scholarly journals PENENTUAN HARGA KONTRAK OPSI TIPE ASIA MENGGUNAKAN MODEL SIMULASI NORMAL INVERSE GAUSSIAN (NIG)

2014 ◽  
Vol 3 (3) ◽  
pp. 123
Author(s):  
I PUTU OKA PARAMARTHA ◽  
KOMANG DHARMAWAN ◽  
DESAK PUTU EKA NILAKUSMAWATI
Keyword(s):  
Monte Carlo ◽  
Stock Prices ◽  
Stock Price ◽  
Monte Carlo Model ◽  
Asian Option ◽  
Inverse Gaussian ◽  
Fair Price ◽  
Simulation Accuracy ◽  
Two Parameters ◽  
Normal Inverse Gaussian

The aim to determine of the simulation results and to calculate the stock price of Asian Option with Normal Inverse Gaussian (NIG) method and Monte Carlo method using MATLAB program. Results of both models are compared and selected a fair price. Besides to determine simulation accuracy of the stock price, speed of program execution MATLAB is calculated for both models for time efficiency. The first part, set variabels used to calculate the trajectory of stock prices at time t to simulate the stock price at the time. The second part, simulate the stock price with NIG model. The third part, simulate the stock price with Monte Carlo model. After simulating the stock price, calculated the value of the pay-off of the Asian Option, and then estimate the price of Asian Option by averaging the entire value of pay-off from each iteration. The last part, compare result of both models. The results of this research is price of Asian Option calculated using Monte Carlo simulation and NIG. The rates were calculated using the NIG produce a fair price, because of the pricing contract NIG using four parameters ?, ?, ?, and ?, while Monte Carlo is using only two parameters ? and ?. For execution time of the program, the Monte Carlo model is better in all iterations.

scholarly journals Increments of Normal Inverse Gaussian Process as Logarithmic Returns of Stock Price

2018 ◽  
Vol 21 ◽  
pp. 93-97
Author(s):  
Oskars Rubenis ◽  
Andrejs Matvejevs
Keyword(s):  
Gaussian Process ◽  
Normal Distribution ◽  
Stock Prices ◽  
Stock Price ◽  
High Accuracy ◽  
Price Dynamics ◽  
Inverse Gaussian ◽  
Inverse Gaussian Process ◽  
Normal Inverse Gaussian ◽  
New Distribution

Normal inverse Gaussian (NIG) distribution is quite a new distribution introduced in 1997. This is distribution, which describes evolution of NIG process. It appears that in many cases NIG distribution describes log-returns of stock prices with a high accuracy. Unlike normal distribution, it has higher kurtosis, which is necessary to fit many historical returns. This gives the opportunity to construct precise algorithms for hedging risks of options. The aim of the present research is to evaluate how well NIG distribution can reproduce stock price dynamics and to illuminate future fields of application.

scholarly journals Pricing Chinese Convertible Bonds with Default Intensity by Monte Carlo Method

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xin Luo ◽  
Jinlin Zhang
Keyword(s):  
Monte Carlo ◽  
Stock Prices ◽  
Default Risk ◽  
Emerging Market ◽  
Cash Flows ◽  
Convertible Bonds ◽  
Martingale Measure ◽  
Default Intensity ◽  
Long Run ◽  
Two Parameters

This article proposes a new way to price Chinese convertible bonds by the Longstaff-Schwartz Least Squares Monte Carlo simulation. The default intensity and the volatility are the two important parameters, which are difficultly obtained in the emerging market, in pricing convertible bonds. By developing the Merton theory, we find a new effective method to get the theoretical value of the two parameters. In the pricing method, the default risk is described by the default intensity, and a default on a bond is triggered by the bottom Q(T) (default probability) percentile of the simulated stock prices at the maturity date. In the present simulation, a risk-free interest rate is used to discount the cash flows. So, the new pricing model is considered to tally with the general pricing rule under martingale measure. The empirical results of the CEB and the XIG convertible bonds by the proposed method are compared with those obtained by the credit spreads method. It is also found that the theoretical prices calculated by the method proposed in the article fit the market prices well, especially, in the long run tendency.

