Option Pricing Theory Research Articles

A Study of Black-Scholes-Merton Model

This study introduces the Option Pricing Theory improved by Black, Scholes, and Merton, which is also known as the Black-Scholes-Merton model, in detail and investigates its derivation process and historical development process. Despite the content above, it also includes its characteristics and mechanism. The newest Option Pricing formula proposed by Black, Scholes, and Merton was derived from mathematical methods such as the stochastic integral equation and Ito theorem. This essay concludes that the Black Scholes Merton model paved the way for the development and innovation of the subject of Financial Mathematics, which was found by the person who first came up with the Option Pricing Theory, which also contributes to the investment field to reduce the risk.

Evolution of option pricing models: From Black-Scholes to Heston and beyond

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.

Market consistent bid-ask option pricing under Dempster-Shafer uncertainty

We refer to the discrete-time market model under ambiguity introduced in [Cinfrignini, A., Petturiti, D. and Vantaggi, B., Dynamic bid–ask pricing under Dempster-Shafer uncertainty. J. Math. Econ., 2023a, 107, 102871], formed by a frictionless risk-free bond and a non-dividend paying stock with bid-ask spread. For a European derivative, we generalize the classical binomial pricing formula by allowing for bid-ask prices and investigate the properties of the ensuing replicating strategies. Next, for an American derivative, we propose a backward bid-ask pricing procedure and prove that the resulting discounted price processes are the bid-ask Choquet-Snell envelopes of the discounted payoff process, respectively. Moreover, for an American call option, we prove a generalization of the well-known Merton's theorem [Merton, R.C., Theory of rational option pricing. Bell J. Econ. Manage. Sci., 1973, 4, 141–183] holding for both the bid and the ask price processes. Finally, we introduce a market consistent calibration procedure and show the use of the calibrated model in bid-ask option pricing.

Financial Innovation and Risk Management in Japan

Purpose: The aim of the study was to investigate the Financial Innovation and Risk Management. Methodology: This study adopted a desk methodology. A desk study research design is commonly known as secondary data collection. This is basically collecting data from existing resources preferably because of its low cost advantage as compared to a field research. Our current study looked into already published studies and reports as the data was easily accessed through online journals and libraries. Findings: Japan has seen a surge in financial innovation driven by fintech startups and digitalization efforts by traditional banks. However, this innovation comes with regulatory challenges and risks that must be managed. Regulatory frameworks are being updated to address new risks like cybersecurity threats. There's also a growing focus on corporate governance, risk culture, and sustainability integration. Unique Contribution to Theory, Practice and Policy: Option pricing theory, capital asset pricing model (CAPM) & modern portfolio theory (MPT) may be used to anchor future studies on the financial innovation and risk management. Foster a culture of innovation within financial institutions by promoting collaboration between risk management professionals and product development teams. Establish regulatory sandboxes and innovation hubs to facilitate responsible experimentation with financial innovations while maintaining regulatory oversight.

Numerical Methods for Option Pricing

Nowadays, financial markets have become more complex and have given rise to more research opportunities, one of which focuses on research related to the pricing of various financial instruments used in options trading. In this essay, a gradual process of reflection is used to deepen the option pricing theory. Firstly, an effective mathematical method for pricing option contracts is using the binomial tree model, a relatively straightforward way of calculating the value of an option. However, it has only two upward and downward trends and has limitations that are the most different from the actual market conditions. That is why the study will have to continue in-depth to get as close as possible to the real situation in the market. The next step is to make the model more in line with market reality by adding a possible rate of change, resulting in the Trinomial Tree Model. The model incorporates the possibility of future price increases, decreases, or stabilization (the third change). The Trinomial Tree Model follows the no-arbitrage principle and removes the assumption of a risk-free market opportunity. This paper derives a method for constraining market prices under risk-neutral conditions. This is crucial for investors seeking profitable outcomes in options trading. The main objective of this research-based paper is to develop a complete theory of option pricing in a one-step trinomial tree model.

The Black–Scholes equation in finance: Quantum mechanical approaches

In this paper, the Black–Scholes equation of the option pricing theory in order to minimize the risk through the stocks is studied. The solutions are obtained in terms of exceptional Laguerre polynomials. Moreover, higher-order supesymmetric representations are studied with a special case of third order. The Darboux transformation of the heat equation linked to the Black–Scholes system is given and a new potential is shown.

Progress of the Study on the Models of Option Pricing

Option pricing, a core part of options trading, has been fruitfully researched over the years. This article reviews the history of the emergence and advancement of option pricing in terms of a thorough classification of the widely used option pricing models and their empirical studies that follow. The three option pricing models are summarized, including the Black-Scholes pricing model, the tree diagram model, and the Monte Carlo simulation techniques, which have all represented significant progress in the field of option pricing theory. Moreover, the differences between various pricing models are analyzed and compared to show their applications and to provide an outlook on future work in this theory. It is vital to carry out some research on option pricing in order to better suit the preferences of investors. In order to meet the continuous development of financial markets, valuation of financial derivative securities is the key to effective investment in risky assets.

