scholarly journals PENERAPAN METODE BINOMIAL TREE DALAM MENGESTIMASI HARGA KONTRAK OPSI TIPE AMERIKA

2016 ◽  
Vol 5 (4) ◽  
pp. 156
Author(s):  
I GUSTI AYU MITA ERMIA SARI ◽  
KOMANG DHARMAWAN ◽  
TJOKORDA BAGUS OKA
Keyword(s):  
Stock Price ◽  
Price Movement ◽  
Binomial Tree ◽  
Option Contracts ◽  
Black Scholes ◽  
Risk Neutral ◽  
Price Option ◽  
Tree Method

Binomial tree is a method that can be used to determine price option contracts. In this method, the stock price movement is presented in the form of a  tree with each branch representing the probability of the stock price to move up or move down. The purpose of this paper was to determine the price of the options contracts with the American type on Binomial Tree method and compare the three methods that is variance matching, proportional , and risk neutral of determining the value of price option contracts used in Binomial Tree method with Black-Schole method. The result of this research was the value of the options contract using the variance matching more similar with the value of the Black-Scholes contract.

scholarly journals PENENTUAN HARGA KONTRAK OPSI KOMODITAS EMAS MENGGUNAKAN METODE POHON BINOMIAL

2017 ◽  
Vol 6 (2) ◽  
pp. 99
Author(s):  
I GEDE RENDIAWAN ADI BRATHA ◽  
KOMANG DHARMAWAN ◽  
NI LUH PUTU SUCIPTAWATI
Keyword(s):  
Option Prices ◽  
European Option ◽  
Binomial Tree ◽  
Call Options ◽  
Option Contracts ◽  
Put Option ◽  
Black Scholes ◽  
Tree Method

Holding option contracts are considered as a new way to invest. In pricing the option contracts, an investor can apply the binomial tree method. The aim of this paper is to present how the European option contracts are calculated using binomial tree method with some different choices of strike prices. Then, the results are compared with the Black-Scholes method. The results obtained show the prices of call options contracts of European type calculated by the binomial tree method tends to be cheaper compared with the price of that calculated by the Black-Scholes method. In contrast to the put option prices, the prices calculated by the binomial tree method are slightly more expensive.

scholarly journals On the Uniqueness of Martingales with Certain Prescribed Marginals

2013 ◽  
Vol 50 (2) ◽  
pp. 557-575
Author(s):  
Michael R. Tehranchi
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Asset Price ◽  
Simple Random Walk ◽  
Option Prices ◽  
Tree Model ◽  
Binomial Tree ◽  
Black Scholes ◽  
Risk Neutral ◽  
Binomial Tree Model

This note contains two main results. (i) (Discrete time) Suppose that S is a martingale whose marginal laws agree with a geometric simple random walk. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Cox-Ross-Rubinstein binomial tree model.) Then S is a geometric simple random walk. (ii) (Continuous time) Suppose that S=S0eσ X-σ2〈 X〉/2 is a continuous martingale whose marginal laws agree with a geometric Brownian motion. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Black-Scholes model with volatility σ>0.) Then there exists a Brownian motion W such that Xt=Wt+o(t1/4+ ε) as t↑∞ for any ε> 0.

On the Uniqueness of Martingales with Certain Prescribed Marginals

2013 ◽  
Vol 50 (02) ◽  
pp. 557-575
Author(s):  
Michael R. Tehranchi
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Asset Price ◽  
Simple Random Walk ◽  
Option Prices ◽  
Tree Model ◽  
Binomial Tree ◽  
Black Scholes ◽  
Risk Neutral ◽  
Binomial Tree Model

This note contains two main results. (i) (Discrete time) Suppose that S is a martingale whose marginal laws agree with a geometric simple random walk. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Cox-Ross-Rubinstein binomial tree model.) Then S is a geometric simple random walk. (ii) (Continuous time) Suppose that S=S 0eσ X-σ2〈 X〉/2 is a continuous martingale whose marginal laws agree with a geometric Brownian motion. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Black-Scholes model with volatility σ>0.) Then there exists a Brownian motion W such that X t =W t +o(t 1/4+ ε) as t↑∞ for any ε> 0.

