The option pricing model introduced by Black-Scholes in 1974 gained wide acceptance for its simplicity but was inefficient in pricing options as it relied on implied volatility. Despite the evolution of various versions of option pricing models since their seminal work, little progress had been documented on the use of implied volatility, leaving Black-Scholes to be a mathematical identity to calculate the instantaneous implied volatility as it fails to be an efficient pricing equation. Although interpreted as market expectation of future volatility of stocks, implied volatility is literally a black box that captures market information that is not specifically known yet also internally inconsistent (e.g., having a different implied volatility surface for put and call options). The four main objectives of this thesis are: first, to empirically studying the performance of the Oscillator model developed by Baaquie (2019) and examining its efficiency in pricing options as compared to Black-Scholes model. The Oscillator model has only two sets of parameters in addition to the classical form of Black-Scholes; one to model for the underlying stochastic evolution of the stock price, and the second are of market time. Market time is a behavioural parameter introduced by Baaquie and Bouchaud (2004) which scales the time to maturity to capture the market sentiment of the underlying instrument. This thesis also introduced an alternative version of Black-Scholes by adjusting it for market time. Second, the thesis tested the put-call parity violation. Third, the thesis tested three main option hedging Greeks; Delta, Gamma, and Theta, which are partial differentiations of the option pricing equation. Fourth, the thesis discussed the calibrated output and parameters' behaviour to provide insights into the implied volatility information content and gain new understanding of the parametric gap of Black-Scholes particularly in the light of the Oscillator and Black-Scholes models adjusted for market time.

Over the last few years, a number of archaeological discoveries have been made that have raised questions and opened up possibly new understanding of the ancient history of Bangladesh. The findings at Wari-Bateshwar point to the possibility of a city-based civilization in the Ganges-Brahmaputra delta dating back to 4,000 BC. Another new discovery, which is being actively studied, is the possible existence of a branch of the Silk Road going through Bangladesh. A theoretical framework is required to guide an investigation as well as to acquire and interpret data. This paper explores a framework based on the existence of a southern branch of the Silk Road going through Bangladesh; and then goes on to study the impact that the existence of this route could have had on the history of Bangladesh and, in particular, on the advent of Islam.

In the Islamic finance capital market spectrum, the potential of mudharabah and musyarakah sukuk is hampered with criticism by Shariah scholars. Among the criticisms include the presence of uncertainties surrounding sukuk returns, the risk of losses that the rabbul-mal (investors) have to bear, and the need to mitigate agency costs (for mudharabah contracts). This have made it a deterrent for both issuers and investors in seeing the instrument as a viable alternative to debt-based sukuk structures. This study proposes an improvement to musyarakah sukuk. It begins with a qualitative examination of the structure of corporate mudharabah and musyarakah sukuk issued in Malaysia. The examination finds risk-sharing sukuk structures in Malaysia contain features that supresses the risk sharing element between the sukuk investors and issuer. Findings from qualitative analysis is supported by generalized method of moments (GMM) and threshold analysis. Based on the sample of 86 corporate mudharabah and musyarakah sukuk issuances, the introduction of partnership sukuk in the firm's capital structure is found to be insignificant in affecting both firm risk and firm performance. The present partnership sukuk structure is then modified to incorporate variable returns (coupon payments) proportionate to the firm's net profits and variable principal repayment proportionate to the firm's total assets value. This study finds that when sukuk returns are made variable, sukuk investors are able to earn better/ equitable returns compared what they are earning in the current sukuk structure.

The history of China is briefly reviewed to ascertain the features that are common to the various dynasties. Our study shows that China has repeatedly gone through a historical phase of fragmentation and a historical phase of unification. In our view, the single most important factor in the unity, stability and longevity of a dynasty is the system for determining the succession of the emperor. Given the vastly changed circumstances of the present era, we discuss the relevance of China's historical pattern of fragmentation and unification. The contemporary rise of China is shown to follow a pattern that is similar to the case of many previous dynasties. A few tentative predictions are made about the future course of China. An appendix provides a brief summary of the history of China since its first unification in 221 BC.

