scholarly journals The Black-Scholes Model Guideline For Options Course As Taught At Notre Dame University - Lebanon

2011 ◽  
Vol 4 (1) ◽  
Author(s):  
Viviane Y. Naimy
Keyword(s):  
Option Price ◽  
Stochastic Calculus ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Calculus I ◽  
Relationship Of ◽  
The Relationship

This paper presents the methodology used for Notre Dame University’s finance students to explain and explore the Black-Scholes model without going through the complexity of mathematics to model random movements or through stochastic calculus. I will name and develop the steps that I follow in order to allow students to properly use the Black-Scholes model and to understand the relationship of the model’s inputs to the option price while monitoring the risk via delta and gamma hedging.

Employees’ Attitudes Toward Equity-Based Compensation

2012 ◽  
Vol 44 (5) ◽  
pp. 246-253 ◽  
Author(s):  
Menachem (Meni) Abudy ◽  
Efrat Shust
Keyword(s):  
Stock Options ◽  
Field Survey ◽  
Financial Education ◽  
Employee Stock Options ◽  
The Past ◽  
Black Scholes Model ◽  
Subjective Value ◽  
Black Scholes ◽  
Objective Value ◽  
The Relationship

This article presents a field study that examines the subjective value of equity-based compensation and investigates the relationship between attitude toward risk and compensation preferences. The participants in the field survey received equity-based compensation in the past but lack financial education background. We find that the respondents exhibit difficulty in estimating the value of employee stock options, which usually results in a subjective value that is lower than the objective value (calculated using the Black–Scholes model). Additional findings demonstrate the presence of behavioral biases such as priming and mental anchoring. Finally, we document an absence of transitivity in the preferences of 10% of the respondents.

AN APPLICATION OF MELLIN TRANSFORM TECHNIQUES TO A BLACK–SCHOLES EQUATION PROBLEM

2007 ◽  
Vol 05 (01) ◽  
pp. 51-66 ◽  
Author(s):  
MARIANITO R. RODRIGO ◽  
ROGEMAR S. MAMON
Keyword(s):  
Existence And Uniqueness ◽  
Mellin Transform ◽  
Formal Solution ◽  
Option Price ◽  
Contingent Claims ◽  
Time Dependent ◽  
European Option ◽  
Equation Problem ◽  
Black Scholes Model ◽  
Black Scholes

In this article, we use a Mellin transform approach to prove the existence and uniqueness of the price of a European option under the framework of a Black–Scholes model with time-dependent coefficients. The formal solution is rigorously shown to be a classical solution under quite general European contingent claims. Specifically, these include claims that are bounded and continuous, and claims whose difference with some given but arbitrary polynomial is bounded and continuous. We derive a maximum principle and use it to prove uniqueness of the option price. An extension of the put-call parity which relates the aforementioned two classes of claims is also given.

scholarly journals VOLATILITY SMILE AT THE RUSSIAN OPTION MARKET

2006 ◽  
Vol 7 (1) ◽  
pp. 9-15
Author(s):  
D. Golembiovsky ◽  
I. Baryshnikov
Keyword(s):  
Normal Distribution ◽  
Option Price ◽  
Underlying Asset ◽  
Basic Model ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Basic Purpose ◽  
Log Normal ◽  
In The Beginning ◽  
Log Normal Distribution

The main derivative exchange in Russia is FORTS (Futures and Options in RTS) which is a division of Russian Trade System (RTS). The underlying assets of option contracts are futures on Russian companies’ shares: OJSC “EES"1, OJPC “Lukoil"2 and OJSC “Gazprom"3. A basic model for estimation of fair option price is Black‐Scholes model, developed in the beginning of 70‐s’ years of the last century. This model defines the option premium as a cost of its hedging by underlying asset. It uses a number of assumptions: prices of underlying assets follow log‐normal distribution; hedging is accomplished continuously; an underlying asset is infinitely divisible; a volatility is constant on all period of option life. However, according to practice, prices of shares and futures do not follow normal or log‐normal distribution, a volatility can change during a life of option, and hedging is a discrete process. Thus, Black‐Scholes model can yield inexact results in real markets, especially it concerns deeply “in the money” or deeply “out of the money” options. The basic purpose of the paper is to investigate opportunities to apply Black‐Scholes model for an estimation of option premiums in the Russian market.

scholarly journals ESTIMASI NILAI IMPLIED VOLATILITY MENGGUNAKAN SIMULASI MONTE CARLO

2018 ◽  
Vol 7 (3) ◽  
pp. 239
Author(s):  
MAKBUL MUFLIHUNALLAH ◽  
KOMANG DHARMAWAN ◽  
NI MADE ASIH
Keyword(s):  
Monte Carlo ◽  
Capital Market ◽  
Implied Volatility ◽  
Option Price ◽  
European Options ◽  
Price Variation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Alternative Investment ◽  
The Capital Market

