scholarly journals ANALISIS SENSITIVITAS HARGA OPSI MENGGUNAKAN METODE GREEK BLACK SCHOLES

2018 ◽  
Vol 7 (2) ◽  
pp. 148
Author(s):  
DEVI NANDITA. N ◽  
KOMANG DHARMAWAN ◽  
DESAK PUTU EKA NILAKUSMAWATI
Keyword(s):  
Sensitivity Analysis ◽  
Stock Price ◽  
Price Change ◽  
European Option ◽  
Strike Price ◽  
Expiry Date ◽  
Hedging Strategies ◽  
Black Scholes

Sensitivity analysis can be used to carry out hedging strategies. The sensitivity value measures how much the price change of the option influenced by some parameters. The aim of this study is to determine the sensitivity analysis of the buying price of European option by using the Greek method on Black Scholes Formula. From this study we get the values of delta, gamma, theta, vega, and rho. The values of deltas, gamma, vega, and rho are positive, which means that the value of the option is more sensitive than the corresponding parameter. The most sensitive value of gamma is obtained when the stock price approaches the strike price and approaches the expiry date. The value of theta obtained is negative and hence the most sensitive theta value is when the value is getting smaller. While, the most sensitive value of vega is obtained when the stock price is close to the strike price and is far from the expiry date. The most sensitive value of rho is obtained when the stock price gets bigger and farther from the expiry date.

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.

THE ENTROPY THEORY OF STOCK OPTION PRICING

1999 ◽  
Vol 02 (03) ◽  
pp. 331-355 ◽  
Author(s):  
LES GULKO
Keyword(s):  
Option Pricing ◽  
Interest Rates ◽  
Stock Price ◽  
Price Change ◽  
Price Volatility ◽  
Stock Option ◽  
Market Uncertainty ◽  
Gamma Model ◽  
Black Scholes ◽  
Market Beliefs

An informationally efficient price keeps investors as a group in the state of maximum uncertainty about the next price change. The Entropy Pricing Theory (EPT) captures this intuition and suggests that, in informationally efficient markets, perfectly uncertain market beliefs must prevail. When the entropy functional is used to index the market uncertainty, then the entropy-maximizing market beliefs must prevail. The EPT resolves the ambiguity of asset valuation in incomplete markets, notably, the valuation of derivative securities. We use the EPT to derive a new stock option pricing model that is similar to Black–Scholes' with the lognormal distribution replaced by a gamma distribution. Unlike the Black–Scholes model, the gamma model does not restrict the dynamics of the stock price or the short-term interest rate. Option replication based on the gamma model accounts for random changes in the stock price, price volatility and interest rates.

scholarly journals Spectral Approximation of Infinite-Dimensional Black-Scholes Equations with Memory

2009 ◽  
Vol 2009 ◽  
pp. 1-37
Author(s):  
Mou-Hsiung Chang ◽  
Roger K. Youree
Keyword(s):  
Stock Price ◽  
Payoff Function ◽  
Fourier Series Expansion ◽  
Spectral Approximation ◽  
European Option ◽  
Bank Account ◽  
Smoothness Assumption ◽  
Infinite Dimensional ◽  
Black Scholes ◽  
With Memory

This paper considers the pricing of a European option using a -market in which the stock price and the asset in the riskless bank account both have hereditary price structures described by the authors of this paper (1999). Under the smoothness assumption of the payoff function, it is shown that the infinite dimensional Black-Scholes equation possesses a unique classical solution. A spectral approximation scheme is developed using the Fourier series expansion in the space for the Black-Scholes equation. It is also shown that the th approximant resembles the classical Black-Scholes equation in finite dimensions.

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.

scholarly journals Delta-gamma-theta Hedging of Crude Oil Asian Options

2015 ◽  
Vol 63 (6) ◽  
pp. 1897-1903
Author(s):  
Juraj Hruška
Keyword(s):  
Market Price ◽  
Options Pricing ◽  
Exotic Options ◽  
Asian Options ◽  
Hedging Strategy ◽  
Strike Price ◽  
Put Options ◽  
Hedging Strategies ◽  
Black Scholes ◽  
The Difference

Since Black-Scholes formula was derived, many methods have been suggested for vanilla as well as exotic options pricing. More of investing and hedging strategies have been developed based on these pricing models. Goal of this paper is to derive delta-gamma-theta hedging strategy for Asian options and compere its efficiency with gamma-delta-theta hedging combined with predictive model. Fixed strike Asian options are type of exotic options, whose special feature is that payoff is calculated from the difference of average market price and strike price for call options and vice versa for the put options. Methods of stochastic analysis are used to determine deltas, gammas and thetas of Asian options. Asian options are cheaper than vanilla options and therefore they are more suitable for precise portfolio creation. On the other hand their deltas are also smaller as well as profits. That means that they are also less risky and more suitable for hedging. Results, conducted on chosen commodity, confirm better feasibility of Asian options compering with vanilla options in sense of gamma hedging.

scholarly journals PERHITUNGAN HARGA OPSI EROPA MENGGUNAKAN MODEL BINOMIAL MULTIPERIODA (STUDI KASUS SAHAM TELKOM.JK)

2020 ◽  
Vol 12 (1) ◽  
pp. 25
Author(s):  
Noor Sofiyati
Keyword(s):  
Real World ◽  
Stock Price ◽  
Option Price ◽  
Binomial Model ◽  
European Option ◽  
Strike Price ◽  
Knowing How ◽  
Risk Neutral

Binomial Model is one of method to determine the option price. In this model, assumed that  the stock price only move  up or down in the each steps. In this journal will be reviewed the risk neutral world assumption and real world to determine option price and knowing how to calculate option payoff for european option from stock price use Binomial Multiperoid Model with different strike price.

The Value of the Tax Deferral Option

2020 ◽  
pp. 0148558X2098021
Author(s):  
Nan-Ting Kuo ◽  
Cheng-Few Lee
Keyword(s):  
Stock Price ◽  
Price Change ◽  
Tax Rates ◽  
Trading Volumes ◽  
Tax Savings ◽  
Stock Dividends ◽  
Stock Dividend

This study explores the value of the tax deferral option. By examining ex-day stock-price-change ratios for taxable stock dividends in Taiwan, we find that the tax deferral option is valuable to investors. For a $1 taxable stock dividend, the tax deferral option produces 33.9 ¢ in tax savings, which suggests a tax deferral parameter of 11.3%. We also find that stocks with the tax deferral option have higher trading volumes around ex-days than those without this option, and that higher investor-level tax rates lead to higher value of the tax deferral option. We contribute to the literature by cleanly determining the value of the tax deferral option; our result is not confounded by the restart option.

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