scholarly journals PENENTUAN HARGA JUAL OPSI BARRIER TIPE EROPA DENGAN METODE ANTITHETIC VARIATE PADA SIMULASI MONTE CARLO

2018 ◽  
Vol 7 (2) ◽  
pp. 71
Author(s):  
LUH HENA TERECIA WISMAWAN PUTRI ◽  
KOMANG DHARMAWAN ◽  
I WAYAN SUMARJAYA
Keyword(s):  
Monte Carlo ◽  
Analytic Solution ◽  
Asset Price ◽  
Selling Price ◽  
Barrier Options ◽  
Option Prices ◽  
Barrier Option ◽  
Underlying Asset ◽  
Closing Price ◽  
Path Dependent

The purpose of this research is to compare the selling price of down and out barrier option when the prices are simulated by the Antithetic Variate Monte Carlo and the standar Monte Carlo. Barrier options are path dependent options and the payoff depend on whether the underlying asset price touched the barrier or not during the life of the option. In this research, we conducted simulations against the closing price of the shares of PT Adhi Karya using Standard Monte Carlo simulation and the Monte Carlo-Antithetic Variate simulation. After the simulation, we obtained that the option prices using Antithetic Variate produces a cheaper price than the standar one. We also found that the analytic solution has a smaller error on its confidence interval compare to the Monte Carlo Standar.

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.

scholarly journals A Technical Note, Looback Options: a comparison between Monte Carlo Techniques

2020 ◽  
Vol 14 (2) ◽  
pp. 119
Author(s):  
Marcelo González A. ◽  
Antonio Parisi F. ◽  
Arturo Rodríguez P.
Keyword(s):  
Monte Carlo ◽  
Performance Measures ◽  
Asset Price ◽  
Contingent Claims ◽  
Technical Note ◽  
Time Interval ◽  
Underlying Asset ◽  
Monte Carlo Techniques ◽  
Lookback Options ◽  
Path Dependent

Looback options are path dependent contingent claims whose payoffs depend on the extrema of the underlying asset price over a certain time interval. In this note we compare the performance of two Monte Carlo techniques to price lookback options, a crude Monte Carlo estimator and Antithetic variate estimator. We find that the Antithetic estimator performs better under a variety of performance measures.

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 PENENTUAN HARGA OPSI BELI TIPE ASIA DENGAN METODE MONTE CARLO-CONTROL VARIATE

2017 ◽  
Vol 6 (1) ◽  
pp. 29
Author(s):  
NI NYOMAN AYU ARTANADI ◽  
KOMANG DHARMAWAN ◽  
KETUT JAYANEGARA
Keyword(s):  
Monte Carlo ◽  
Standard Error ◽  
Asset Price ◽  
Option Price ◽  
Asian Option ◽  
Underlying Asset ◽  
Average Value ◽  
Control Variate ◽  
Exercise Price ◽  
Maturity Date

Option is a contract between the writer and the holder which entitles the holder to buy or sell an underlying asset at the maturity date for a specified price known as an exercise price. Asian option is a type of financial derivatives which the payoff taking the average value over the time series of the asset price. The aim of the study is to present the Monte Carlo-Control Variate as an extension of Standard Monte Carlo applied on the calculation of the Asian option price. Standard Monte Carlo simulations 10.000.000 generate standard error 0.06 and the option price convergent at Rp.160.00 while Monte Carlo-Control Variate simulations 100.000 generate standard error 0.01 and the option price convergent at Rp.152.00. This shows the Monte Carlo-Control Variate achieve faster option price toward convergent of the Monte Carlo Standar.

scholarly journals NUMERICAL STABILITY OF A HYBRID METHOD FOR PRICING OPTIONS

2019 ◽  
Vol 22 (07) ◽  
pp. 1950036
Author(s):  
MAYA BRIANI ◽  
LUCIA CARAMELLINO ◽  
GIULIA TERENZI ◽  
ANTONINO ZANETTE
Keyword(s):  
Interest Rate ◽  
Asset Price ◽  
Option Prices ◽  
Underlying Asset ◽  
Binomial Tree ◽  
Price Process ◽  
Pricing Options ◽  
Model Following ◽  
Jump Model ◽  
The Interest Rate

We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a finite-difference approach in order to handle the underlying asset price process. We also propose hybrid simulations for the model, following a binomial tree in the direction of both the volatility and the interest rate, and a space-continuous approximation for the underlying asset price process coming from a Euler–Maruyama type scheme. We test our numerical schemes by computing European and American option prices.

