Theoretical Price Research Articles

Metode Penilaian Harga Call Option Atas Warant Perbankan Di Indonesia Menggunakan Metode Penilaian Harga Call Option Dibandingkan Dengan Harga Pasar

The purpose of this research is to know the application from the valuation method of the call option price for the warrant of the banking sector in the Indonesian Stock Exchange, after that the theoretical price from the valuation method of the call option price could be compare with the market price. The research conducted with four warrants of the banking sector that have quite active transactions, there are BNII-W, BNII-W2, BNLI-W, and PNBN-W. The research begin with the calculation of the risk from the stock as the underlying asset for the warrant. Then continued with the recognition for other indicators that need to calculate the theoretical price of the call option price with the Black-Scholes Option Pricing Model, there are stock price, exercise price, risk free interest rate (SBI), and remaining time of the warrant from the exercise date. Theoretical price with the Black-Scholes Option Pricing Model could be compare with the market price of the warrant. Then could be known the comparison of the movement between theoretical price with the market price. From the result of the research showed that the market price is different with the theoretical price with the Black-Scholes Option Pricing Model for BNII-W, BNII-W2, BNLI-W, and PNBN-W. The difference for BNII-W2 is not statistically significant, while the difference for BNII-W, BNLI-W, and PNBN-W are statistically significant. The movement of the market price for BNII-W, BNII-W2, BNLI-W, and PNBN-W are not always move to the new theoretical equilibrium price with the Black-Scholes Option Pricing Model. The difference in the value and the movement between market price with the theoretical price could be caused by the condition of the Indonesian capital market that is not in the efficient condition yet, this could be indicated that the transaction have not reflect for full information. Besides that the option instrument is still not completely traded in the Indonesian Stock Exchange, so the investor could not used the difference between the market price and the theoretical price with some arbitrage to get gain.

Analysis of Option Prices Using Black Scholes Model

A mathematical formula used in finance to calculate the theoretical price of an option and ascertain its option premium is known as the Black Scholes option pricing model, which aids option traders in making informed decisions. This article estimates the option premium of various call and put options using the Black Scholes Model. The three distinct option chains chosen for this essay are all Mid-Cap companies that are listed on the Indian National Stock Exchange. The companies are Suzlon Energy, Kalyan jewellers India, and Exide Industries Ltd. The analysis demonstrates that the options are expensive because the Black Scholes model's computation of the option premium is lower than the actual premium in the market. Keywords: Option, Black Scholes Option Pricing Model, Call, Put, Option Premium

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

The pioneering work in finance by Black, Scholes and Merton during the 1970s led to the emergence of the Black-Scholes (B-S) equation, which offers a concise and transparent formula for determining the theoretical price of an option. The establishment of the B-S equation, however, relies on a set of rigorous assumptions that give rise to several limitations. The non-local property of the fractional derivative (FD) and the identification of fractal characteristics in financial markets have paved the way for the introduction and rapid development of fractional calculus in finance. In comparison to the classical B-S equation, the fractional B-S equations (FBSEs) offer a more flexible representation of market behavior by incorporating long-range dependence, heavy-tailed and leptokurtic distributions, as well as multifractality. This enables better modeling of extreme events and complex market phenomena, The fractional B-S equations can more accurately depict the price fluctuations in actual financial markets, thereby providing a more reliable basis for derivative pricing and risk management. This paper aims to offer a comprehensive review of various FBSEs for pricing European options, including associated solution techniques. It contributes to a deeper understanding of financial model development and its practical implications, thereby assisting researchers in making informed decisions about the most suitable approach for their needs.