scholarly journals Pricing Exotic Options Using Some Lattice Procedures

2021 ◽  
Vol 41 (1) ◽  
pp. 26-40
Author(s):  
Sadia Anjum Jumana ◽  
ABM Shahadat Hossain
Keyword(s):  
Stock Price ◽  
Lattice Models ◽  
Exotic Options ◽  
Barrier Options ◽  
Tree Model ◽  
Binomial Tree ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Binomial Tree Model ◽  
Trinomial Tree Model

In this work, we discuss some very simple and extremely efficient lattice models, namely, Binomial tree model (BTM) and Trinomial tree model (TTM) for valuing some types of exotic barrier options in details. For both these models, we consider the concept of random walks in the simulation of the path which is followed by the underlying stock price. Our main objective is to estimate the value of barrier options by using BTM and TTM for different time steps and compare these with the exact values obtained by the benchmark Black-Scholes model (BSM). Moreover, we analyze the convergence of these lattice models for these exotic options. All the results have been shown numerically as well as graphically. GANITJ. Bangladesh Math. Soc.41.1 (2021) 26-40

scholarly journals Pricing arithmetic asian options under the cev process

2010 ◽  
Vol 15 (29) ◽  
pp. 7-13
Author(s):  
Bin Peng ◽  
◽  
Fei Peng ◽  
Keyword(s):  
Stock Price ◽  
Numerical Results ◽  
Asian Options ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Binomial Tree ◽  
Cev Process ◽  
Parameter Values ◽  
Tree Method

This paper discusses the pricing of arithmetic Asian options when the underlying stock follows the constant elasticity of variance (CEV) process. We build a binomial tree method to estimate the CEV process and use it to price arithmetic Asian options. We find that the binomial tree method for the lognormal case can effectively solve the computational problems arising from the inherent complexities of arithmetic Asian options when the stock price follows CEV process. We present numerical results to demonstrate the validity and the convergence of the approach for the different parameter values set in CEV process.

scholarly journals Entropic Dynamics of Stocks and European Options

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 765 ◽  
Author(s):  
Mohammad Abedi ◽  
Daniel Bartolomeo
Keyword(s):  
Stock Price ◽  
Inductive Inference ◽  
Planck Equation ◽  
Derivative Securities ◽  
European Options ◽  
Scale Invariant ◽  
No Arbitrage ◽  
Black Scholes ◽  
Risk Neutral ◽  
Log Price

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The objective of the paper is to lay down an alternative framework for modeling dynamics. An important information about the dynamics of a stock’s price is scale invariance. By imposing the scale invariant symmetry, we arrive at choosing the logarithm of the stock’s price as the proper variable to model. The dynamics of stock log price is derived using two pieces of information, the continuity of motion and the directionality constraint. The resulting model is the same as the Geometric Brownian Motion, GBM, of the stock price which is manifestly scale invariant. Furthermore, we come up with the dynamics of probability density function, which is a Fokker–Planck equation. Next, we extend the model to value the European Options on a stock. Derivative securities ought to be prices such that there is no arbitrage. To ensure the no-arbitrage pricing, we derive the risk-neutral measure by incorporating the risk-neutral information. Consequently, the Black–Scholes model and the Black–Scholes-Merton differential equation are derived.

Robust Option through Binomial Tree Method

2015 ◽  
Vol 6 (4) ◽  
pp. 42-53 ◽  
Author(s):  
Payam Hanafizadeh ◽  
Amir Hossein Mortazavi Qahi ◽  
Kumaraswamy Ponnambalam
Keyword(s):  
Stock Prices ◽  
Stock Price ◽  
Historical Data ◽  
European Option ◽  
Binomial Tree ◽  
Robust Approach ◽  
Spot Prices ◽  
Uncertainty Region ◽  
Option Model ◽  
Tree Method

This study proposes a robust approach for pricing a European option using the binomial tree method. This method considers stock up and down prices in a closed and convex region, called the uncertainty region, defined by the covariance matrix of high and low stock prices. The option model uses this uncertainty region for pricing instead of spot prices. The method proposes an interval of prices for an option considering incidences of the worst and the best states of the stock price. The interval is flexible as it takes into account the covariance of the historical data of a stock's high and low prices and the radius of an uncertainty region.

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.

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