This paper applies Zipf rank approach to measure how long it will take for the individual economy to reach the final state of equilibrium by using local-level data of China's urban areas. The indicators, the gross domestic product (GDP) per capita and the market capitalization (MCAP per capita of 150 major cities in China are used for analyzing their convergence. Besides, the power law relationship is examined for GDP and MCAP. Our findings show that, compared to the classical approaches:β-convergence and σ-convergence, the Zipf ranking predicts that, in approximately 16 years, all the major cities in China will reach comparable values of GDP per capita. However,the MCAP per capita tends to follow the periodic fluctuation of the economic cycle, while the mean-log derivation (MLD) confirms the results of our study. Moreover, GDP per capita and MCAP per capita follow a power law with an average value of α = 0.41 which is higher than α= 0.38 obtained based on a large number of countries around the world.

This study empirically investigates the stochastic corporate coupon bond pricing model proposed by Baaquie (2020b) and the pioneering structural risky bond pricing model proposed by Merton (1974). Merton's risky zero-coupon bond pricing model is converted into a portfolio of zeros to study corporate coupon bonds. The seminal work of Merton (1974) is considered as the backbone of corporate bond pricing. Merton's model is based on the generalization of Black and Scholes (1973) option pricing theory. The coupon bond pricing model, proposed by Baaquie (2020b), is based on Merton's bond pricing theory, but coupons are stochastic. Hence, we can call it a stochastic coupon bond pricing model where coupon varies from payment to payment based on the issuer's performance. The proposed model of stochastic coupons has a built-in hedge for the issuer and has the feature of profit and loss sharing between investor and issuer, making it a viable instrument for Islamic finance. The model can be calibrated and tested using market data. This thesis is structured into six chapters, including an introductory chapter, a review chapter, three core chapters, and a concluding chapter. The introductory chapter highlights the motivation, problem statement, and objectives of this study. In review chapter, theoretical and empirical works along with derivation of Merton (1974) and Baaquie (2020b) are reviewed. In conclusion, a summary of the thesis, policy recommendation, limitation, and future directions are discussed. In the third chapter of the thesis, we investigate the following three questions. First, how can one use the proposed model for an empirical study of fixed coupon bonds, since apparently, the model implies stochastic coupons being paid continuously? Second, how the newly introduced parameters, three exogenous parameters - market time and firm's effective valuation and two endogenous parameters - stochastic coupon and firm value volatility, behave for different categories of the bonds and contribute to the improvement of the model's fit? Third, does the stochastic coupon model estimate the bonds' market price more accurately compared to Merton's model? To answer these questions, we have shown how to calibrate and test the stochastic corporate coupon bond pricing model along with newly introduced parameters using a sample of fixed coupon bonds issued by the US corporations. Estimated coupon bond prices from the stochastic model are then compared with the estimated prices from the extended version, portfolio of zeros, of the Merton model.

A statistical generalization of microeconomics has been made in Baaquie (2013), where the market price of every traded commodity, at each instant of time, is considered to be an independent random variable. The dynamics of commodity market prices is modeled by an action functional and the focus of this paper is to empirically determine the action functionals for different commodities. The correlation functions of the model are defined using a Feynman path integral. The model is calibrated using the unequal time correlation of the market commodity prices as well as their cubic and quartic moments using a perturbation expansion. The consistency of the perturbation expansion is verified by a numerical evaluation of the path integral. Nine commodities drawn from the energy, metal and grain sectors are studied and their market behavior is described by the model to an accuracy of over 90% using only six parameters. The paper empirically establishes the existence of the action functional for commodity prices that was postulated to exist in Baaquie (2013)

Why is rubber elastic? Why are leaves green? Why can a gecko climb a wall? Answering these and a myriad of other puzzles of nature, Exploring Integrated Science shows how the simplest questions that arise from our daily experiences can lead us through a chain of reasoning that explains some of the most fascinating principles of science. Written in a non-technical entertaining style to engage those without a science background while maintaining the academic rigor required by more advanced readers, the book follows a unique format that enhances the learning process. Each chapter begins with a pertinent question that forms the basis for explaining a scientific principle. Step by step, the text then delves into the more sophisticated scientific matter necessary for providing insight into the question presented, elucidating key principles and concepts. Each chapter contains a summary highlighting the salient points, answers the question definitively, and concludes with a series of exercises to test readers' assimilation of the material.

