ANALISIS PENERAPAN METODE POHON BINOMIAL DAN METODE BLACK-SCHOLES DALAM PENENTUAN HARGA OPSI BELI

Opsi adalah salah satu surat perjanjian jual beli saham antara pihak penjual dan pembeli untuk melakukan suatu kesepakatan dengan harga dan periode yang ditentukan. Seseorang yang membeli opsi bisa memilih untuk melaksanakan haknya ataupun tidak. Penelitian ini bertujuan mengetahui hasil perbandingan harga Opsi Beli Apple Inc., dengan penggunaan dua metode yaitu metode Pohon Binomial dan metode Black-Scholes. Hasil dari penelitian ini menunjukkan bahwa dengan asumsi suku bunga bebas risiko dan strike price yang ditentukan sama, maka hasil perhitungan harga Opsi Beli dengan kedua metode tersebut hampir sama. Dapat disimpulkan bahwa harga Opsi Beli yang didapat dengan metode Pohon Binomial mendekati harga Opsi Beli dengan metode Black-Scholes. Sehingga kedua metode tersebut layak digunakan untuk perhitungan awal harga Opsi Beli.Kata kunci: Metode black-scholes, metode pohon binomial, opsi tipe eropa

At-Tahur’s IPO: Creating Pakistan’s First Public Company in Pasteurized Dairy Segment

This case examines the initial public offering (IPO) decision made by At-Tahur Limited during 2017. The outstanding performance of the equity market led the company to decide in favour of stock issuance to finance its required expansion. However, soon after the company started its IPO process till the month when the shares were floated in the market, Pakistan Stock Exchange experienced its worst decline since the financial crisis, with the index dropping by 17% over the one year from July 2017 to July 2018. The IPO was oversubscribed, and the company was able to sell its shares at PKR 21 per share, higher than the floor price of PKR 20. The strong demand for the company’s shares and a successfully completed stock offering transaction during one of the most difficult periods in capital market history left the IPO management team confused about whether PKR 21 was an appropriate price for the company’s share and if it was the correct time for the company to go public. The case provides an opportunity to discuss the valuation of unseasoned equity using market multiples and discounted cash flow models. Students are invited to value At-Tahur’s stock in light of the company’s planned expansion and take a position on whether the IPO strike price of PKR 21 was correct. The case also allows for a discussion of IPO trends, costs and benefits of going public and the IPO underpricing phenomenon.

Restricted Stock is on the Rise: What Does this Mean for Whistleblowing?

The use of restricted stock compensation to supplement or to give a bonus to executives is on the rise. What happens when things go wrong? Research finds that those in private companies are less likely to whistleblow than those in public companies overall. Literature also reveals that restricted stock may positively influence whistleblowing when large financial rewards are present. Further, vesting period and strike price influence whistleblowing for those with stock option compensation. Yet, little is investigated regarding whistleblowing related to the vesting period of the restricted stock and the type of organization -public or private- granting this compensation. We find that for those in public companies, whistleblowing tends to increase as the vesting period of the stock compensation is farther in the future. Those in private companies have the opposite behavior. Agency theory focused within whistleblowing theory helps resolve this seeming juxtaposition. Implications for practice and policy are offered.

Using Logistic Regression of Machine Learning Method to Evaluate American Options

Aims: The main purpose of this study is to understand whether Logistic regression has certain benefits in the evaluation of American options. As far as the Monte Carlo method is concerned, the least square method is traditionally used to evaluate American options, but in fact, Logistic regression is generally quite good in classification performance. Therefore, this study wants to know if Logistic regression can improve the accuracy of evaluation in American options. Study Design: The selection of options parameters required in the simulation process mainly considers the average level of actual market conditions in the past few years in terms of dividend yield and risk-free interest rate. The part of the stock price and the strike price mainly considers three different situations: in-the-money, out-of-the-money and at the money. Methodology: This study applied the Logistic regression in Monte Carlo method for the pricing of American. Uses the ability of logistic regression to help determine whether the American option should be exercised early for each stock price path. The validity of the proposed method is supported by some vanilla put cases testing. The parameters used in all cases tested are considered the current state of the market. Conclusion: This study demonstrates the effectiveness of the proposed approach using numerical examples, revealing significant improvements in numerical efficiency and accuracy. Several test cases showed that the relative error of all tests are below 1%.

