Momentum-Driven Option Pricing: Integrating Intraday Trends into Financial Derivative Models

This thesis consists of three essays on inferring information from option contracts and other financial derivatives in the U.S. market as well as in the international markets. The first essay examines corporate bankruptcy probabilities inferred from option prices and credit default swaps (CDS) spreads around the 2008 financial crisis in the U.S. market. Option pricing framework is used where the risk-neutral density of the underlying asset is assumed to be a mixture of two lognormals augmented with a probability of default, to calibrate to the market option prices. The CDS model assumes a constant default probability which is solved from the non-linear equation that equates the present value of expected premium payments with the present value of expected payoffs. The essay documents that both sources provide ex-ante bankruptcy probabilities, but there is no significant evidence suggesting one predicts the other. The second essay constructs volatility indices for 15 markets around the world and examines implied volatility spillover between these markets. Volatility indices are constructed using option prices based on the new VIX methodology with modification to address its limitations. Spillover effects are then examined using vector autoregressive analysis, impulse response functions and forecast error variance decomposition. Empirical results show that the U.S. is unambiguously the dominant source of uncertainty in the world. Correlation between markets largely depends on geographical proximity. The findings support the notion of informationally efficient international stock markets, in that information transmitted from one market to another is processed within one or two days. The third essay further investigates spillover effects in variance risk premiums, which has been interpreted as the difference between the realised variance under the physical measure and the risk-neutral measure. Realized variance under the physical measure is constructed for each market using the HAR-RV model, which is able to capture long-memory characteristic of volatility. Risk-neutral expectation of future variance is approximated by a portfolio of option contracts, as calculated in the second essay. Steps are taken to address serial correlation and dependence, and variance risk premium spillovers are examined using vector autoregressive analysis, impulse response functions, and Granger Causality tests. The findings are consistent with those found in implied volatility spillovers. The U.S. market is the distributor of uncertainty in the global market. Information transmitted from one market to another is quickly digested, but it may take longer in crisis period due to greater uncertainty.

Stochastic volatility of underlying assets has been shown to affect significantly the price of many financial derivatives. In particular, a fast mean-reverting factor of the stochastic volatility plays a major role in the pricing of options. This paper deals with the interest rate model dependence of the stochastic volatility impact on defaultable interest rate derivatives. We obtain an asymptotic formula of the price of defaultable bonds and bond options based on a quadratic term structure model and investigate the stochastic volatility and default risk effects and compare the results with those of the Vasicek model.

Option and other financial derivatives are becoming more and more important in financial market. As one of the most important financial activities, reasonable option pricing not only makes the trade market steady and orderly, but also provides investors valuable information to make decisions. As the growth of the financial data and the inherent complexity of option pricing methods, option pricing is facing more and more challenges, such as the random problem of solution and time consuming. Monte Carlo is one of the most common used methods in option pricing. However, in order to obtain a better solution, Monte Carlo method requires huge number of simulations. It may be up to tens of millions of simulations and generates large amounts of data. That is, Monte Carlo simulation is inherently computingintensive. Meanwhile, the implementation of traditional parallel Monte Carlo method is complicated. Massive data and huge computational cost limit the further application of Monte Carlo method. In order to deal with the above problems, this paper researches the efficient B-S option pricing problem with Monte Carlo and proposes a parallel Monte Carlo method for option pricing. This method extends the Monte Carlo simulation to the MapReduce framework, which is a simple powerful parallel programming technique. It divides the Monte Carlo simulation into three phases and they are implemented with one MapReduce job. With the help of a large-scale cluster computing power and the excellent scalability of MapReduce, the proposed method scales well and solves the option pricing efficiently. The experimental results also demonstrates the good characteristic of speedup and sizeup.

This essay explores the evolution of option pricing models, tracing their development from the foundational Black-Scholes model to more advanced frameworks such as the Heston model and beyond. Beginning with an introduction to option pricing theory, the essay discusses the origins of the Black-Scholes model and its assumptions, as well as the challenges and limitations it faces. It then examines the extension of the Black-Scholes model, so-called the Black-Scholes-Merton model. It incorporates dividends, and lays the groundwork for further research into options pricing and financial derivatives. Then various stochastic volatility models emerge, and the essay chooses the Heston model as a typical example for analysis, highlighting its advantages and applications in option pricing. Furthermore, the essay compares the Heston model with other option pricing models, including the SABR model and Bates model. At the end of the essay, recent advances and future directions in option pricing are introduced and discussed. Through this comprehensive exploration, readers can gain a deeper understanding of the evolution of option pricing models and their significance in modern finance.

Econometric analysis of financial derivatives: An overview

This research offers an in-depth exploration into the intersections of entertainment and finance, focusing on Disney's expansive business ecosystem and its influence on option pricing dynamics. The empirical findings pinpoint significant correlations: Disney Plus’s subscriber trends and Average Revenue Per User (ARPU) exhibit a notable relationship with option prices, suggesting a complex interplay between digital revenue streams and financial derivatives. Additionally, revenue surges and operational shifts in Disney's theme parks have discernible impacts on option pricing. Furthermore, case studies on major film releases, including Thor: Love and Thunder and Avatar: The Way of Water, illuminate the profound influence of pop culture events on financial market fluctuations. The rapid responsiveness of option prices to film-related factors, such as reviews and box office performance, emphasizes the intertwined nature of entertainment products and investor sentiment. This research unravels the multifaceted connections between entertainment sectors and global financial markets, providing a robust foundation for future investigations into the evolving entertainment industry and its economic reverberations.