Exploring the Invisible Universe covers the gamut of topics in advanced modern physics and provides extensive and well substantiated answers to these questions and many more. Discussed in a non-technical, yet also non-trivial manner, are topics dominated by invisible things - such as Black Holes and Superstrings as well as Fields, Gravitation, the Standard Model, Cosmology, Relativity, the Origin of Elements, Stars and Planetary Evolution, and more. Just giving the answer, as so many books do, is really not telling anything at all. To truly answer the "why" questions of nature, one needs to follow the chain of reasoning that scientists have used to come to the conclusions they have.

In earlier centuries kings and governments employed astrologists to help them take the best decisions. Present-day governments no longer employ astrologists but still have no clear analytical tool to replace them. Over the past two decades we have developed a methodology for the scientific investigation of recurrent historical events. It consists in two steps. (i) Identification and comparison of historical episodes driven by a common mechanism. (ii) Under the reasonable assumption that what has happened several times in the past is likely to happen again, one then derives testable predictions. This of course is nothing other than the protocol used in experimental science when exploring new phenomena. We believe such a tool can give decision makers much better insight ...

Present day Islamic economics is about 60 years old and takes its foundation to be the Qur'an as well as the way (sunnat) of Prophet Muhammad (pbuh). Views of Muslim scholars vary considerably regarding Islamic economics, from considering it to be: a) branch of conventional mainstream economics; b) a discipline that is neither capitalist nor socialist; c) a discipline that is guided by Islamic law in all its aspects. There have not yet emerged concepts or principles that are widely accepted by Muslim scholars as the foundation of Islamic economics and finance. The main advance made so far has been in Islamic finance, a branch of Islamic economics, where a number of rules are commonly accepted. These are: a) the prohibition of riba (interest), rishwah (bribery, corruption) gharar (deception), jahl (profiting from others ignorance) and mysir (gambling and speculation) in all financial contracts; b) all investments must be made in the permissible sector of the real economy; with the investor sharing in the profit, loss and risks of the enterprise.

The linearized Hamiltonian model is proposed to extend the London Interbank Offered Rate (LIBOR) Market Model (LMM). Firstly, we studied the Hamiltonian of LMM in the framework of quantum finance, and the nontrivial upper triangle form of LIBOR drift is derived. The linearized Hamiltonian is derived to improve the explanatory capability of the model for market data. Our approach uses one more parameter to explain the initial condition and the model can be used to calibrate LIBORs with extremely high accuracy. Furthermore, the market time index is required for applying the model to multi-LIBOR, and the results imply that the LIBOR future time lattice becomes shorter as one goes from near future to distant future.

Merton has proposed a model for contingent claims on a firm as an option on the firms value, and is based on a generalization of the Black-Scholes stochastic equation (Merton, 1974). A special case of Merton's model is proposed - based on the quantum oscillator - for pricing options. Two cases of the option price are obtained: both these cases yield possible candidates for the generalization of the Black-Scholes option pricing formula. However, one of the proposed option prices does not obey the martingale condition and the other does not yield the correct discounting of future cash flows. For these reasons, the option prices do not obey put-call parity. The options can, however, be used to approximately price market traded options. The oscillator model for the option price has an extra parameter that is absent for the Black-Scholes case. Similar to the model studied by Baaquie et al. (2014), which that does not obey put-call parity, the option's price can be studied empirically and the extra parameter in the model could, in principal, generate implied volatility.

A statistical generalization of microeconomics has been made in Baaquie (2013). In Baaquie et al. (2015), the market behavior of single commodities was analyzed and it was shown that market data provides strong support for the statistical microeconomic description of commodity prices. The case of multiple commodities is studied and a parsimonious generalization of the single commodity model is made for the multiple commodities case. Market data shows that the generalization can accurately model the simultaneous correlation functions of up to four commodities. To accurately model five or more commodities, further terms have to be included in the model. This study shows that the statistical microeconomics approach is a comprehensive and complete formulation of microeconomics, and which is independent to the mainstream formulation of microeconomics.