Investing among investors is an exciting activity to gain profit in the financial world. The development of investment in the financial world affects the number of alternative investment instruments that can be offered to investors in the capital market. The management of instruments in finance depends on the accuracy of forecasting of variables for example volatility. Volatility is a statistic of the degree of price variation in one period to the next which is expressed by ?. Volatility values can be estimated using Implied Volatility. Implied Volatility is the volatility used in determining the price of European options obtained by equalizing the price of the theoretical options, the price obtained from the Black-Scholes model, with the option price in the market. In this research will discuss how to estimate Implied Volatility value using the option obtained from simulation with Monte Carlo.

scholarly journals The Impact of Liquidity on GARCH Option Pricing Error during Financial Crisis

2017 ◽  
Vol 4 (4) ◽  
pp. 160
Author(s):  
Han Ching Huang ◽  
Yong Chern Su ◽  
Wei-Shen Chen
Keyword(s):  
Financial Crisis ◽  
Option Pricing ◽  
Garch Model ◽  
Black Scholes Model ◽  
Pricing Errors ◽  
Black Scholes ◽  
Out Of Sample ◽  
Pricing Error ◽  
The Impact ◽  
The Relationship

In this paper, we explore the valuation performance of Heston and Nandi GARCH (HN GARCH) model on the pricing of options of financial stocks listed for AMEX during pre and post financial crisis periods. We find that the GARCH pricing model presents better performance than the traditional Black-Scholes model for the out-of-sample option pricing, no matter what the moneyness and the time-to-maturity. Specifically, the models show the effects of liquidity is not significant. Intuitionally, smaller liquidity tends to exhibit more pricing errors, especially for longer mature options. Unfortunately, we cannot get the expected outcomes, which is that the period of post financial crisis tend to have larger pricing errors. In sum, except more computational convenience, the HN GARCH model offers another vision of the relationship between liquidity and its effect on pricing errors.

scholarly journals Radial Basis Function in Nonlinear Black-Scholes Option Pricing Equation with Transaction Cost

2019 ◽  
pp. 1-11
Author(s):  
Godwin Onwona-Agyeman ◽  
Francis T. Oduro
Keyword(s):  
Differential Equations ◽  
Radial Basis Function ◽  
Basis Function ◽  
Numerical Technique ◽  
Option Price ◽  
Meshfree Approximation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
The World ◽  
Radial Basis

Differential equations play significant role in the world of finance since most problems in these areas are modeled by differential equations. Majority of these problems are sometimes nonlinear and are normally solved by the use of numerical methods. This work takes a critical look at Nonlinear Black-Scholes model with special reference to the model by Guy Barles and Halil Mete Soner. The resulting model is a nonlinear Black-Scholes equation in which the variable volatility is a function of the second derivative of the option price. The nonlinear equation is solved by a special class of numerical technique, called, the meshfree approximation using radial basis function. The numerical results are presented in diagrams and tables.

Option pricing under multifractional Brownian motion in a risk neutral framework

2020 ◽  
Vol 38 (3) ◽  
Author(s):  
Fabrizio Di Sciorio
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Market Price ◽  
Option Price ◽  
Mathematical Framework ◽  
Call Option ◽  
Multifractional Brownian Motion ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes

In this paper, we introduce a new method to compute the European Call Option price (ct) under multi-fractional Brownian motion (mBm) with deterministic Hurst function. We build a mathematical framework using a Lebovits et al. study to approximate mBm to fractional Brownian motion (fBm). As a result we obtain ct , through the simulation of the logarithmic price under mBm, using a Vasicek model for the discount factor. Finally, we compare the results with those computed with the Black Scholes model and Call market price (SPX).

scholarly journals Simple Heuristic Approach To Introduction Of The Black-Scholes Model

2010 ◽  
Vol 3 (2) ◽  
pp. 31-42
Author(s):  
Rossitsa Yalamova
Keyword(s):  
Option Pricing ◽  
Protocol Analysis ◽  
Heuristic Approach ◽  
Probability Measures ◽  
Pricing Model ◽  
Black Scholes Model ◽  
Visual Illustration ◽  
Black Scholes ◽  
Option Pricing Model ◽  
The Relationship

A heuristic approach to explaining of the Black-Scholes option pricing model in undergraduate classes is described. The approach draws upon the method of protocol analysis to encourage students to `think aloud' so that their mental models can be surfaced. It also relies upon extensive visualizations to communicate relationships that are otherwise inaccessible at the average student's level of mathematical sophistication. This paper presents visual illustration of the changes in the probability measures with concrete examples breaking the option premium into four different components. The relationship between changes in variables and those components are graphically and algebraically illustrated.

The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽  
1980 ◽  
Vol 6 (02) ◽  
pp. 146-160 ◽  
Author(s):  
William A. Oliver
Keyword(s):  
Critical Points ◽  
Scleractinian Corals ◽  
Convincing Evidence ◽  
Early Triassic ◽  
Rugose Corals ◽  
History Of ◽  
The Subject ◽  
Relationship Of ◽  
The Relationship ◽  
Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

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