BIBECHANA 18 (2) (2021) 50-60 

50 
 

 

 

Use of geometric Brownian motion to forecast stock market 

scenario using post covid-19 NEPSE index 
 

Prabin Thapa*, Binil Aryal** 

Central Department of Physics, Tribhuvan University, Kirtipur 
*Email: physicpract@gmail.com 
 

**Email: binil.aryal@cdp.tu.edu.np       
 

 

Article Information: 

Received: September 13, 2020 

Accepted: February 25, 2021 

 

Keywords:  

Stochastic process 

Geometric Brownian motion 

NEPSE Index 

Python simulation  

 

 

 

 
 

 

 

ABSTRACT 

Stock market is one of the fields where the randomness is prominent factor to be 

considered. Although many stochastic processes deal which the randomness found 

in nature through the interdisciplinary subject like Econophysics, many of them 

exhibits cumbersome trends. So, Geometric Brownian motion (GBM) is used to 

analyze the market scenario of Nepal on the basis of the parameter; NEPSE Index 

along with the prediction of indices through python programming platform. Python 

simulation was carried out to check the consistency by implying it to the stable 

market timeline 2003/2004. And after the verification of the model proposed in the 

stable market year, the model (GBM) is employed to the unstable timeline; 

pandemic situation by COVID-19 in 2020. Mapping of Nepal stock market through 

GBM was found to be consistent with the standard forecasting accuracy making 

GBM one of the flexible and consistent to predict stock market scenario of Nepal 

accounting the random nature. 

DOI: https://doi.org/10.3126/bibechana.v18i2.31180 

This work is licensed under the Creative Commons CC  BY-NC License. https://creativecommons.org/licenses/by-nc/4.0/ 

 

 
1. Introduction 

 

Stock Market 
 

Stock generally referred as equities or equity 

securities of any company or corporation determines 

the share in the ownership of esteemed company or 

corporation. Stocks are mainly divided into two: 

public stock in which public are allowed taking 

certain portion of corporation securities or 

ownership through investment and private stock 

which is owned by private companies and sold only 

to investors. And the market facilitating the sales and 

purchase of this ownership among individuals, 

companies and investors is share market [1]. There 

are many indicators to measure the status of stock 

market, one of them is the stock index; in the context 

of Nepal, Nepal Stock Exchange (NEPSE) Index 

which indicates the increase or decrease of total 

market capitalization of companies’ transactions 

that are enlisted in Nepal Stock Exchange. This 

BIBECHANA 
ISSN 2091-0762 (Print), 2382-5340 (Online) 

Journal homepage: http://nepjol.info/index.php/BIBECHANA 

Publisher: Department of Physics, Mahendra Morang A.M. Campus, TU, Biratnagar, Nepal 

mailto:physicpract@gmail.com
https://doi.org/10.3126/bibechana.v18i2.31180
https://creativecommons.org/licenses/by-nc/4.0/
http://nepjol.info/index.php/BIBECHANA


PrabinThapa and Binil Aryal / BIBECHANA 18 (2) (2021) 50-60  

51 
 

indicates the increase or decrease of overall market; 

therefore, it has significant importance to investors. 
  

Factors affecting Stock Market 
 

The attractiveness of stock price is affected by 

several factors that results in the inconsistency or the 

randomness in the stock index. Some of them are: 

• The After-Hours Trading (AHT) where the 

trading between the closing bell of present day 

and opening bell of next day fluctuates the value 

of stock price. 

• Sudden news about companies listed in share 

market during non-trading period. 

• Political condition, natural calamities, epidemic 

and pandemic and many others. 
 

From above it can be said that figuratively stock 

market has the random nature inherent in it [1, 2]. 

So, modeling of such random nature of stock market 

needs to be accounted that is where stochastic 

process comes into play which shows the connection 

between physics and economics [3].  
 

Stochastic process 
 

Stochastic process is a process where there are 

observations at the certain times and the outcomes 

or the observed values at each time has the 

randomness inherent in them; random variable. In 

terms of probability concept, there is a certain 

probability to acquire certain outcome and that 

probability depends upon the previously obtained 

observations [4]. This means that more the 

observations, more accuracy the stochastic process 

addresses to the outcome. But generally, such 

processes are cumbersome and become difficult to 

treat in long run. So, different simplified stochastic 

processes are proposed over time in the field of 

Econophysics like Markov process, Step process. 

Levy process, Random walk, Weiner process, 

Brownian motion etc. [4, 5]. 
 

Brownian motion 
 

Brownian motion generally referred as the motion 

defined by a particle (Brownian particle) suspended 

in a liquid where the particle is small enough to be 

influenced by the underlying molecular motion. 