scholarly journals A QUASI-MONTE CARLO ALGORITHM FOR THE NORMAL INVERSE GAUSSIAN DISTRIBUTION AND VALUATION OF FINANCIAL DERIVATIVES

2006 ◽  
Vol 09 (06) ◽  
pp. 843-867 ◽  
Author(s):  
FRED ESPEN BENTH ◽  
MARTIN GROTH ◽  
PAUL C. KETTLER
Keyword(s):  
Monte Carlo ◽  
Value At Risk ◽  
Scale Parameter ◽  
Monte Carlo Algorithm ◽  
Asian Options ◽  
Inverse Gaussian ◽  
Option Prices ◽  
Quasi Monte Carlo ◽  
Normal Inverse Gaussian Distribution ◽  
Normal Inverse Gaussian

We propose a quasi-Monte Carlo (qMC) algorithm to simulate variates from the normal inverse Gaussian (NIG) distribution. The algorithm is based on a Monte Carlo technique found in Rydberg [13], and is based on sampling three independent uniform variables. We apply the algorithm to three problems appearing in finance. First, we consider the valuation of plain vanilla call options and Asian options. The next application considers the problem of deriving implied parameters for the underlying asset dynamics based on observed option prices. We employ our proposed algorithm together with the Newton Method, and show how we can find the scale parameter of the NIG-distribution of the logreturns in case of a call or an Asian option. We also provide an extensive error analysis for this method. Finally we study the calculation of Value-at-Risk for a portfolio of nonlinear products where the returns are modeled by NIG random variables.

scholarly journals Stock Price Simulation Using Bootstrap and Monte Carlo

2017 ◽  
Vol 64 (2) ◽  
pp. 155-170 ◽  
Author(s):  
Martin Pažický
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stock Price ◽  
Error Term ◽  
Monte Carlo Experiment ◽  
Asian Option ◽  
Heteroscedastic Error ◽  
Maturity Date ◽  
The Future ◽  
The Difference

Abstract In this paper, an attempt is made to assessment and comparison of bootstrap experiment and Monte Carlo experiment for stock price simulation. Since the stock price evolution in the future is extremely important for the investors, there is the attempt to find the best method how to determine the future stock price of BNP Paribas′ bank. The aim of the paper is define the value of the European and Asian option on BNP Paribas′ stock at the maturity date. There are employed four different methods for the simulation. First method is bootstrap experiment with homoscedastic error term, second method is blocked bootstrap experiment with heteroscedastic error term, third method is Monte Carlo simulation with heteroscedastic error term and the last method is Monte Carlo simulation with homoscedastic error term. In the last method there is necessary to model the volatility using econometric GARCH model. The main purpose of the paper is to compare the mentioned methods and select the most reliable. The difference between classical European option and exotic Asian option based on the experiment results is the next aim of tis paper.

scholarly journals CONSISTENT UPPER PRICE BOUNDS FOR EXOTIC OPTIONS

2021 ◽  
pp. 2150011
Author(s):  
NICOLE BÄUERLE ◽  
DANIEL SCHMITHALS
Keyword(s):  
Stock Prices ◽  
Stock Price ◽  
Exotic Options ◽  
Asian Option ◽  
Worst Case ◽  
No Arbitrage ◽  
Price Process ◽  
Model Free ◽  
Marginal Pricing ◽  
Predetermined Time

We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for these maturities. A model-free approach is used, only taking into account that the (discounted) stock price process is a martingale under the no-arbitrage condition. In case the payoff is directionally convex we obtain the worst case marginal pricing measures. The speed of convergence of the upper price bound is determined when the number of observed stock prices increases. We illustrate our findings with some numerical computations.

scholarly journals Price Index Modeling and Risk Prediction of Sharia Stocks in Indonesia

