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.

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.

Option Pricing Under Multifractional Process and Long-Range Dependence

2020 ◽  
pp. 2150008
Author(s):  
Raffaele Mattera ◽  
Fabrizio Di Sciorio
Keyword(s):  
Brownian Motion ◽  
Probability Distribution ◽  
Option Pricing ◽  
Option Price ◽  
Long Range Dependence ◽  
Call Option ◽  
Closed Formula ◽  
Multifractional Brownian Motion ◽  
Put Option ◽  
European Call Option

We introduced a new method to compute the European Call (and Put) Option price under the assumption of multifractional Brownian motion (mBm). The reason why we need a procedure for estimating the Option price is due to the absence of a closed formula for this process. To compute the Option price, we first simulated the logarithmic price under mBm and, by using a discount factor, we computed the option’s pay-off. Then, we fitted the best probability distribution associated to the discounted pay-off, computing the European Call Option price as its average.

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 EMPIRICAL TEST OF PUT-CALL PARITY ON SPX OVER THE SHORT BAN 2008

2017 ◽  
Vol 33 (2) ◽  
Author(s):  
Huyen Do
Keyword(s):  
Empirical Test ◽  
Supply And Demand ◽  
Option Price ◽  
Short Selling ◽  
No Arbitrage ◽  
Put Option ◽  
Key Word ◽  
Momentum Trading ◽  
The Relationship ◽  
Trading Behaviour

Put call parity is a theoretical no-arbitrage condition linking a call option price to a put option price written on the same stock or index. This study finds that Put call parity violations are quite symmetric over the whole sample. However during the ban period 2008 in the U.S., puts are significantly and economically overpriced relative to calls. Some possible explanations are the short selling restriction, momentum trading behaviour and the changes in supply and demand of puts over the short ban. One interesting finding that the relationship between time to expiry, put call parity deviations and returns on the index is highly non-linear. Key word: Put-call parity, SPX, short ban 2008 .

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.

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 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 Martingale Approach to Pricing Perpetual American Options

1994 ◽  
Vol 24 (2) ◽  
pp. 195-220 ◽  
Author(s):  
Hans U. Gerber ◽  
Elias S.W. Shiu
Keyword(s):  
Stock Price ◽  
Sampling Theorem ◽  
Call Option ◽  
Martingale Approach ◽  
Put Option ◽  
American Contingent Claim ◽  
Russian Option ◽  
American Put ◽  
The Relationship ◽  
Optional Sampling Theorem

AbstractThe method of Esscher transforms is a tool for valuing options on a stock, if the logarithm of the stock price is governed by a stochastic process with stationary and independent increments. The price of a derivative security is calculated as the expectation, with respect to the risk-neutral Esscher measure, of the discounted payoffs. Applying the optional sampling theorem we derive a simple, yet general formula for the price of a perpetual American put option on a stock whose downward movements are skip-free. Similarly, we obtain a formula for the price of a perpetual American call option on a stock whose upward movements are skip-free. Under the classical assumption that the stock price is a geometric Brownian motion, the general perpetual American contingent claim is analysed, and formulas for the perpetual down-and-out call option and Russian option are obtained. The martingale approach avoids the use of differential equations and provides additional insight. We also explain the relationship between Samuelson's high contact condition and the first order condition for optimality.

scholarly journals MENENTUKAN HARGA OPSI DENGAN METODE MONTE CARLO BERSYARAT MENGGUNAKAN BARISAN KUASI ACAK FAURE

2021 ◽  
Vol 10 (3) ◽  
pp. 141
Author(s):  
PUTU WIDYA ASTUTI ◽  
KOMANG DHARMAWAN ◽  
KARTIKA SARI
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Random Sequence ◽  
Random Number Generator ◽  
Option Price ◽  
Call Option ◽  
Standard Distribution ◽  
Real Value ◽  
Conditional Monte Carlo ◽  
The Right

An option contract is a contract that gives the owner the right to sell or even to buy an asset at the predetermined price and period time. The conditional Monte Carlo is one of the several methods that is used to determine the option price which in the process uses random numbers with normal standard distribution. At the same time, the random number generator can be substituted by using a quasi-random sequence, as in Faure's quasi-random sequence. The aim of this study is to determine the contract price of the call option with the European type by applying the conditional Monte Carlo method. This method used the Faure quasi-random sequence and compared it with the method of Monte Carlo standard, Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. The results of this study showed that the call option calculated using the conditional Monte Carlo method using the quasi-random Faure sequence began to stabilize at the 5000th simulation for K = 32575 and K = 34725 and in the 10000th simulation for K = 33000 and K = 33950. Research also show that with the conditional Monte Carlo in using the quasi-random sequence of Faure is more stable. Therefore, it is obtained its real value faster than the Monte Carlo standard, Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. The MAPE value of conditional Monte Carlo in using the quasi-random sequences of Faure and the Monte Carlo standard is smaller than the Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. Therefore, it can be said to be more accurate when calculating the European type call option price at BBCA.JK stocks.

scholarly journals A fuzzy jump-diffusion option pricing model based on Merton formula

2021 ◽  
Author(s):  
Satrajit Mandal ◽  
Sujoy Bhattacharya
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Search Algorithm ◽  
Option Price ◽  
Jump Diffusion ◽  
Call Option ◽  
Pricing Model ◽  
Model Based ◽  
Option Pricing Model ◽  
Jump Diffusion Model

Abstract This paper proposes a fuzzy jump-diffusion option pricing model based on Merton's normal jump-diffusion price dynamics. The logarithm of the stock price is assumed to be a Gaussian fuzzy number and the diffusion and jump parameters of the Merton model are assumed to be triangular fuzzy numbers to model the impreciseness which occur due to the variation in financial markets. Using these assumptions, a fuzzy formula for a European call option has been proposed. Given any value of the option price, its belief degree is obtained by using the bisection search algorithm. The fuzzy call option prices have been defuzzified and it has been found that the fuzzy jump-diffusion model outperforms Wu's fuzzy Black- Scholes model. This is one of the first studies where the impreciseness of the stock price and input parameters has been modelled taking into account occasional large jumps in stock price trajectory and thereby proposing a fuzzy option pricing model.

Sign in / Sign up

Export Citation Format

Share Document