Such types of motion of small particles in liquid 

demonstrate dissipation and fluctuation. Moreover, 

the motion is governed by two kinds of force; the 

systematic force which is responsible for damping 

by an exchange of energy and momentum between 

Brownian particle and molecules of liquid, 

providing dissipation and the force by the irregular 

interactions from the collision between Brownian 

particles and molecules of liquid may change the 

direction and velocity of Brownian particles 

providing fluctuation in the system. In spite of 

dissipation and fluctuation, diffusion; an irregular 

way Brownian particle is spread out in the system 

gives the concept of diffusion constant [4].  

The Brownian particle can also be influenced by 

external factors like presence of charged ions, 

presence of electric fields, temperature, pressure etc.  
 

Geometric Brownian motion (GBM) 
 

Geometric Brownian motion is continuous-time 

stochastic process also referred as Wiener process 

with drift. It is the most used model for mathematical 

finance in modeling stock prices [4]. 

For stochastic process X (t) to follow GBM, it 

satisfies stochastic differential equation (SDE) as [5-

8] 

𝑑𝑋(𝑡) = 𝜇𝑋(𝑡)𝑑𝑡 + 𝜎𝑋(𝑡)𝑑𝐵(𝑡)                 (1) 
 

where 𝐵(𝑡) represents the Wiener process or 

Brownian motion 𝜇 represents drift accounting for 

deterministic trend 𝜎 represents volatility 

accounting for unpredictable events Under Itô's 

interpretation [5], for arbitrary initial value X0 the 

equation has the analytic solution 

𝑋𝑇 = 𝑋0𝑒
(𝜇−

1

2
𝜎2)𝑇+𝐵𝑇                   (2) 

With the incorporation of such deterministic trend 

and unpredictable events in Geometric Brownian 

motion [9], it is well suited for modeling of stock 

market. 
 

2. Materials and Methods 
 

Modeling of stock market 
The prediction of Nepal Stock market scenario on 

the basis of NEPSE Index using Brownian notion is 

python simulation-based work. So, to use Brownian 



PrabinThapa and Binil Aryal / BIBECHANA 18 (2) (2021) 50-60  

52 
 

motion in stock market we make appropriate 

analogy between Brownian motion and stock market 

parameters. 
 

𝑋0 = Initial NEPSE Index which in our case is the 

last date NEPSE Index of our historical data. 
 

𝑑𝑡 = Increment in time (For our case one day) As the 

NEPSE index of the day is published in every 

one day. dt =1day. 

𝑇 = length of our prediction horizon, in our case it is 

22 days as trading days is only 22 days with the 

exclusion of weekend. 

𝑁 = Number of time points in the prediction time 

horizon = 𝑇/𝑑𝑡 

𝜇 = Mean return of NEPSE Index i.e. 

           𝜇 =
1

𝑇𝑜𝑡𝑎𝑙 𝐷𝑎𝑦𝑠(𝑁)
∑

𝑋𝑘−𝑋𝑘−1

𝑋𝑘
 𝑁

𝑘=1          (3) 

𝜎 = Standard deviation of historical daily return-

index 

           𝜎 = √
1

𝑁
∑ (𝑋𝑘 − 𝜇)2𝑁

𝑘=1              (4) 

𝐵 = Brownian increment which follows normal 

distribution with mean zero and variance 

equal to interval of time in our case it is one as 

dt =  1day. 

Drift:  Drift reflects the longer-term trend in stock 

index. They have constant value calculated 

from the historical data set. 

            𝐷𝑟𝑖𝑓𝑡 =  𝜇 −
1

2
 𝜎2            (5) 

Note: If we keep applying drift without any random 

shock the stock price smoothly goes up for positive 

drift and smoothly goes down for negative drift. So, 

the stock price is non-zero due to drift. 

Diffusion: Diffusion consists of the short-term 

fluctuations so it consists of the 

variable Bk which contains random 

shock information. 

        𝐷𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 = 𝜎𝐵𝑘           (6) 

Algorithm 
 

Step 1: Select the historical data set when the market 

is pretty stable. 

Step 2: Calculate drift and diffusion coefficient from 

the historical data set. 

 

Step 3: Predict NEPSE Index for certain period 

using the simulation model. 

Step 4: Compare actual Index and predicted one; is 

it consistent with MAPE (Mean Absolute 

Percentage Error) table. 

Step 5: If the prediction is consistent with MAPE 

then apply the simulation model for prediction when 

the market is not stable enough. 

Step 6: If the prediction is inconsistent with MAPE 

then search for the parameterization of the model for 

making it consistent and GOTO step 1. 
 