The industry standard Black-Scholes option pricing formula is based on the current value of the underlying security and other fixed parameters of the model. The Black-Scholes formula, with a fixed volatility, cannot match the market's option price; instead, it has come to be used as a formula for generating the option price, once the so called implied volatility of the option is provided as additional input. The implied volatility not only is an entire surface, depending on the strike price and maturity of the option, but also depends on calendar time, changing from day to day. The point of view adopted in this paper is that the instantaneous rate of return of the security carries part of the information that is provided by implied volatility, and with a few (time-independent) parameters required for a complete pricing formula. An option pricing formula is developed that is based on knowing the value of both the current price and rate of return of the underlying security which in physics is called velocity. Using an acceleration Lagrangian model based on the formalism of quantum mathematics, we derive the pricing formula for European call options. The implied volatility of the market can be generated by our pricing formula. Our option price is applied to foreign exchange rates and equities and the accuracy is compared with Black-Scholes pricing formula and with the market price.

This paper develops a volatility formula for option on an asset from an acceleration Lagrangian model and the formula is calibrated with market data. The Black-Scholes model is a simpler case that has a velocity dependent Lagrangian. The acceleration Lagrangian is defined, and the classical solution of the system in Euclidean time is solved by choosing proper boundary conditions. The conditional probability distribution of final position given the initial position is obtained from the transition amplitude. The volatility is the standard deviation of the conditional probability distribution. Using the conditional probability and the path integral method, the martingale condition is applied, and one of the parameters in the Lagrangian is fixed. The call option price is obtained using the conditional probability and the path integral method.

This paper develops a model to describe the unequal time correlation between rate of returns of different stocks. A non-trivial fourth order derivative Lagrangian is defined to provide an unequal time propagator, which can be fitted to the market data. A calibration algorithm is designed to find the empirical parameters for this model and different denoising methods are used to capture the signals concealed in the rate of return. The detailed results of this Gaussian model show that the different stocks can have strong correlation and the empirical unequal time correlator can be described by the model's propagator. This preliminary study provides a novel model for the correlator of different instruments at different times.

We study the range accrual swap in the quantum finance formulation of the LIBOR market model (LMM). It is shown that the formulation can exactly price the path dependent instrument. An approximate price is obtained as an expansion in the volatility of Libor. The Monte Carlo simulation method is used to study the nonlinear domain of the model and determine the range of validity of the approximate formula. The price of accrual swap is analyzed by generating daily sample values by simulating a two dimension Gaussian quantum field.

The global bond market is the main component of the capital market, being about three times larger than the global equity markets. In 2009, the global bond market (total outstanding debt) was estimated to be $82.2 trillion; the US dominated the bond market with th outstanding U.S. bond debt at approximately $35.2 trillion. Risk-free forward interest rates - and their realization by US Treasury bonds as the leading exemplar - have been studied extensively. The bond market considers US Treasury bonds as being risk-free instruments and consequently have the lowest yields.

The simulation of the Libor Market Model (LMM) is extensively studied in the frame work of quantum finance.The imperfectly correlated Libor rates are simulated based on a Gaussian quantum field and a recursion equation of nontrivial stochastic drift. The Libor options are studied using both the simulation method and the analytical formula. The caplet price of simulation is compared with Black's caplet formula which can be exactly derived from the LMM. The invariance of caplet price for different forward bond numeraire is verified by using the simulation. The simulation results for coupon bond options and swaptions are compared with the approximate price, which are limited for the reason that the approximate price is derived using the small volatility expansion. The simulation method is shown to have great potential in the application of pricing interest rate instruments.

The expression "wage transition" refers to the fact that over the past three decades in almost all developed economies wage increases have leveled off. There has been a widening divergence and decoupling between wages on the one hand and GDP per capita on the other hand. Yet, in China wages and GDP per capita climbed in sync (at least up to now). In the first part of the paper we present comparative statistical evidence which measures the extent of the wage transition effect. In a second part we consider the reasons of this phenomenon, in particular we explain how the transfers of labor from low productivity sectors (such as agriculture) to high productivity sectors (such as manufacturing) are the driver of productivity growth, particularly through their synergetic effects. Although rural flight represents only one of these effects, it is certainly the most visible because of the geographical relocation that it implies; it is also the most well-defined statistically. Moreover, it will be seen that it is a good indicator of the overall productivity and attractiveness of the non-agricultural sector. Because this model accounts fairly well for the observed evolution in industrialized countries, we use it to predict the rate of Chinese economic growth in coming decades. Our forecast for the average annual growth of real wages ranges from 4% to 6% depending on how well China will control offshoring and the development of its healthcare sector.