scholarly journals Penentuan Harga Opsi Barrier Menggunakan Metode Trinomial Kamrad-Ritchken Dengan Volatilitas Model Garch

2019 ◽  
Vol 10 (1) ◽  
pp. 83-92
Author(s):  
S Sulastri ◽  
Lienda Novieyanti ◽  
Sukono Sukono
Keyword(s):  
Stock Price ◽  
Option Price ◽  
Barrier Options ◽  
Barrier Option ◽  
Market Conditions ◽  
Strike Price ◽  
Daily Data ◽  
Closing Price ◽  
The Right ◽  
Initial Price

Abstract. This study aims to minimize the violation of the assumptions of determining price options by taking into account the actual market conditions in order to obtain the right price that will provide high profits for investors. The method used to determine the option price in this study is the Kamrad Ritchken trinomial with volatility values that will be modeled first using GARCH. The data used in this study is daily data (5 working days per week) from the closing price of the stock price of PT. Bank Rakyat Indonesia, Tbk (BBRI. Based on the results of the research, the best model is GARCH (1,1). For the call up barrier option, increase the strike price with the initial price and barrier which causes the option price to call up the barrier "in" and "out" decreases, on the contrary to the put barrier option, an increase in strike price with the initial price and a barrier that causes the put barrier option price to both put up-in and put up-out. initial and barrier which still causes the call down barrier option price both in and out decreases, on the contrary in the put down barrier option, increasing strike price with the initial price and barrier which causes the put down barrier option price to increase in and out.Keywords: Barrier Options, Trinomial, Kamrad Ritchken, Volatility, GARCH  Abstrak. Penelitian ini bertujuan untuk meminimalkan pelanggaran asumsi-asumsi penentuan harga opsi dengan memperhatikan kondisi pasar yang sebenarnya sehingga diperoleh harga yang tepat yang akan memberikan keuntungan tinggi bagi investor. Metode yang digunakan untuk menentukan harga opsi dalam penelitian ini adalah trinomial Kamrad Ritchken dengan nilai volatilitas yang akan dimodelkan terlebih dahulu dengan menggunakan GARCH. Data yang digunakan dalam penelitian ini adalah data harian (5 hari kerja per minggu) dari harga penutupan harga saham PT. Bank Rakyat Indonesia, Tbk (BBRI). Berdasarkan hasil penelitian diperoleh model yang paling baik adalah GARCH (1,1). Untuk opsi call up barrier, peningkatan strike price dengan harga awal dan barrier yang tetap menyebabkan harga opsi call up barrier baik "in" maupun "out" menurun, sebaliknya pada opsi put barrier, peningkatan strike price dengan harga awal dan barrier yang tetap menyebabkan harga opsi put barrier baik put up-in maupun put up-out meningkat. Sedangkan untuk opsi call barrier, peningkatan strike price dengan harga awal dan barrier yang tetap menyebabkan harga opsi call down barrier baik in maupun out menurun, sebaliknya pada opsi put down barrier, peningkatan strike price dengan harga awal dan barrier yang tetap menyebabkan harga opsi put down barrier baik in maupun out meningkat.Kata Kunci :  Opsi Barrier, Trinomial, Kamrad Ritchken, Volatilitas, GARCH

scholarly journals PERBANDINGAN KEKONVERGENAN METODE CONDITIONAL MONTE CARLO DAN ANTITHETIC VARIATE DALAM MENENTUKAN HARGA OPSI CALL TIPE BARRIER

2018 ◽  
Vol 7 (3) ◽  
pp. 271
Author(s):  
NI LUH PUTU KARTIKA WATI ◽  
KOMANG DHARMAWAN ◽  
KARTIKA SARI
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Stock Price ◽  
Option Price ◽  
Life Time ◽  
Barrier Option ◽  
Strike Price ◽  
Stock Volatility ◽  
Volatility Risk ◽  
Conditional Monte Carlo

Barrier option is an option where the payoff price depends  on whether or not the stock price passes the barrier during its life time. The aim of the research is to compare the convergence between conditional Monte Carlo and antithetic variate methods in determining the call barrier option  price. The call barrier option price  is influenced by several factors: initial stock price, stock volatility, risk-free interest rate, maturity, strike price and barrier. The calculation of call barrier option price is obtained by simulating stock price movements with different simulation number. Based on the simulation result, it is obtained that the calculation of call barrier option price with conditional Monte Carlo method converge faster than the antithetic variate method.

scholarly journals OPTIONS WRITTEN ON STOCKS WITH KNOWN DIVIDENDS

2004 ◽  
Vol 07 (07) ◽  
pp. 901-907
Author(s):  
ERIK EKSTRÖM ◽  
JOHAN TYSK
Keyword(s):  
Stock Price ◽  
Option Price ◽  
Option Prices ◽  
Strike Price ◽  
Call Options ◽  
Alternative Approach ◽  
Black Scholes ◽  
Market Practice ◽  
The Difference ◽  
Risk Free Rate