State price density estimation with an application to the recovery theorem

This article introduces a model to estimate the risk-neutral density of stock prices derived from option prices. To estimate a complete risk-neutral density, current estimation techniques use a single mathematical model to interpolate option prices on two dimensions: strike price and time-to-maturity. Instead, this model uses B-splines with at-the-money knots for the strike price interpolation and a mixed lognormal function that depends on the option expiration horizon for the time-to-maturity interpolation. The results of this “hybrid” methodology are significantly better than other risk-neutral density extrapolation methods when applied to the recovery theorem.

THE RELATIONSHIP BETWEEN OPTIONS DERIVATIVES AND FINANCIAL PERFORMANCE OF SELECTED LISTED COMMERCIAL BANKS IN KENYA

Purpose: The purpose of the study was to ascertain the relationship between options derivatives and financial performance of selected listed commercial banks in Kenya. Methodology: Descriptive research design was used when collecting data using closed ended questionnaires from the selected 11 listed commercial banks in Kenya. The target population included 156 respondents who were 25 risk managers, 53 operations managers, 33 credit managers and 45 marketing managers to participate in the study. The study selected all of the 156 respondents through census sampling technique. Pre-test questionnaires was sent to six respondents who were junior officers in risk, credit, operations and marketing departments of non-listed commercial banks in Meru Kenya. The collected data was then coded and analyzed quantitatively using the descriptive statistics such as mean, percentage and standard deviation while inferential statisticsperson correlation analysis were used. Linear regression models were also used. Further on, the tables, graphs were used when indicating the analysis results. Results: Options had a statistically significant relationship with financial performance. Most respondents agreed that there were clear procedures used to solve options price discrepancies. It had a mean of 4.79 and standard deviation of 0.62. However, most respondents disagreed that options derivatives market activities were improving in the banks. It had a mean of 3.85 and standard deviation of 1.05. The results further indicated that options had an R value of .793a and Durbin Watson value of 1.292 showing there was a strong correlation between the two variables, while the R-square was 0.629. This implied that options as a paradigm predicted 62.9% of financial performance variable in this study.Options also had a significant p-value of 0.018. Unique contribution to theory, policy and practice: The results indicated that commercial banks were really incurring more costs as compared to profits generated due to errors made by the employees when engaging in various options derivatives markets. In addition, when financial derivatives owners were given the rights and not forced to purchase or vend an underlying asset at a strike price or exercise price, at or earlier than the expiry date of the options, there was an above average purchase. The study recommends that the bank staff should explain full information on the options derivatives so that when a client is making the purchase, they are well knowledgeable. This knowledge should begin from the procedures followed when making a purchase, sale or transfer of option derivatives in the securities exchange market. In addition, any costs associated with the options derivatives should be fully communicated to clients priorly to avoid premature termination of options derivatives contracts. Further on, there should be more training on banks staffs by the bank management so that they are equipped with knowledge on the specifics of options derivatives trading. By doing so, the chances of errors would be minimized.

American Basket Option Pricing Formulas in Uncertain Environment

American basket option is a contract containing multiple underlying assets, and its payoff is correlated with average prices or weighted average prices of these assets on or before the expiration date. The type of option entitles a holder the right to trade at the strike price within a specified date, and this right can be waived. Therefore, there is a certain price to be paid for acquiring this right, which produces the problem of option pricing. A lot of literature shows blackthat basket option price is usually cheaper than option portfolios on individual underlying assets. Based on this advantage, basket option blackbecomes popular among investors. Consequently, this paper predominantly explores four types of American basket option pricing in uncertain financial environment. Specifically they are American arithmetic basket call option, American arithmetic basket put option, American geometric basket call option and American geometric basket put option. Assuming that these stocks prices follow corresponding uncertain differential equations, we derive corresponding option pricing formulas. Some numerical examples are taken to illustrate the feasibility of pricing formulas. Simultaneously, this paper discusses the relationship between option price and some parameters.

