optimal model sales in gold ounce and s&p 500 markets on the basis of optimal stopping

Subject Areas : Computational economics

amir mahmoudian ¹ , maryam khalili araghi ² , hamidreza vakilifard ³

1 - Faculty member
2 - faculty member
3 - Department of Accounting, Science and Research Unit, Islamic Azad University.Tehran,

Received: 2023-11-20 Accepted : 2024-01-30 Published : 2024-03-17

Keywords: Optimal Stopping, , , , , Simulation Modeling, , , , , Financial Markets Forecasting,

Abstract :

Extended Abstract Throughout history, predicting price in financial markets has always been of high interest to financial activists and analysts. Recently, various methods have been proposed and adopted to predict the dynamism of financial markets using time series of records of prices. However, high-precision predication of financial prices is still a deemed long-term challenge that constantly call for state-of-the-art approaches. Purpose Thus, the purpose of the current study was to examine the efficacy of optimal stopping, also known as early stopping and use its connection with branching processes to predict the optimal buying and selling prices in several financial markets. gold ounce market and S&P 500 index have been predicted in short term and long-term frameworks on the basis of fixed horizon. And for each. frame work, different time frames have been selected. Closing price data from 1995 to 2022 have been used for every time frame. Methodology Advanced methods for optimal stopping include approximating the value function and then using that approximation in a policy. Although such policies can work very well, they are generally not guaranteed to be interpretable (Siokan and Mišić 2020). On the other hand, some researchers have proposed that the optimal stop models are too complicated to solve well and the strategies of buying at a low price and selling at a high price are not very practical in this theory (Liu and Mo 2022). According to the issues raised, the researcher intends to use the optimal stop theory and its connection with branch processes to implement and examine this theory in a number of prominent international financial markets. In this research, we are going to use the optimal stop statistical theory to predict the time of buying and selling in these markets in an optimal way. Finding The optimal stopping algorithm seeks to determine the maximum value from a set of random variables that are exhibited in the order they are generated. Each variable should either be selected when exhibited or be skipped in favor of the next variable, and if all the variables till the nth variable are skipped, this variable is selected automatically. It should be borne in mind that the theory of optimal stopping first examines the previous data and finds out whether there is a divergence, according to which it determines which market cannot be predicted based on this theory. In general, these random variables are considered as independent and co-distributed. Yet, due to the complexity of this theory, even in this case, solving problems directly proves to be very difficult, and hence the correlation between this theory and branch processes are employed to simplify solution. The steps of this process are as follows: Step 1 The analyst finds the planning horizon (20 - horizon in the present paper) Step 2 Determine the statistical distribution of values using statistical tests, including the goodness of fit, chi-square, Chebyshev's inequality, and Q-Qplot (Moud et al. 1973) Step 3 Transforming it to a normal distribution using Box-Cox Transformations (Cox-Box 1964), and converting to the standard normal distribution (minus mean value divided by standard deviation) (Moud et al. 1973) Step 4 Using inverse distribution function (using probability integral transform theorem) (Moud et al. 1973) and transforming it to considered distribution in branching process and determining convergency or divergence of data (Ross 1983; Shishebor et al. 2004) Step 5 Predicting the best point for optimal buy or sell at a determined horizon (Assaf et al. 2000) Step 6 Reversing all transforms and predicting real values (Assaf et al. 2000) Conclusion The results indicate that by optimal stopping for short term framework, S&P 500 index indicates %67 success and gold ounce shows %53 success in the prediction of prices. In long term framework, S&P 500 index's success equals to %68 and gold ounce equals to %85 in prediction of prices. The obtained results show that the optimal stop theory has performed better in predicting the gold price in the long-term time frame and the S&P 500 in the short-term time frame. The S&P 500 market and the gold market have obtained the most predictability based on the optimal stop theory. This can be confirmed by market traders because the S&P 500 and gold market are interesting markets from a technical and trading point of view. The number of transactions and high liquidity and the difference in spread and commission in these two markets compared to other markets can be indicative of this. Also, the high volatility in the two mentioned markets due to the uncertainty regarding the continuation of prices and key economic indicators presents countless opportunities to traders. According to the obtained results, the optimal stopping can be used as a trading and analytical indicator. Also, the characteristic of optimal stopping is that based on historical data, it shows the prediction as the optimal point (buying and selling price) in the future. Due to the fact that examining the financial markets both from the study and analytical point of view and from the trading point of view by using a variety of forecasting patterns and indicators requires understanding the possibilities of market behavior, choosing a time frame and having a strategy.