Economies ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 17
Author(s):  
Hersugondo Hersugondo ◽  
Imam Ghozali ◽  
Eka Handriani ◽  
Trimono Trimono ◽  
Imang Dapit Pamungkas
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Risk Prediction ◽  
Stock Prices ◽  
Value At Risk ◽  
Stock Price ◽  
Price Index ◽  
Simulation Approach ◽  
Trading Period ◽  
Short Time

This study aimed to predict the JKII (Jakarta Islamic Index) price as a price index of sharia stocks and predict the loss risk. This study uses geometric Brownian motion (GBM) and Value at Risk (VaR; with the Monte Carlo Simulation approach) on the daily closing price of JKII from 1 August 2020–13 August 2021 to predict the price and loss risk of JKII at 16 August 2021–23 August 2021. The findings of this study were very accurate for predicting the JKII price with a MAPE value of 2.03%. Then, using VaR with a Monte Carlo Simulation approach, the loss risk prediction for 16 August 2021 (one-day trading period after 13 August 2021) at the 90%, 95%, and 99% confidence levels was 2.40%, 3.07%, and 4.27%, respectively. Most Indonesian Muslims have financial assets in the form of Islamic investments as they offer higher returns within a relatively short time. The movement of all Islamic stock prices traded on the Indonesian stock market can be seen through the Islamic stock price index, namely the JKII (Jakarta Islamic Index). Therefore, the focus of this study was predicting the price and loss risk of JKII as an index of Islamic stock prices in Indonesia. This study extends the previous literature to determine the prediction of JKII price and the loss risk through GBM and VaR using a Monte Carlo simulation approach.

scholarly journals Existence Conditions of Super-Replication Cost in a Multinomial Model

2017 ◽  
Vol 9 (4) ◽  
pp. 185
Author(s):  
Mei Xing
Keyword(s):  
Stock Price ◽  
Gaussian Model ◽  
Time Interval ◽  
Inverse Gaussian ◽  
Multinomial Model ◽  
Liquidity Premium ◽  
Gamma Model ◽  
Existence Conditions ◽  
Variance Gamma Model ◽  
Normal Inverse Gaussian

This paper gives a theorem for the continuous time super-replication cost of European options in an unbounded multinomial market. An approximation multinomial scheme is put forward on a finite time interval [0,1] corresponding to a pure jump Lévy model with unbounded jumps. Under the assumption that the expected underlying stock price at time 1 is bounded, the limit of the sequence of the super-replication cost in a multinomial model is proved to be greater than or equal to an optimal control problem. Furthermore, it is discussed that the existence conditions of a super-replication cost and a liquidity premium for the multinomial model. This paper concentrates on a multinomial tree with unbounded jumps, which can be seen as an extension of the work of (Xing, 2015). The super-replication cost and the liquidity premium under the variance gamma model and the normal inverse Gaussian model are calculated and illustrated.

scholarly journals IPO Underpiricing, Konservatisme Akuntansi, dan Sentimen Investor

2021 ◽  
Vol 20 (2) ◽  
pp. 145-156
Author(s):  
Buddi Wibowo ◽  
Keyword(s):  
Stock Prices ◽  
Stock Price ◽  
Investor Sentiment ◽  
Secondary Market ◽  
Accounting Conservatism ◽  
Fair Price ◽  
Ipo Underpricing ◽  
Accrual Quality ◽  
Holding Period ◽  
Lack Of Information

Abstract. The significant increase of stock price compared to its IPO price is difficult to explain. Companies which issue their stock are impossible to set underpriced IPO voluntarily, while investors who buy an overpriced stock are only they who are not rational or lack of information. Conservative financial statements and high accrual quality provide an opportunity for all investors to be able to estimate the fair price of IPO shares so that the disagreement among investors is not too wide and price fluctuations due to speculation are not too high in the secondary market. Using Indonesia Stock Exchanges, the results show that influence of accounting conservatism and accrual quality are stronger in the 30 holding period after the IPO because the uncertainty of financial statement information led to wider speculation opportunities in the long period. The rise in stock prices after IPO is also influenced by investor’s sentiment and market conditions Keywords: IPO, underpricing, accounting conservatism; accrual quality, investor sentiment

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