A novel stochastic modeling framework for coal production and logistics through options pricing analysis

We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory. The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model. We derive a three-dimensional Fast Fourier Transform (“FFT”) lower bound approximation to value the inherent real optionality and for robustness check, we compare the semi-analytical pricing accuracy with the Monte Carlo simulation. Model parameters are estimated from the historical monthly data, and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross (“CIR”) model.

Prediction of Barrier Option Price Based on Antithetic Monte Carlo and Machine Learning Methods

Option pricing has become a popular topic in the fields of finance and mathematics with the rapid development of stock and option markets. Now, more and more academics, financial companies and investors are attracted to study and do research about it. The theory of option pricing can also be used to price financial instruments with the similar structure to options and contribute to risk control and management. The Black-Scholes model is the basic and famous method applied for different options pricing with modifications and adjustments, and the results can be solved by some traditional numerical methods such as the binomial model, finite difference method, Monte Carlo method and so on. Machine learning has risen recently and begins to replace some complex work in traditional methods with the evolution of computers and computing power. How to use machine learning methods to predict the option price is a problem worthy to be solved. In this research, using the antithetic Monte Carlo method generates the prices of the up-and-out barrier options without rebate based on the Black-Scholes model. The generated dataset is divided into a training set and a test set for support vector regression, random forest, adaptive boosting and artificial neural networks. We compare the fitting and performance of all machine learning methods and find that random forest and artificial neural network methods fit better than others with fewer errors in predictions.

Valuation of Corporate Debt and Equity in Uncertain Markets

In practice, financial decisions are made in the context of indeterminacy. Randomness, uncertainty, and fuzziness are three basic types of indeterminacy. A multiplicity of differential equations have been designed to depict various processes powered by different kinds of indeterminacy. Among others, these differential equations include uncertain differential equations, stochastic differential equations, and fuzzy differential equations. In this study, we propose that the value of a firm can be described by an uncertain differential equation powered by a geometric canonical Liu process. Uncertain differential equations describe processes driven by uncertainty. Implementing the uncertain Liu option pricing theory, we develop and analyse a framework for valuing debt and equity for a levered firm in uncertain markets. Numerical calculations are demonstrated.

Interior second derivatives estimates for nonlinear diffusions

<p style='text-indent:20px;'>By obtaining some new estimates for classical solutions of filtration equations and singular parabolic equations we derive consequences for fully nonlinear parabolic equations of dual filtration type, with nonlinearities that can be both singular and degenerate elliptic and also non-homogeneous. Such equations appear in the theory of option pricing with market impact.</p>

Application of Malliavin Calculus and Wiener Chaos to Option Pricing Theory (1st Phd Manuscript)

Application of Malliavin Calculus and Wiener Chaos to Option Pricing Theory (1st Phd Manuscript)

Pricing of vulnerable options based on an uncertain CIR interest rate model

<abstract><p>The traditional Cox-Ingersoll-Ross (CIR) interest rate model follows a stochastic differential equation that cannot obtain the closed solution while the uncertain CIR interest rate model is an uncertain differential equation. First, this paper gives the solution in terms of the distribution of the uncertain CIR interest rate model based on uncertainty theory. Second, the pricing formulas of vulnerable European call option and vulnerable European put option are obtained by using the uncertain CIR interest rate model. Finally, according to the proposed pricing formula, the corresponding numerical algorithms are designed and several numerical examples are given to verify the effectiveness of the algorithm. Our results not only enrich the option pricing theory, but they also have a certain guiding significance for the derivatives market.</p></abstract>

Gallup Democracy in Exercising the NATO Membership Option: The Cases of Finland and Sweden

Abstract The article asks whether the exercising of the NATO membership option is justified for Finland and Sweden in the light of their geopolitical state after Russia’s attack on Ukraine. It was the Gallup democracy, which launched the political moves toward the membership. In both countries, the majority of people turned to favor the membership within 2–3 months. Finland activated first. Sweden was fast in catching up with the Finnish process. The theory of option pricing is employed to analyze the optimal timing of exercising the option when the uncertainty regarding the value of the membership is rapidly diluting. The Turkish intervention in the membership process after the membership applications of Finland and Sweden were delivered suggests a bargaining phase once the application is delivered. Finally, the effects of the Gallup surveys on the political equilibrium are analyzed in a voter–politician model (JEL codes: D72, D74, and H56).