Lie Symmetry Analysis for the Fractal Bond-Pricing Model of Mathematical Finance

The classical bond-pricing models, as important financial tools, show strong vitality in bond pricing. However, these models also expose their theoretical defects, which leads to inconsistencies with the actual observation results and usually causes the theoretical prices of bonds to be lower than the actual market prices in the financial market. In order to change this situation, considering that the price change of the underlying is regarded as a fractal transmission system, the fractal derivative is introduced into the bond-pricing equation. In order to solve the fractal bond-pricing equation, we first convert it into an equivalent equation by using a fractal two-scale transform. Only in this case can we start to study it by means of the Lie symmetry analysis method. Then the geometric vector fields, the symmetry reductions, and the exact solution to the equations are obtained. Furthermore, the dynamic behaviors of the fractal bond-pricing equation are discussed. The results show that the fractal dimension bond-pricing formula can better explain price changes in the capital market than the classical one. That is to say, the classical bond-pricing equation is only a special case of the fractal-bond pricing equation, which makes up for the defect that the theoretical bond price given by the classical bond-pricing equation is often lower than the actual market price. The results of this paper provide a basis for bond pricing in the financial market in order to seek a more appropriate and real price.

Can textual sentiment partially explain differences in the prices of dual-listed stocks?

Can textual sentiment partially explain differences in the prices of dual-listed stocks?

Pricing formula for a Barrier call option based on stochastic delay differential equation

Pricing formula for a Barrier call option based on stochastic delay differential equation

An Empirical Study of Stock Price Returns Using Black-Scholes Option Pricing Model

Abstract: This study examined empirically the predictive ability of Black-Scholes Option pricing model in Nigerian Stock Market by testing whether there is any significant difference between the market (underlying) price of the stock and the theoretical prices. The data used for this study was Coca-Cola Stock prices from 2018 to 2022 obtained from http://www.investing.com and were analyzed using Statistical packages such as Microsoft Excel and Minitab to obtain the result. The results showed that there is a significant difference between the underlying and the theoretical price (Black-Scholes Option Pricing Model). Based on the findings of this study, we conclude that the Black- Scholes model is not accurate in its price predictive ability on the Coca-Cola Stock prices over the years under study.

Pricing Multi-Event-Triggered Catastrophe Bonds Based on a Copula–POT Model

The constantly expanding losses caused by frequent natural disasters pose many challenges to the traditional catastrophe insurance market. The purpose of this paper is to develop an innovative and systemic trigger mechanism for pricing catastrophic bonds triggered by multiple events with an extreme dependence structure. Due to the bond’s low cashflow contingencies and the CAT bond’s high return, the multiple-event CAT bond may successfully transfer the catastrophe risk to the huge financial markets to meet the diversification of capital allocations for most potential investors. The designed hybrid trigger mechanism helps reduce the moral hazard and increase the bond’s attractiveness with a lower trigger likelihood, displaying the determinants of the wiped-off coupon and principal by both the magnitude and intensity of the natural disaster events involved. As the trigger indicators resulting from the potential catastrophic disaster might be associated with heavy-tailed margins, nested Archimedean copulas are introduced with marginal distributions modeled by a POT-GP distribution for excess data and common parametric models for moderate risks. To illustrate our theoretical pricing framework, we conduct an empirical analysis of pricing a three-event rainstorm CAT bond based on the resulting losses due to rainstorms in China during 2006–2020. Monte Carlo simulations are carried out to analyze the sensitivity of the rainstorm CAT bond price in trigger attachment levels, maturity date, catastrophe intensity, and numbers of trigger indicators.

Put an eye on the future: Rethinking the theoretical price of fossil energy based on the perspective of intergenerational equity

Discovering the true value of fossil energy resources can make full use of the price regulation leverage to adjust the energy structure, relieve carbon emissions, and gain more time for renewable energy to replace fossil energy. As exhaustible resources, the exploitation and consumption of coal, oil, and natural gas can directly affect the environment and resources reserve of future generations, which will directly destroy the fairness of intergenerational transmission. To make the price of fossil resources work better, the theoretical energy prices composed of production costs (PC), user costs (UC), environmental costs (EC), and especially intergenerational compensation costs (IC) are taken into consideration in this study. In addition, the study probes the impact of the theoretical and actual prices of fossil energy resources on carbon intensity with the path analysis method and detects the key paths. Results show that the theoretical price of natural gas is compensated the most, followed by coal and oil. From the result of intergenerational equity, the theoretical prices of coal and oil have higher impacts on carbon intensity than their actual prices, while the condition of natural gas is not the same. It is necessary for decision-makers to fully consider the characteristics of environmental damage, scarcity, and especially intergenerational compensation when repricing coal and oil price. Fortunately, the actual price of natural gas is the most effective for realizing the intergenerational equality target. It is crucial to put an eye on the future in reexamining fossil energy prices and formulating relevant emission reduction policies.