Simulation set up 
 

Stock market scenario was simulated for two 

different scenarios. First, for the stable market year 

which in our case is the year 2003/2004 where there 

is no sudden change in the political situation of 

Nepal, less closing of market in business days and 

less external factors to affect market. We took 

historical NEPSE Index data from July 17 2003 to 

June 15 2004 for the prediction of scenario of market 

from June 16 2004 to July 15 2004. We simulated 

one thousand possible market scenarios for this 

prediction time and tabulated them for percentile 

calculation. Calculating the percentile for k values: 

0.01 (predicted decreasing index), 0.50 (predicted 

stable index) and 0.99 (predicted increasing index), 

the three scenarios were deducted from the thousand 

simulated scenarios. Considering all the scenario of 

that time line of Nepal, out of three, one scenario was 

selected and made comparison with the standard 

table of forecasting. 

 

Table I: A scale of judgment of forecast accuracy 

[8]. 

Absolute 

Percentage 

Error 

Judgment of forecasting 

accuracy 

< 10% Highly accurate 

11% to 20% Good accurate 

21% to 50% Reasonable Forecast 

> 51% Inaccurate Forecast 

 



PrabinThapa and Binil Aryal / BIBECHANA 18 (2) (2021) 50-60  

53 
 

On the comparison with the standard table for 

forecasting, the simulation outcome yielded error 

less than 10 percentages. So, we adopted that the 

simulation must be sufficient to predict the scenarios 

for unstable market year. Moreover, best fit for the 

stable year along with R-squared value was 

calculated as it also should be consistent with the 

next simulation which in our case is for the year 

2020. 
 

3. Results and Discussion 
 

For the stable year 2003/2004 
 

 

In order to simulate 1000 scenarios for the year 

2003/2004 we took into account NEPSE Index from 

July 17, 2003 to June 15, 2004. The simulation 

yielded 1000 scenarios from June 16, 2004 to July 

15, 2004 as shown in Fig. 1. 

 

 
Fig. 1: Thousand possible scenarios of stock market 

for 2003/2004. 

After the percentile calculation, deductions to three 

scenarios of market from thousand scenarios are able 

II 
 

Table II: Comparison between predicted indices 

and actual NEPSE Index for year 2004 

Date 

(D/M) 

Predicted Indices Actual 

NEPSE 

Index 
Decreasing Stable Increasing 

6/15 211.31 211.31 211.31 211.31 

6/16 208.64 211.34 214.18 211.45 

6/21 204.54 211.47 218.62 211.51 

6/22 203.57 211.24 219.13 213.25 

6/23 203.61 211.37 220.02 215.10 

6/24 202.62 211.36 220.32 216.51 

6/25 202.88 211.48 220.24 217.46 

6/28 201.85 211.61 221.60 217.41 

6/29 201.40 211.63 222.24 217.72 

6/30 201.54 211.65 222.39 218.65 

7/1 201.18 211.73 222.86 219.41 

7/2 200.83 211.78 222.66 220.75 

7/5 200.76 212.08 223.63 225.15 

7/6 200.17 212.02 223.68 227.83 

7/8 199.69 212.08 225.12 226.88 

7/9 199.28 212.19 225.57 226.30 

7/12 198.75 212.60 227.34 226.16 

7/13 198.57 212.64 227.49 226.42 

7/14 198.29 212.66 227.80 226.61 

7/15 198.18 212.65 228.12 222.04 

 

We refer the situation of the market in order to select 

preferred index to represent market. As year 

2003/2004 was selected as the stable market period 

with less inconsistency, we predict that the indices 

should either increase or remain stable which can 

also be seen through bar plot. From Fig 2 and Table 

II we can say that out of three predicted indices the 

increasing predicted index is found to have the close 

resemblance to actual NEPSE Index for the 

respective prediction days. Now on selecting the 

increasing predicted index as our final index we 

calculate percentage error for the respective days as 

shown in able III. 



PrabinThapa and Binil Aryal / BIBECHANA 18 (2) (2021) 50-60  

54 
 

 
Fig 2: Bar plot of three different scenarios for market 

year 2004 taking first five dates. 

 

Table III: Error Analysis between selected 

predicted index and actual NEPSE index for 2004 

Date 

(D/M) 

Increasing 

Predicted 

Index 

Actual 

NEPSE 

Index 

Percentage 

Error 

6/15 211.31 211.31 0.00 

6/16 214.18 211.45 -1.29 

6/21 218.62 211.51 -3.36 

6/22 219.13 213.25 -2.76 

6/23 220.02 215.10 -2.29 

6/24 220.32 216.51 -1.76 

6/25 220.24 217.46 -1.28 

6/28 221.60 217.41 -1.93 

6/29 222.24 217.72 -2.08 

6/30 222.39 218.65 -1.71 

7/1 222.86 219.41 -1.57 

7/2 222.66 220.75 -0.86 

7/5 223.63 225.15 0.67 

7/6 223.68 227.83 1.82 

7/8 225.12 226.88 0.78 

7/9 225.57 226.30 0.32 

7/12 227.34 226.16 -0.52 

7/13 227.49 226.42 -0.47 

7/14 227.80 226.61 -0.53 

7/15 228.12 222.04 -2.74 

On comparison with the standard table for 

forecasting accuracy Table I, we found that our 

prediction of indices is quite accurate as the error lies 

below 10%. So, for further discussions we infer best-

fit analysis along with R-squared value as in Fig 3.  