There are two common methods for pricing European call options on a stock with known dividends. The market practice is to use the Black–Scholes formula with the stock price reduced by the present value of the dividends. An alternative approach is to increase the strike price with the dividends compounded to expiry at the risk-free rate. These methods correspond to different stock price models and thus in general give different option prices. In the present paper we generalize these methods to time- and level-dependent volatilities and to arbitrary contract functions. We show, for convex contract functions and under very general conditions on the volatility, that the method which is market practice gives the lower option price. For call options and some other common contracts we find bounds for the difference between the two prices in the case of constant volatility.

scholarly journals Pricing of Barrier Options on Underlying Assets with Jump-Diffusion Dynamics: A Mellin Transform Approach

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1271
Author(s):  
Marianito R. Rodrigo
Keyword(s):  
Mellin Transform ◽  
Jump Diffusion ◽  
Futures Contracts ◽  
Barrier Options ◽  
Barrier Option ◽  
Underlying Asset ◽  
Diffusion Dynamics ◽  
Path Dependent ◽  
The Right ◽  
Right To Buy

A barrier option is an exotic path-dependent option contract where the right to buy or sell is activated or extinguished when the underlying asset reaches a certain barrier price during the lifetime of the contract. In this article we use a Mellin transform approach to derive exact pricing formulas for barrier options with general payoffs and exponential barriers on underlying assets that have jump-diffusion dynamics. With the same approach we also price barrier options on underlying futures contracts.

PENENTUAN HARGA OPSI DENGAN MODEL BLACK-SCHOLES MENGGUNALKAN METODE BEDA HINGGA FORWARD TIME CENTRAL SPACE

2018 ◽  
Vol 1 (1) ◽  
pp. 45
Author(s):  
Werry Febrianti
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Option Price ◽  
Call Option ◽  
Put Option ◽  
Daily Data ◽  
Black Scholes ◽  
One Year ◽  
The Right

Option can be defined as a contract between two sides/parties said party one and party two. Party one has the right to buy or sell of stock to party two. Party two can invest by observe the put option price or call option price on a time period in the option contract. Black-Scholes option solution using finite difference method based on forward time central space (FTCS) can be used as the reference for party two in the investment determining. Option price determining by using Black-Scholes was applied on Samsung stock (SSNLF) by using finite difference method FTCS. Daily data of Samsung stock in one year was processed to obtain the volatility of the stock. Then, the call option and put option are calculated by using FTCS method after discretization on the Black-Scholes model. The value of call option was obtained as $1.457695030014260 and the put option value was obtained as $1.476925604670225.

scholarly journals OPSI SAHAM PADA PASAR MODAL DI INDONESIA (STUDI PASAR OPSI SAAT PASAR OPSI MASIH BERLANGSUNG DI BURSA EFEK INDONESIA)

2019 ◽  
Vol 2 (2) ◽  
pp. 300
Author(s):  
Syanti Dewi ◽  
Ishak Ramli
Keyword(s):  
Interest Rate ◽  
Stock Prices ◽  
Stock Price ◽  
Stock Exchange ◽  
Option Price ◽  
Stock Option ◽  
Exchange Market ◽  
Strike Price ◽  
Option Trading ◽  
Put Option

Stock option exchange market is not working anymore in the Indonesian Stock Exchange, using the data option exchange market for the running period 2007-2008, we analyzed the effect of stock price, strike price, time to maturity, volatility and risk- free interest rate on the stock option’s price of listed stock call or put option trading at the Indonesian Stock Exchange during 2007-2008. The results found that the stock price, strike price, time to maturity, volatility and risk-free interest rate are positive significantly affecting the stock option price either the buying option price or the selling option price in Indonesia Stock Exchange 2007-2008 period. While there were no variables that significantly affected the call option during the periode 2007-2008, furthermore stock prices and strike prices significantly affected the put option prices. Time to maturity, Volatility, and risk free interest rate did not significantly affect the put option prices.That is why the stock option exchange market stop since the investor were not sure to the stock option price versus the risk of the volatility, time to maturity, and riskfree rate.

