scholarly journals Estimasi Harga Multi-State European Call Option Menggunakan Model Binomial

CAUCHY ◽  
2011 ◽  
Vol 1 (4) ◽  
pp. 182
Author(s):  
Mila Kurniawaty, Endah Rokhmati ◽  
Endah Rokhmati
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Call Option ◽  
Expiration Date ◽  
Strike Price ◽  
Underlying Asset ◽  
Put Option ◽  
European Call Option ◽  
Black Scholes

Option merupakan kontrak yang memberikan hak kepada pemiliknya untuk membeli (call option) atau menjual (put option) sejumlah aset dasar tertentu (underlying asset) dengan harga tertentu (strike price) dalam jangka waktu tertentu (sebelum atau saat expiration date). Perkembangan option belakangan ini memunculkan banyak model pricing untuk mengestimasi harga option, salah satu model yang digunakan adalah formula Black-Scholes. Multi-state option merupakan sebuah option yang payoff-nya didasarkan pada dua atau lebih aset dasar. Ada beberapa metode yang dapat digunakan dalam mengestimasi harga call option, salah satunya masyarakat finance sering menggunakan model binomial untuk estimasi berbagai model option yang lebih luas seperti multi-state call option. Selanjutnya, dari hasil estimasi call option dengan model binomial didapatkan formula terbaik berdasarkan penghitungan eror dengan mean square error. Dari penghitungan eror didapatkan eror rata-rata dari masing-masing formula pada model binomial. Hasil eror rata-rata menunjukkan bahwa estimasi menggunakan formula 5 titik lebih baik dari pada estimasi menggunakan formula 4 titik.

scholarly journals TESTING OF THE BLACK SCHOLES AND GARCH MODELS IN LQ45 USING LONG STRADDLE STRATEGY IN 2009-2018

2021 ◽  
Vol 22 (1) ◽  
pp. 30-39
Author(s):  
Riko Hendrawan ◽  
Anggadi Sasmito
Keyword(s):  
Time Series Data ◽  
Mean Squared Error ◽  
Series Data ◽  
Call Option ◽  
Due Date ◽  
Average Percentage ◽  
Put Option ◽  
Option Contract ◽  
Black Scholes ◽  
Better Than

The purpose of this study is to examine the implementation of option contracts using Black Scholes and GARCH on the LQ45 index using the long straddle strategy. This study uses time-series data as a time frame for conducting research, using a sample of closing price data for the LQ 45 daily index for 2009-2018. For the test the model, we used the secondary data of the closing stock price index from February 28, 2009 to March 31, 2019The results of this study are seen by comparing the average percentage value of Average Mean Squared Error (AMSE) of Black Scholes and GARCH with the application of a long straddle strategy, where the smaller the percentage value, the better the model will be. Within one month of option contract due date, Black Scholes is better than GARCH, with an error value on the call option of 2.77% and the put option of 1.56%. Within two months of option contract due date, GARCH is better than Black Scholes, with an error value on the call option of 8.12% and the put option of 4.00%. Within three months of option contract due date, Black Scholes is better than GARCH, with an error value on the call option of 12.38% and on the put option of 5.50%. The long straddle strategy in the LQ45 index only reached a maximum of 60% of possible profits, with an average of around 30% possible profits.

STOCHASTIC VOLATILITY

2002 ◽  
Vol 05 (05) ◽  
pp. 515-530 ◽  
Author(s):  
SOTIRIOS SABANIS
Keyword(s):  
Brownian Motion ◽  
Stochastic Volatility ◽  
Series Representation ◽  
Random Variable ◽  
Call Option ◽  
Underlying Asset ◽  
European Call Option ◽  
Practical Convergence ◽  
Security Price ◽  
Simulation Results

Hull and White [1] have priced a European call option for the case in which the volatility of the underlying asset is a lognormally distributed random variable. They have obtained their formula under the assumption of uncorrelated innovations in security price and volatility. Although the option pricing formula has a power series representation, the question of convergence has been left unanswered. This paper presents an iterative method for calculating all the higher order moments of volatility necessary for the process of proving convergence theoretically. Moreover, simulation results are given that show the practical convergence of the series. These results have been obtained by using a displaced geometric Brownian motion as a volatility process.

