatus when cells are cultured to confluence. AMPK α2 appears to be associated with a structural cellular component, but neither α1 nor α2 complexes appear to translocate in response to VEGF-A stimulation. The present study confirms previous reports that when measured using the MTS cell proliferation assay, AMPK is required for VEGF-A-stimulated endothelial cell proliferation. However, parallel experiments measuring cell proliferation using the Real-Time Cell Analyzer xCELLigence system, do not agree with these previous reports, suggesting that AMPK may in fact be required for an aspect of mitochondrial metabolism which is enhanced by VEGF-A. Studies into the mitochondrial activity of endothelial cells have proved inconclusive at this time, but further studies into this are warranted. During previous studies in our laboratory, it was suggested that VEGF-A-stimulated AMPK activation may be mediated via the diacylglycerol (DAG)-sensitive transient receptor potential cation channel (TRPCs -3, -6 or -7) family of ion channels. The present study can neither confirm, nor exclude the expression of TRPCs in vascular endothelial cells, nor rule out their involvement in VEGF-A-stimulated AMPK activation; more specific investigative tools are required in order to characterise their involvement. Furthermore, nicotinic acid adenine dinucleotide phosphate (NAADP)-stimulated Ca2+ release from acidic intracellular organelles is not required for AMPK activation by VEGF-A. Despite what is known about the mechanisms by which AMPK is activated, far less is known concerning the downregulation of AMPK activity, as observed in human and animal models of metabolic disease. Phosphorylation of AMPK α1 Ser485 (α2 Ser491) has recently been characterised as a mechanism by which the activity of AMPK is negatively regulated. We report here for the first time that VEGF-A stimulates AMPK α1 Ser485 phosphorylation independently of the previously reported AMPK α1 Ser485 kinases Akt (protein kinase B) and ERK1/2 (extracellular signal-regulated kinase 1/2). Furthermore, inhibition of protein kinase C (PKC), the activity of which is reported to be elevated in metabolic disease, attenuates VEGF-A- and phorbol 12-myristate 13-acetate (PMA)-stimulated AMPK α1 Ser485 phosphorylation, and increases basal AMPK activity. In contrast to this, PKC activation reduces AMPK activity in human vascular endothelial cells. Attempts to identify the PKC isoform responsible for inhibiting AMPK activity suggest that it is one (or more) of the Ca2+-regulated DAG-sensitive isoforms of PKC, however cross regulation of PKC isoform expression has limited the present study. Furthermore, AMPK α1 Ser485 phosphorylation was inversely correlated with human muscle insulin sensitivity. As such, enhanced AMPK α1 Ser485 phosphorylation, potentially mediated by increased PKC activation may help explain some of the reduced AMPK activity observed in metabolic disease.