American Basket Option Pricing Formulas in Uncertain Environment

2021 ◽  
pp. 2150011
Author(s):  
Rong Gao ◽  
Xiaofang Yin
Keyword(s):  
Option Pricing ◽  
Option Price ◽  
Weighted Average ◽  
Call Option ◽  
Strike Price ◽  
Basket Option ◽  
Put Option ◽  
The Right ◽  
The Relationship ◽  
Financial 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.

scholarly journals Forecasting the Stock Price by using Holt’s Method

2019 ◽  
Vol 1 (1) ◽  
pp. 15
Author(s):  
Omar Sharif ◽  
Md Zobaer Hasan
Keyword(s):  
Stock Price ◽  
Stock Exchange ◽  
Share Price ◽  
Long Period ◽  
Daily Data ◽  
Short Period ◽  
Closing Price ◽  
Long Time ◽  
Short Time ◽  
A Share

This study proposed to develop a stock indicator that can forecast the value of a share by considering the daily closing price or opening price with the different parameter of Holt’s method. Most of the indicator which is existing in most of the stock market which forecasted value is based on a long period forecast. But, Holt’s method will be easy to analyze the price of an individual company with maximum accuracy for short period forecasting. The daily data, the closing price of the different company, are collected from the Dhaka Stock Exchange (DSE) for the period of 2016. The variables: level, trend, forecast as well as smoothing constant (α, β) are used for quick reaction to systematic changes in the time series. By using Holt’s method, a buyer can predict, how much of a share price will be the next day. The research finds that Holt’s method forecasting is better for short time then long time as evidence shows that the fourth day predicted value is closer to the actual value. In addition, the analysis discovers that for prediction the forecast value, the fifteen and seven days’ data of any company are more accurate than 30 days’ data. This study notices that different smoothing constant is the big factor for forecasting and suggests to use smoothing constant α = 0.5, β = 0.1.

scholarly journals Penentuan Harga Opsi Asia dengan Metode Monte Carlo

2017 ◽  
Vol 3 (1) ◽  
pp. 44-48
Author(s):  
Surya Amami Pramuditya
Keyword(s):  
Monte Carlo ◽  
Confidence Interval ◽  
Stock Price ◽  
Variance Reduction ◽  
Option Price ◽  
Numerical Procedure ◽  
Reduction Technique ◽  
Asian Options ◽  
Call Option ◽  
Strike Price

An option is a contract between a holder and a writer in which the writer grants the rights (not obligations) to the holder to buy or sell the assets of the writer at a certain price (strike price) at maturity time. Asian options are included in the dependent path option. This means that Asia's payoff option depends not only on the stock price at maturity time, but it is the average stock price during its maturity and symbolized A (average). Monte Carlo is basically used as a numerical procedure to estimate the expected value of pricing product derivatives. The techniques used are the standard Monte Carlo and variance reduction. The result obtained the Asia call option price and put for both techniques with 95% confidence interval. The variance reduction technique looks faster reducing 95% confidence interval than standard method.

scholarly journals Volatility Timing: Pricing Barrier Options on DAX XETRA Index

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 722
Author(s):  
Carlos Esparcia ◽  
Elena Ibañez ◽  
Francisco Jareño
Keyword(s):  
Option Pricing ◽  
Term Structure ◽  
Barrier Options ◽  
Barrier Option ◽  
Probability Term ◽  
Volatility Timing ◽  
The Right ◽  
The Impact ◽  
Complementary Study ◽  
Frequency Current

This paper analyses the impact of different volatility structures on a range of traditional option pricing models for the valuation of call down and out style barrier options. The construction of a Risk-Neutral Probability Term Structure (RNPTS) is one of the main contributions of this research, which changes in parallel with regard to the Volatility Term Structure (VTS) in the main and traditional methods of option pricing. As a complementary study, we propose the valuation of options by assuming a constant or historical volatility. The study implements the GARCH (1,1) model with regard to the continuously compound returns of the DAX XETRA Index traded at daily frequency. Current methodology allows for obtaining accuracy forecasts of the realized market barrier option premiums. The paper highlights not only the importance of selecting the right model for option pricing, but also fitting the most accurate volatility structure.

On the impact of a scrip dividend on an equity forward

2016 ◽  
Vol 03 (04) ◽  
pp. 1650024
Author(s):  
German Bernhart ◽  
Jan-Frederik Mai
Keyword(s):  
Stock Price ◽  
Strike Price ◽  
Stock Volatility ◽  
Time Period ◽  
Black Scholes ◽  
Forward Contract ◽  
Averaging Time ◽  
The Right ◽  
The Impact ◽  
Time Point

We consider an equity forward contract on a stock which pays a dividend during the forward’s lifetime. Furthermore, the stock owner is assumed to have the right to opt for either cash or scrip dividend. In the latter case, the stock owner receives the dividend in the form of additional shares and the number of shares to be received depends on the average stock price in a certain averaging time period. The decision between scrip or cash must be made by the stock owner at some time point during the averaging period. Within a Black–Scholes-type setup we derive a closed formula for the fair strike price of such an equity forward contract in dependence on the stock volatility parameter. If the decision between scrip or cash can be delayed until close to the end of the averaging period, it is demonstrated how the optionality for the stock owner has a non-negligible value which lowers the forward equity strike.

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