Option pricing is one of the fundamental problems in finance. This chapter proposes a novel idea for pricing options using a nature inspired meta-heuristic algorithm called Ant Colony Optimization (ACO). ACO has been used in many NP-hard combinatorial optimization problems and most recently in self-organized environments in dynamic networks such as ad hoc and sensor networks. The dynamic changes in financial asset prices poses greater challenges to exercise the option at the right time. The dynamic nature of the option pricing problem lends itself very easily in using the ACO technique to the solution of computing option prices. ACO is as intuitive as other techniques such as binomial lattice approach. ACO searches the computational space eliminating areas that may not provide a profitable solution. The computational cost, therefore, tends to decrease during the execution of the algorithm. There has been no study reported in the literature on the use of ACO for pricing financial derivatives. We first study the suitability of ACO in finance and confirm that ACO could be applied to financial derivatives. We propose two ACO based algorithms to apply to derivative pricing problems in computational finance. The first algorithm, named Sub-optimal Path Generation is an exploitation technique. The second algorithm named the Dynamic Iterative Algorithm captures market conditions by using an exploration and exploitation technique. We analyze the advantages and disadvantages of both the algorithms. With both the algorithms we are able to compute the option values and we find that the sub-optimal path generation algorithm outperforms the binomial lattice method. The dynamic iterative algorithm can be used on any random graph and the uncertainties in the market can be captured easily but it is slower when compared to the sub-optimal path generation algorithm.

Currently, financial derivatives are important financial instruments. Financial derivatives can provide investors with the opportunity to hedge, speculate, and arbitrage. But due to the impact of COVID-19. The performance of financial derivatives has changed dramatically compared to the pre-epidemic period. This dissertation focuses on the performance of three major financial derivatives which include futures, options, and credit under COVID-19. The phenotypes of these three major financial derivatives are analyzed separately. In this paper, we examine the extensive literature to demonstrate the changes in financial derivatives during COVID-19. By collecting a large amount of data about financial derivatives during the COVID-19 period and before. And the data are quantitatively analyzed to show the specific performance of financial derivatives under COVID-19. The study found that there is a huge variation in the performance of these three financial derivatives in COVID-19. For futures, foreign performance futures can bring a negative impact on financial markets. As for domestic, the performance is different during the emergency resistance period and the normalized resistance period. The performance of the emergency resistance period is significantly less than the normalized resistance period. For options, the volatile market sentiment and panic caused by recurring epidemics affect investors' judgment, which leads to changes in the implied volatility of options and affects the price of options. For swap specify its basic means of operation in an epidemic state and the basic types.

Accepted by: Giorgio Consigli Accurate pricing of basket options, which are financial derivatives on multiple underlying assets, is a challenging and practically important task for financial institutions. We propose several new control variates for accurate, fast and efficient pricing of basket options. The first approach to deriving new control variates is the use of Hermite polynomial approximation of appropriate function of the underlying asset prices, which leads to a Black–Scholes-like analytic solution. This approach is new in the option pricing context and opens up new possibilities in derivative pricing. Further control variates are analytically derived using Jensen’s inequality in one case, and distributional properties of multivariate Wiener processes in other cases. All the newly proposed control variates are shown to lead to excellent variance reduction in numerical experiments based on realistic data. The proposed methods are novel, computationally simple and have a strong potential to replace more conventional methods, such as the geometric lower bound in simulation-based pricing of basket options and similar products used in financial risk management.

Investment in financial derivatives becomes popular around the world. In Thailand, the Thailand Futures Exchange (TFEX) which is a place where financial derivatives are traded has also been an attractive recently. One of the common question of investor is what the price of financial instrument will be. There are several models has been used in forecasting option price. The most popular one is the Black-Scholes option pricing formula. In this paper, we investigate a widely-used statistical model, GARCH model to forecast the option price. We use SET50 option as case studies and compare the result with a well-known model, Black-Scholes model.