Pricing derivatives with fractional volatility

2017 ◽  
Vol 04 (01) ◽  
pp. 1750014 ◽  
Author(s):  
Hideharu Funahashi
Keyword(s):  
Brownian Motion ◽  
Analytical Formula ◽  
Approximation Formula ◽  
Barrier Options ◽  
Hurst Index ◽  
Option Prices ◽  
Important Lesson ◽  
Highly Sensitive ◽  
Path Dependent ◽  
The Impact

This paper studies the effect of fractional volatility on path-dependent options, which are highly sensitive to the volatility structure of a targeted underlying asset process. To this end, we propose an approximation formula for average and barrier options when volatility follows a fractional Brownian motion. Furthermore, using the analytical formula, we investigate the impact of the Hurst index on option prices. Overall, our important finding is that when the maturity is short and speed of mean-reversion is slow, the impact of the Hurst index strongly influences the option prices and that is non-negligible. This is an important lesson for practitioners who uses standard Brownian motion.

Brownian Excursions and Parisian Barrier Options

1997 ◽  
Vol 29 (1) ◽  
pp. 165-184 ◽  
Author(s):  
Marc Chesney ◽  
Monique Jeanblanc-Picqué ◽  
Marc Yor
Keyword(s):  
Essential Role ◽  
Fixed Number ◽  
Time Interval ◽  
Barrier Options ◽  
Barrier Option ◽  
Underlying Asset

In this paper we study a new kind of option, called hereinafter a Parisian barrier option. This option is the following variant of the so-called barrier option: a down-and-out barrier option becomes worthless as soon as a barrier is reached, whereas a down-and-out Parisian barrier option is lost by the owner if the underlying asset reaches a prespecified level and remains constantly below this level for a time interval longer than a fixed number, called the window. Properties of durations of Brownian excursions play an essential role. We also study another kind of option, called here a cumulative Parisian option, which becomes worthless if the total time spent below a certain level is too long.

PRICING PARISIAN-STYLE OPTIONS WITH A LATTICE METHOD

1999 ◽  
Vol 02 (01) ◽  
pp. 1-16 ◽  
Author(s):  
MARCO AVELLANEDA ◽  
LIXIN WU
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Convertible Bonds ◽  
Barrier Option ◽  
Lattice Method ◽  
Underlying Asset

A Parisian-style barrier option expires if the price of the underlying asset remains above or below some level(s) continuously over a specified period of time (the "window"). A trinomial-lattice scheme is developed for calculating the price and the sensitivities of such options. Monte–Carlo simulation of hedging events using the resulting deltas show errors which are of the same magnitude as for hedging vanilla options, confirming the validity of proposed scheme. We use these results to price callable and convertible bonds with this "window" feature.

BARRIER OPTIONS PRICING WITH JOINT DISTRIBUTION OF GAUSSIAN PROCESS AND ITS MAXIMUM

2017 ◽  
Vol 20 (06) ◽  
pp. 1750042
Author(s):  
PINGJIN DENG ◽  
XIUFANG LI
Keyword(s):  
Gaussian Process ◽  
Joint Distribution ◽  
Options Pricing ◽  
Time Interval ◽  
Exotic Options ◽  
Barrier Options ◽  
Rate Process ◽  
Barrier Option ◽  
Explicit Formulas ◽  
Underlying Asset

Barrier options are one of the most popular exotic options. In this contribution, we propose a performance barrier option, which is a type of barrier option defined with the [Formula: see text]th period logarithm return rate process on an underlying asset over the time interval [Formula: see text], [Formula: see text]. We show that the price of this performance barrier option is determined by the joint distribution of a Slepian process and its maximum. Furthermore, we derive a tractable formula for this joint distribution and obtain explicit formulas for the up-out-call performance option and up-out-put performance option.

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