Options Pricing Comparison between the Black-Scholes Model and the Binomial Tree Model: A Case Study of American Equity Option and European-style Index Option

In recent years, quantitative researchers used a wide range of models to price options, from the Black-Scholes model to more complex models such as the Heston model. This paper aims to analyze the effectiveness of the Black-Scholes model and the Binomial Tree model by using them to price Berkshire Hathaway’s equity options and European-style S&P 100 index options. The method used in this paper is gathering the market data of the options first. Second, using the data gathered to price the options by applying the Black-Scholes and Binomial Tree models. Third, comparing the derived theoretical price with the market price by getting the Sum of Square Errors. Lastly, determining the best model for each type of option. Through this research, the author found that comparing the two models, the Binomial Tree model derives a smaller Sum of Square Errors when pricing European-style index options, and the Black-Scholes model derives a smaller Sum of Square Errors when pricing American equity options. Thus, the Binomial Tree model is a better model to price European-style index options, and the Black-Scholes model is more effective when pricing American equity options.

Pricing strategy for household energy-saving option (HESO): A novel option-based intervention for promoting household energy efficiency

Household energy-saving interventions are essential in reducing energy consumption in residential buildings. One of the effective interventions is Household Energy-Saving Option (HESO). However, the pricing strategy of this innovative intervention has not been explored. This study aims to establish a feasible valuation strategy for HESO to facilitate the application of market-based energy-saving interventions among households. This study first provides a pricing strategy of HESO from a market zero-profit perspective. It continues by developing a price cap and floor for HESO's market price. The theoretical pricing model was validated by a field experiment consisting of two-tiered HESO trading among 67 households in Singapore. The results revealed decisive implications for both environmental policymakers and HESO suppliers. Policymakers are suggested to launch HESO in countries or regions with stable and relatively high electricity prices and low discount rates. HESO suppliers may choose to adjust rewards and duration accordingly when the market price deviates from the zero-profit equilibrium price of HESO. The valuation strategy of HESO also helps quantitative estimation of households' perceived value of HESO. • The theoretical pricing model of HESO was derived from zero-profit equilibrium. • A field experiment was conducted to validate the HESO pricing strategy. • Key determinants of HESO market equilibrium and boundary prices were investigated. • Decisive implications can be drawn from the appropriate HESO launching places.

Regime recovery using implied volatility in Markov modulated market model

AbstractIn the regime switching extension of Black–Scholes–Merton model of asset price dynamics, one assumes that the volatility coefficient evolves as a hidden pure jump process. Under the assumption of Markov regime switching, we have considered the locally risk minimizing theoretical price of European vanilla options. By pretending these prices or their numerical approximations as traded prices, we have first computed the implied volatility (IV) of the underlying asset. Then by performing several numerical experiments on ternary regime models we have investigated the dependence of IV on the time to maturity (TTM) and strike price of the vanilla options. We have observed a clear dependence that is at par with the empirically observed stylized facts. Furthermore, we have experimentally validated that IV time series, obtained from contracts with moneyness and TTM varying in a particular narrow range, can recover the transition instances of the hidden Markov chain having three states. Such regime recovery for any arbitrary state‐space and transition parameters has also been established in a theoretical setting. Moreover, the novel scheme for computing option price is shown to be stable.