PurposeThe purpose of this study is to analyse and compile the literature on various option pricing models (OPM) or methodologies. The report highlights the gaps in the existing literature review and builds recommendations for potential scholars interested in the subject area.Design/methodology/approachIn this study, the researchers used a systematic literature review procedure to collect data from Scopus. Bibliometric and structured network analyses were used to examine the bibliometric properties of 864 research documents.FindingsAs per the findings of the study, publication in the field has been increasing at a rate of 6% on average. This study also includes a list of the most influential and productive researchers, frequently used keywords and primary publications in this subject area. In particular, Thematic map and Sankey’s diagram for conceptual structure and for intellectual structure co-citation analysis and bibliographic coupling were used.Research limitations/implicationsBased on the conclusion presented in this paper, there are several potential implications for research, practice and society.Practical implicationsThis study provides useful insights for future research in the area of OPM in financial derivatives. Researchers can focus on impactful authors, significant work and productive countries and identify potential collaborators. The study also highlights the commonly used OPMs and emerging themes like machine learning and deep neural network models, which can inform practitioners about new developments in the field and guide the development of new models to address existing limitations.Social implicationsThe accurate pricing of financial derivatives has significant implications for society, as it can impact the stability of financial markets and the wider economy. The findings of this study, which identify the most commonly used OPMs and emerging themes, can help improve the accuracy of pricing and risk management in the financial derivatives sector, which can ultimately benefit society as a whole.Originality/valueIt is possibly the initial effort to consolidate the literature on calibration on option price by evaluating and analysing alternative OPM applied by researchers to guide future research in the right direction.

Risk mitigation and control are critical for investors in the finance sector. Purchasing significant instruments that eliminate the risk of price fluctuation helps investors manage these risks. In theory and practice, option pricing is a substantial issue among many financial derivatives. In this scenario, most investors adopt the Black–Scholes model to describe the behavior of the underlying asset in option pricing. The exceptional memory effect prevalent in fractional derivatives makes it easy to understand and explain the approximation of financial options in terms of their inherited characteristics prompted by the given reason. Finding numerical solutions that are both successful and suitably precise is crucial when working with financial fractional differential equations. Hence, this paper proposes an innovative method, designated the Chromatic polynomial collocation method (CPM), for the theoretical study of the Time fractional Black–Scholes equation (TFBSE) that regulates European call options. The newly developed numerical algorithm CPM is on a functional basis of the Chromatic polynomials of Complete graphs (Kn) and operational matrices of the basis polynomials. The CPM transforms the TFBSE into a framework of nonlinear algebraic equations with the help of operational matrices and equispaced collocation points. The fractional orders in the PDE are concerned in the Caputo sense. The CPM findings further corroborate the results of the most recent numerical schemes to show the effectiveness of the suggested numerical algorithm.

The emergence of financial derivatives has helped people to effectively hedge the risks present in the financial markets while giving them the ability to make leveraged investments in the financial markets. Although derivatives did not originate in the financial market, it still has a huge role in the financial market so far. In recent years, science and technology innovation is known as a growing concern for governments due to factors such as environmental issues. In this paper, we choose to study the financial derivative, European call option pricing problem of technology-based companies AMZN and GOOGL. In this paper, the European call options of these two companies are priced by using the BSM model, and the results predicted by the BSM model are improved by using Monte Carlo Simulation. Ultimately, the paper finds that Monte Carlo Simulation prices European call options on technology-based firms nearly three times higher than those priced by the BSM model. The results suggest that using a single model to price European call options on technology-based firms is inaccurate. The purpose of this paper is to help investors in pricing European call options on technology-based firms and to warn investors about the inaccuracy of a single option pricing model.

This study aims to develop an accurate option pricing model for car leases by introducing a put option valuation framework based on the Weibull distribution. Traditional models typically assume asset values follow a lognormal distribution, failing to capture the left-skewed nature and bounded dynamics. To address this limitation, this study compares the performance of the Weibull distribution with that of the lognormal model using residual value data from two popular car models in South Korea, evaluating each model’s ability to reflect unique depreciation patterns. The findings demonstrate that the Weibull distribution provides a superior fit to the data, leading to more precise option pricing. This enhanced accuracy is crucial for auto finance companies navigating uncertainties in used car prices, particularly as the mobility services and car leasing markets continue to expand. Moreover, the practical implications of this research extend beyond the auto finance industry; insights from this study can inform sectors dealing with skewed or bounded assets, such as insurance products and financial derivatives, thereby enabling improved risk assessment and decision-making processes. This research introduces a novel approach to modeling put option values using the Weibull distribution, filling a significant gap in the existing literature on car lease option pricing. However, as this is the first study to model put option values using the Weibull distribution, further research is necessary. Specifically, investigating volatility patterns over the lifecycle of used cars could significantly enhance the value of this framework.

Path Integral is a method to transform a function from its initial condition to final condition through multiplying its initial condition with the transition probability function, known as propagator. At the early development, several studies focused to apply this method for solving problems only in Quantum Mechanics. Nevertheless, Path Integral could also apply to other subjects with some modifications in the propagator function. In this study, we investigate the application of Path Integral method in financial derivatives, stock options. Black-Scholes Model (Nobel 1997) was a beginning anchor in Option Pricing study. Though this model did not successfully predict option price perfectly, especially because its sensitivity for the major changing on market, Black-Scholes Model still is a legitimate equation in pricing an option. The derivation of Black-Scholes has a high difficulty level because it is a stochastic partial differential equation. Black-Scholes equation has a similar principle with Path Integral, where in Black-Scholes the share's initial price is transformed to its final price. The Black-Scholes propagator function then derived by introducing a modified Lagrange based on Black-Scholes equation. Furthermore, we study the correlation between path integral analytical solution and Monte-Carlo numeric solution to find the similarity between this two methods.