Penentuan Harga Opsi Dengan Volatilitas Stokastik Menggunakan Metode Monte Carlo

ABSTRAKHal yang utama dalam perdagangan opsi adalah penentuan harga jual opsi yang optimal. Namun pada kenyataan sebenarnya fluktuasi harga aset yang terjadi di pasar menandakan bahwa volatilitas dari harga aset tidaklah konstan, hal ini menyebabkan investor mengalami kesulitan dalam menentukan harga opsi yang optimal. Artikel ini membahas tentang penentuan harga opsi tipe Eropa yang optimal dengan volatilitas stokastik menggunakan metode Monte Carlo dan pengaruh harga saham awal, harga strike, dan waktu jatuh tempo terhadap harga opsi Eropa. Adapun model volatilitas stokastik yang digunakan dalam penelitian ini adalah model Heston, yang mengasumsikan bahwa proses harga saham (St) mengikuti distribusi log-normal, dan proses volatilitas saham (Vt) mengikuti Proses Cox-Ingersoll-Ross. Hal pertama yang dilakukan dalam penelitian ini adalah mengestimasi parameter model Heston untuk mendapatkan harga saham dengan menggunakan metode ordinary least square dan metode numerik Euler-Maruyama. Langkah kedua adalah melakukan estimasi harga saham untuk mendapatkan harga opsi tipe Eropa menggunakan metode Monte Carlo. Hasil dari penelitian ini menunjukkan bahwa penggunaan metode Monte Carlo dalam penentuan harga opsi tipe Eropa dengan volatilitas stokastik model Heston menghasilkan solusi yang cukup baik karena memiliki nilai error yang kecil dan akan konvergen ke solusi eksaknya dengan semakin banyak simulasi. Selain itu, simulasi Monte Carlo memberikan kesimpulan bahwa parameter harga strike, harga saham awal dan waktu jatuh tempo memiliki pengaruh terhadap harga opsi yang konsisten dengan teori harga opsi. ABSTRACTWhat is important in options trading is determining the optimal selling price. However, in real market conditions, fluctuations in asset prices that occur in the market indicate that the volatility of asset prices is not constant, this causes investors to experience difficulty in determining the optimal option price. This article discusses the optimal determination of the European type option price with stochastic volatility using the Monte Carlo method and the effect of the initial stock price, strike price, and expiration date on European option prices. The stochastic volatility model used in this study is the Heston model, which assumes that the stock price process (S) follows the normal log distribution, and the stock volatility process (V) follows the Ingersoll-Ross Cox Process. The first thing to do in this study is to estimate the parameters of the Heston model to get stock prices using the ordinary least square method and the Euler-Maruyama numerical method. The second step is to estimate the share price to get the European type option price using a Monte Carlo Simulation. This study indicates that using the Monte Carlo method in determining the price of European type options with the Heston model of stochastic volatility produces a fairly good solution because it has a small error value and will converge to the exact solution with more simulations. Also, the Monte Carlo simulation concludes that the parameters of the strike price, initial stock price, and maturity date influence the option price, which is consistent with the option price theory.

How Should Performance Signals Affect Contracts?

The informativeness principle states that a contract should depend on informative signals. This paper studies how it should do so. Signals indicating that the output distribution has shifted to the left (e.g., weak industry performance) reduce the threshold for the manager to be paid; those indicating that output is a precise measure of effort (e.g., low volatility) decrease high thresholds and increase low thresholds. Surprisingly, “good” signals of performance need not reduce the threshold. Applying our model to performance-based vesting, we show that performance measures should affect the strike price, rather than the number of vesting options, contrary to practice.

A new method to solve fuzzy stochastic finance problem

PurposeThe authors discuss the value of portfolio and Black–Scholes (B–S)-option pricing model in fuzzy environment.Design/methodology/approachThe B–S option pricing model (OPM) is an important role of an OPM in finance. Here, every decision is taken under uncertainty. Due to randomness or vagueness, these uncertainties may be random or fuzzy or both. As the drift µ, the degree of volatility s, interest rate r, strike price k and other parameters of the value of the portfolio V(t), market price S_0 (t) and call option C(t) are not known exactly, so they are treated as positive fuzzy number. Partial expectation of fuzzy log normal distribution is derived. Also the value of portfolio at any time t and the B–S OPM in fuzzy environment are derived. A numerical example of B–S OPM is illustrated.FindingsFirst, the authors are studying some various paper and some stochastic books.Originality/valueThis is a new technique.