Reconstruction of local volatility surface from American options

Abstract In this paper, we discuss the reconstruction of a local volatility surface from American option prices. First of all, the American option prices are calculated by an accurate and fast finite difference scheme. Then the local volatility is obtained by minimizing the distance between theoretical prices and market option prices, which yields an optimization problem. The Bicubic spline regularization technique is used to overcome the ill-posedness of the reconstruction problem. We solve the nonlinear optimization problem by using a gradient-based optimization algorithm. Finally, we test our model with numerical examples and real market American put option data. The results show the good performance of our method.

The language of pluralism from the history of the theory of price determination: Natural price, equilibrium price and administered price

AbstractThis paper seeks to identify terminology to aid in distinguishing the approaches to the theory of price determination as presented in classical political economy, neoclassical economics and post‐Keynesian economics. Through a review of the respective literature, a dominant usage is identified for the theoretical price concept in each theory. Natural price is identified with classical theory, equilibrium price with neoclassical theory and administered price with post‐Keynesian theory. Use of the differentiated terminology is advocated for improving clarity in pluralist discourse on the theory of price determination and the role of prices in modern market economies with their inherent complexity.

Some Recent Developments IN The Explanation of The Empirical Relationship Between Prices and Distribution

Abstract The paper complements recent contributions towards the explanation of the regularities in the behaviour of prices and capital intensities as an effect of hypothetical changes in the rate of profits in empirical production-price models. It is shown that theoretical price and capital curves, i.e. prices and capital values as a function of the rate of profits, depend on the product of the eigenvalues and what we call the eigenlabours —the representation of the labour vector in the space spanned by the eigenvectors of the input matrix. We report robust evidence that the eigenvalues by themselves cannot produce the curves regularly reported in the literature, but rather it is the joint action of the eigenvalues and the eigenlabours. It is conjectured that the tendency towards zero of the subdominant eigenlabours is driven by the statistical tendency towards proportionality between the labour vector and the Perron–Frobenius eigenvector of the input matrix.

Experimental Research on the Impact of Interest Rate on Real Estate Market Transactions

Based on the close relationship between real estate and capital financing, this paper specifically discusses the impact of interest rate changes in China on real estate market transactions. Housing price regulation has been a hot and focused topic of economics research. It is important to explore the effect of interest rate on real estate market transactions, for the interest rate is an important tool for the government to carry out macrocontrol of the real estate market and affects residents’ consumption choices of goods. Currently, most scholars believe that interest rate changes have a significant impact on house prices, but their studies are often based on empirical analysis of macro data, making it difficult to exclude the effects of economic differences, geographic characteristics, and other factors. Also, some scholars believe that it is difficult for interest rates to have a long‐term impact on real estate prices. This paper applies the experimental economics method to simulate real estate transactions in the real market and control the irrelevant variables to study the movements of housing prices, transaction volumes, consumer transaction intentions and bubble indices under different deposit and lending rates. The results show that: (1) The level of deposit interest rate has a significant inhibitory effect on housing price and a significant promoting effect on real estate market transaction volume and traders’ house‐buying behavior. The higher the level of deposit interest rate is, the better the degree of regulating house prices deviating from the theoretical price is and the better the effect of inhibiting market bubbles. (2) The level of lending rate has a significant inhibiting effect on the volume of real estate transactions and a significant promoting effect on the house‐buying behavior of traders, but its effect on housing prices and market bubbles is not significant. The higher the level of lending rate is, the better the degree of regulating housing prices deviating from the theoretical price is. (3) The effect of deposit interest rate and lending rate policies on the house selling behavior of market traders is not significant.