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.

THE EARLY EXERCISE PREMIUM IN AMERICAN OPTIONS BY USING NONPARAMETRIC REGRESSIONS

2018 ◽  
Vol 21 (07) ◽  
pp. 1850039
Author(s):  
WEIPING LI ◽  
SU CHEN
Keyword(s):  
Mean Square Error ◽  
Nonparametric Regression ◽  
American Options ◽  
Mean Square ◽  
Early Exercise ◽  
American Put Option ◽  
Put Option ◽  
Out Of Sample ◽  
American Put ◽  
Early Exercise Premium

The early exercise premium and the price of an American put option are evaluated by using nonparametric regression on the time to expiration, the moneyness and the volatility of underlying assets. In terms of mean square error (MSE), our nonparametric methods of American put option pricings outperform the existing classical methods for both in-the-sample (1 September 2011–31 January 2012) and out-of-sample (1 September 2012–28 February 2013) testings on the S&P 100 Index (OEX). Our methods have better predictions and more accurate approximations. The Greek letters for both the early exercise premium and the American put option are computed numerically.

scholarly journals Analytical Solution of Black-Scholes Equation in Predicting Market Prices and Its Pricing Bias

2020 ◽  
pp. 17-23
Author(s):  
Azor, Promise Andaowei ◽  
Amadi, Innocent Uchenna
Keyword(s):  
Analytical Solution ◽  
Goodness Of Fit ◽  
Call Option ◽  
Option Prices ◽  
Goodness Of Fit Test ◽  
Market Prices ◽  
European Call Option ◽  
Black Scholes

This paper is geared towards implementation of Black-Scholes equation in valuation of European call option and predicting market prices for option traders. First, we explained how Black-Scholes equation can be used to estimate option prices and then we also estimated the BS pricing bias from where market prices were predicted. From the results, it was discovered that Black-Scholes values were relatively close to market prices but a little increase in strike prices (K) decreases the option prices. Furthermore, goodness of fit test was done using Kolmogorov –Sminorvov to study BSM and Market prices.

scholarly journals Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing

2018 ◽  
Vol 10 (6) ◽  
pp. 108
Author(s):  
Yao Elikem Ayekple ◽  
Charles Kofi Tetteh ◽  
Prince Kwaku Fefemwole
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Call Option ◽  
Option Prices ◽  
Options Market ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Real Market ◽  
Independent Path

Using market covered European call option prices, the Independence Metropolis-Hastings Sampler algorithm for estimating Implied volatility in option pricing was proposed. This algorithm has an acceptance criteria which facilitate accurate approximation of this volatility from an independent path in the Black Scholes Model, from a set of finite data observation from the stock market. Assuming the underlying asset indeed follow the geometric brownian motion, inverted version of the Black Scholes model was used to approximate this Implied Volatility which was not directly seen in the real market: for which the BS model assumes the volatility to be a constant. Moreover, it is demonstrated that, the Implied Volatility from the options market tends to overstate or understate the actual expectation of the market. In addition, a 3-month market Covered European call option data, from 30 different stock companies was acquired from Optionistic.Com, which was used to estimate the Implied volatility. This accurately approximate the actual expectation of the market with low standard errors ranging between 0.0035 to 0.0275.

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.

Pricing options on a mean-reverting asset by the analytical operator splitting method

2021 ◽  
pp. 2150002
Author(s):  
C. F. Lo ◽  
Y. W. He
Keyword(s):  
Operator Splitting ◽  
Splitting Method ◽  
Dynamical Symmetry ◽  
Call Option ◽  
Option Prices ◽  
Pricing Options ◽  
Operator Splitting Method ◽  
European Call Option ◽  
Price Formula ◽  
Black Scholes

In this paper, we propose an operator splitting method to valuate options on the inhomogeneous geometric Brownian motion. By exploiting the approximate dynamical symmetry of the pricing equation, we derive a simple closed-form approximate price formula for a European call option which resembles closely the Black–Scholes price formula for a European vanilla call option. Numerical tests show that the proposed method is able to provide very accurate estimates and tight bounds of the exact option prices. The method is very efficient and robust as well.

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