PENENTUAN KEPUTUSAN INVESTASI SAHAM MENGGUNAKAN CAPITAL ASSET PRICING MODEL (CAPM) DENGAN PENAKSIR PARAMETER STOKASTIK

CAPM is a method of determining efficient or inefficient stocks based on the differences between individual returns and expected returns based on the CAPM’s positive value for efficient and negative value for inefficient stocks. The move to share prices in the process can influence investors's decisions in investing funds, so that it can be formulated in stochastic differential equations that form the Geometric Brownian Motion model (GBM). The purpose of the study is to determine return value using the CAPM based on share estimates and historical stock prices. The study uses secondary data that data a monthly closing of stock prices from December 2017 to December 2020. The GBG model's estimated stock price is used to determine the expected value return using the CAPM. In this case, it is called CAPM-Stochastic. Then the results of the CAPM-Stochastic was compared to the results of the CAPM-Historical to define efficient stocks and inefficient stocks. The results of research using CAPM-Stochastic obtained that HMSP, ICBP, KLBF, and WOOD shares are efficient stock while UNVR shares are inefficient. The results of CAPM-Historical obtained that HMSP, ICBP, KLBF, and UNVR shares are inefficient stocks and WOOD is an efficient stocks.

CCMV Portfolio Optimization with Stocks and Options using Forecasted Data

Although the future of a financial market is ambiguous and mysterious, historical data play a key role to forecast the future of the market. Along with all the advantages of these data, they may result to some errors and consequently, some losses. In this paper, we consider the cardinality constraints mean-variance (CCMV) portfolio optimization model in the presence of short selling, risk-neutral interest rate and transaction costs. We insure the investment using options against unfavorable outcomes. The Geometric Brownian Motion model is utilized to forecast the stocks prices. Also, to improve the results, we calibrate its parameters using historical data by the maximum likelihood estimation method. We perform numerical experiments using historical and forecasted data on the S&P 500 index, to assess the efficiency of the GBM model in forecasting stocks prices. Also, to examine the effect of options in the portfolio, we compare the portfolio with stocks only versus the portfolio with stocks and options using historical and forecasted data in terms of returns and Sharpe ratios.

Pricing Product Options and Using Them to Complete Markets for Functions of Two Underlying Asset Prices

Options paying the product of put and/or call option payouts at different strikes on two underlying assets are observed to synthesize joint densities and replicate differentiable functions of two underlying asset prices. The pricing of such options is undertaken from three perspectives. The first perspective uses a geometric two-dimensional Brownian motion model. The second inverts two-dimensional characteristic functions. The third uses a bootstrapped physical measure to propose a risk charge minimizing hedge using options on the two underlying assets. The options are priced at the cost of the hedge plus the risk charge.

Comparison of Stochastic Forecasting Models

In this work, we compare several stochastic forecasting techniques like Stochastic Differential Equations (SDE), ARIMA, the Bayesian filter, Geometric Brownian motion (GBM), and the Kalman filter. We use historical daily stock prices of Microsoft (MSFT), Target (TGT) and Tesla (TSLA) and apply all algorithms to try to predict 54 days ahead. We find that there are instances in which all algorithms do well, or do poorly. We find that all three stocks have a strong auto-correlation and a high Hurst factor which shows that it is possible to predict future prices based on a short history of past prices. In our geometric Brownian motion model, we have two parameters for drift and diffusion which are not time dependent. In our more general SDE model (TDNGBM), we have time-dependent drift and time-dependent diffusion terms which makes it more effective than GBM. We measure all algorithms on the correlation between the predicted and actual values, the mean absolute error (MAE) and also the confidence bounds generated by the methods. Confidence intervals are more important than point forecasts, and we see that TDNGBM and ARIMA produce good bounds.

Stochastic resonance of volatility influenced by price periodic information in financial market

General researches show that all kinds of random risk information and periodic information in the financial system are mainly transmitted to the asset price through influencing the volatility, thus impacting the whole market. So can the periodic information and random factors in the price be transmitted to the volatility in reverse and cause volatility changes? Hence, in this paper, we investigate the stochastic resonance of volatility which is influenced by price periodic information in financial market, based on our proposed periodic Brownian Motion model and absolute return volatility. The parameter estimation of the periodic Brownian Motion model is obtained by minimizing the mean square deviation between the theoretical and empirical return distributions for the CSI300 data set. The good agreements of the probability density functions of the price returns, realized volatility (RV) at 5 minutes, RV at 15 minutes and absolute return volatility between theoretical and empirical calculation are found. After simulating the absolute return volatility and signal power amplification (SPA) of volatility via periodic Brownian Motion model, the results indicated that (i) single and double inverse resonance phenomena can be observed in the function of SPA versus random information intensity or economic growth rate; (ii) multiple inverse resonance phenomena can be also observed for SPA versus frequency of periodic information. The results imply that the transmission of stochastic factors and periodic information is not only from the volatility to the price, but also from the price to the volatility.

The voice of Physics in finance: A glance on the theoretical application of heat equation to stock price diffusions

Stock price volatility is considered the main matter of concern within the investment grounds. However, the diffusivity of these prices should as well be considered. As such, proper modelling should be done for investors to stay healthy-informed. This paper suggest to model stock price diffusions using the heat equation from physics. We hypothetically state that, our model captures and model the diffusion bubbles of stock prices with a better precision of reality. We compared our model with the standard geometric Brownian motion model which is the wide commonly used stochastic differential equation in asset valuation. Interestingly, the models proved to agree as evidenced by a bijective relation between the volatility coefficients of the Brownian motion model and the diffusion coefficients of our heat diffusion model as well as the corresponding drift components. Consequently, a short proof for the martingale of our model is done which happen to hold.