Calibration of time-dependent volatility for European options under the fractional Vasicek model

<abstract><p>In this paper, we calibrate the time-dependent volatility function for European options under the fractional Vasicek interest rate model. A fully implicit finite difference method is applied to solve the partial differential equation of option pricing numerically. To find the volatility function, we minimize a cost function that is the sum of the squared errors between the theoretical prices and market prices with Tikhonov $ L_2 $ regularization and $ L_{1/2} $ regularization respectively. Finally numerical experiments with simulated and real market data verify the efficiency of the proposed methods.</p></abstract>

Optimal Investment‐Consumption Strategy of Household Based on CEV Model

To maintain and increase household wealth, this study studies the optimal allocation ratio of household investment and consumption. When considering venture capital, it is assumed that the theoretical price of risky asset obeys the CEV model. Our goal was to maximize the expectation of household cumulative consumption and the discounted utility of terminal wealth and to solve the optimal consumption and investment ratio using the dynamic programming principle and HJB equation. Using logarithmic utility and isoelastic power utility function with residual utility, we get the analytical solution of the household investment‐consumption ratio by means of guessing and variable transformation. Finally, the influence of general parameters on the optimal ratio in the market is analyzed by numerical simulation and diagram, which is consistent with the description of actual situation. This study not only enriches portfolio theory but also provides investors with investment strategies.

Pembentukan Harga Cabai Merah Keriting Secara Teoritis Dan Empiris

High demand for curly red chilies will cause prices to rise while production cannot fulfill consumer desires. This situation was caused by an imbalance of supply-demand, where the supply-demand imbalance can be caused by several changes such as changes in production technology, population growth or number of consumers, changes in income levels per capita and season (., Asriani, and Rasyid 2012). Research data as research subjects were 1) Price time series data, curly red chili production at production centers 2) Supply data of curly red chilies from Cikajang Garut Regency, Caringin Central Market, Gedebage Main Market and Kramat Jati Central Market, 3) Time series data price, production, supply, government policies and supporting data from the West Java Food Crops Agriculture Office, and related agencies. The data used were time series data and supporting data from: Price information centers in production centers, main markets and price information at the West Java Food Crops Agricultural Service, for each marketing agency data was carried out by tracing the marketing chain. The research analysis was carried out in several ways, namely theoretically and empirically at the production center and the wholesale market described descriptively. Theoretical price formation can be explained that prices was formed based on supply and demand. Prices derived from price formation can come from the District or Provincial Agriculture Office and be informed from the Commodity Price Information Center in production centers and forwarded to farmers, dealers, traders and wholesale markets. Price information can be conveyed to between market players, so that farmers and market players know your margin and profit. Empirically, it can be seen that price formation in production centers was not seen to be formed from supply and demand. The price in the wholesale market is the price determined by market players in the wholesale market based on the amount of supply entering the main market and price information between the parent markets. The information center at PIKJ does not have production data from production centers so that when the price hike occurs, the version of the Ministry of Agriculture is imports of chilies ("specifically for curly red chilies, there are no imports"). Imports indicate that the production / supply decreases without knowing the actual amount of production, in this case the price information speed was faster than the production data that was informed per year so that prices in farmers still do not increase, meaning that farmers do not enjoy price increases, in this case it can be said that market mechanism was not working well.

Pricing analysis of wind power derivatives for renewable energy risk management

The objective of this study is to analyse the theoretical pricing of wind power derivatives, which is important for renewable energy risk management but has a problem in the pricing due to the illiquidity of the assets and to show the application of the theory to the practical implementation of the pricing. We make three contributions to the literature. First, to the best of our knowledge, we are the first to conduct a detailed econometric analysis of the wind power futures underlying, i.e., the electricity production based on windmills, resulting in strong support of seasonality and mean reversion in the logit-transformed wind power load factors. Second, after proposing a new model of wind power load factors based on the econometric findings, we analyse the theoretical prices of wind power futures and call option contracts to which the good-deal bounds pricing within an illiquid market situation is applied as well as we show the application of the theory to the practical pricing with the illiquidity. Third, our empirical pricing analysis shows that theoretical wind power futures prices derived using seasonal modelling more accurately reflect reality than those derived without seasonality compared to market observations, resulting in the importance of seasonality modelling in theoretical wind power derivatives pricing. In particular, considering that the upper and lower price boundaries represent the selling and the buying prices in the incomplete market, respectively, we show that the pricing of the short position is more affected by the seasonality than the pricing of the long position. Finally, we illustrate and discuss the practical applications of the results obtained in our study.