Underdiversification puzzle, volatility puzzle and equity premium puzzle: a common solution

PurposeThe purpose of this paper is to use some of the contributions of the option pricing theory to solve three outstanding puzzles in finance: the underdiversification puzzle, the volatility puzzle and the equity premium puzzle.Design/methodology/approachTo approach the issue, this paper considers the applications of the option pricing theory to both sides of the corporate balance sheet. Applications to the left-hand side of the balance sheet has led to the real options theory that has expressed the value of a capital budgeting project as the sum of the values of its “discounted cash flow (DCF) method” and “real options.” This paper argues that, because the balance sheet must balance, the value of equity, which appears on the right-hand side of the balance sheet, should also be expressed as the sum of the values of its “DCF method” and “equity options.”FindingsThis proposed model of equity valuation solves the three outstanding puzzles in finance: the underdiversification puzzle, the volatility puzzle and the equity premium puzzle.Research limitations/implicationsThis study may not be able to explain the full extent of the three puzzles.Practical implicationsThe dividend discount model of equity valuation needs to be augmented by an option component.Social implicationsThe community of finance scholars will become more confident of their scholarly work because three puzzles will be solved to a great extent.Originality/valueTo the best of author’s knowledge, the extant literature does not either solve any single one of the three puzzles through the contributions of option pricing theory or solve all three puzzles at the same time with a single solution. The originality of this paper is that it makes both of these contributions to the extant literature.

If they could see the simpler approach, they would feel much better about option-pricing theory

When Cox Ross and Rubinstein formalized the binomial options pricing model proposed by Bill Sharpe, the goal was demystification. Here we present a conversation from Espen Gaarder Haug�s archives aimed at demystifying Rubinstein himself

CMOs의 가치평가에 관한 연구

This study empirically analyzed whether real estate policies have a significant effect on housing sales, jeonse prices, and land sales prices using MBS is not active in Korea due to difficulties in evaluation. In the appraisal of MBS, the default risk is a cost that someone has to bear even if the government agency removes it through relevant guarantees. In this study, five CMOs data are evaluated and analyzed through the financial model developed based on traditional capital budgeting theory, option pricing theory, and Cho & Jun(2019)’s model recognizing that housing price fluctuation is an important factor affecting the default risk in MBS. Finally, the results drawn from this study help provide a theoretical framework for the valuation of MBS and show relevant implications for rational decision-making to MBS-related entities.

Implicit government guarantees and bank risk

We develop a model on bank risk and implicit government guarantees. This model concerns the willingness and capacity of implicit government guarantees. Using the Option Pricing Theory, we derive a mathematical formulation of maximizing the bank’s net present value (NPV) with implicit government guarantees. Unlike previous work, both the loan portfolio and the bank’s NPV are regarded as a combination of options underlying the risky project. We conduct comparative static analyses and numerical examples to examine how implicit government guarantees and capital control affect bank risk and its asset scale. The main insight of our analysis is that implicit government guarantees have some unintended consequences: (a) Inefficient and excessive risk taking (including bank’s asset and overall risk); (b) Inefficient investment if there is no binding capacity constraint. We show that it is mainly due to the bank's excessive reliance on contingent assets. In addition, we demonstrate the ineffectiveness of capital constraint on risk control under certain circumstances. Therefore, we suggest that the gradual withdrawal of implicit government guarantees should be accompanied by multiple combinations of regulatory measures and proper institutional reform to avoid risk surges.

The Paradoxical Prices of Options

The synchronized relationship between financial and fundamental prices has been topical for years now. It seems that option pricing theory has not been used to disentangle that relationship between two prices during merger and acquisition (M&A) activities. This paper uses Put-Call parity theorem to explore the divergence of financial and fundamental prices in any firm during the acquisition process. The results illustrate that price differentials are persistent; moreover, the differentials are caused by the exponential factor. Despite the fact that some principles are drawn from the real estate investment trust (REIT) literature, the results have wider implications for industries with similar traits to REITs.

Practical Applications of On the Valuation of Performance Fees and Their Impact on Asset Managers’ Incentives

<b>In</b><b><i>On the Valuation of Performance Fees and Their Impact on Managers’ Incentives</i></b>, from the Summer 2021 issue of <b><i>The Journal of Alternative Investments</i></b>, <b>Wei Dai</b> and <b>Savina Rizova,</b> both at <b>Dimensional Fund Advisors</b>,and <b>Robert C. Merton</b> at the <b>MIT Sloan School of Management</b>, remind investors that performance fees can be valued using option pricing theory. Several researchers have applied an option-based approach to the valuation of hedge fund fees and other alternative investments’ performance fees, but few, if any, have done so for long-only systematic managers. The lack of research in that space is mostly because US legislation in the early 1970s banned mutual funds from charging asymmetric incentive fees. Recently, however, more managers of long-only, systematic, separately managed accounts are charging performance fees. The authors, therefore, focus on these types of accounts while illustrating how to use option pricing theory to value a wide variety of performance fee structures. Increased adoption of performance fees in long-only managed accounts coincides with investors’ increased interest in long-only systematic strategies.