 

Fig 3: Line plot of selected predicted index and 

actual index for market year 2004 along with best fit 

and R-squared value 

 

From the Fig 3 above, it is clear that our model of 

prediction is consistent and can be applied to other 

fiscal year of stock market as the R-squared value 

0.921 is nearly equal to 1 and the best fit to two 

degree polynomial shows that the model is capable 

of including the varying nature of stock market. 

Moreover, the consistency with the forecast 

accuracy allows us to imply this model to other 

market years. 
 

For the year 2020 
 

For the prediction of the current running year, we 

have taken account of all the historical data i.e. from 

200

205

210

215

220

225

6/16 6/21 6/22 6/23 6/24

N
E

P
S

E
 I

n
d
ex

Prediction Days (D/M)

Decreasing Predicted Index
Stable Predicted Index
Increasing Predicted Index
Actual NEPSE Index

y = -0.0093x2 + 710.74x - 1E+07

R² = 0.9615
210

212

214

216

218

220

222

224

226

228

230

6
/1

5

6
/2

2

6
/2

9

7
/6

7
/1

3

N
E

P
S

E
 I

n
d
ex

Prediction Days (D/M)

Increasing Predicted Index

Actual NEPSE Index

Poly. (Increasing Predicted Index)



PrabinThapa and Binil Aryal / BIBECHANA 18 (2) (2021) 50-60  

55 
 

2003 to till available date for simulating thousand 

possible scenarios of market as shown in Fig. 4. 

 

 
Fig 4: Thousand possible scenarios of stock market 

for year 2020. 

 
 

After the percentile calculation, deductions to three 

scenarios of market from thousand scenarios are 

shown in table IV. 
 

For the selection among the predicted three indices, 

we select the decreasing predicted indices due to 

scenario of year 2020 (pandemic of COVID-19) 

which can be also seen through bar plot in Fig 5. 
 

On the analysis of Fig 5, we can say that the 

decreasing predicted index is more convenient to 

select for representing actual NEPSE index.  

Table IV: Comparison between predicted indices 

and actual NEPSE Index for year 2020. 

Date 

(D/M) 

Predicted Indices Actual 

NEPSE 

Index 
Decreasing Stable Increasing 

3/11 1423.09 1423.09 1423.09 1423.09 

3/12 1384.84 1423.82 1464.31 1377.18 

3/15 1348.07 1426.78 1509.26 1313.04 

3/16 1346.43 1428.30 1522.36 1316.40 

3/17 1342.36 1429.80 1532.88 1272.07 

3/18 1337.62 1429.18 1539.36 1255.80 

3/19 1332.03 1430.25 1554.57 1269.31 

3/22 1314.95 1437.10 1570.07 1251.46 

5/12 1208.81 1471.64 1827.46 1226.16 

 

 

 
Fig. 5: Bar plot of three different scenarios for 

market year 2020 taking first five dates. 

 

Comparison with the standard table for forecast 

accuracy Table I, we can see that absolute 

percentage error is less than 10% which means our 

prediction is acceptable. The error greater than 4 

percentages in Table V can be accounted by the 

following reasoning: 

 

1200

1250

1300

1350

1400

1450

1500

1550

1600

3/12 3/15 3/16 3/17 3/18

N
E

P
S

E
 I

n
d
ex

Prediction Days (D/M)

Decreasing Predicted Index

Stable Predicted Index

Increasing Predicted Index

Actual NEPSE Index



PrabinThapa and Binil Aryal / BIBECHANA 18 (2) (2021) 50-60  

56 
 

Table V: Comparison between predicted indices 

and actual NEPSE Index for year 2020. 
 

Dates 

(D/M) 

Decreasing 

Predicted 

Index 

Actual 

NEPSE 

Index 

Percentage 

Error 

3/11 1423.09 1423.09 0.00 

3/12 1384.84 1377.18 -0.56 

3/15 1348.07 1313.04 -2.67 

3/16 1346.43 1316.40 -2.28 

3/17 1342.36 1272.07 -5.53 

3/18 1337.62 1255.80 -6.52 

3/19 1332.03 1269.31 -4.94 

3/22 1314.95 1251.46 -5.07 

5/12 1208.81 1226.16 1.41 

 

 

1. The opening of the market in weekend (in our 

case mainly Sunday). 

2. The pandemic of COVID-19 worldwide which 

is responsible for the harsh irregularities in 

market strategy and situation. 

3. Opening of market after 50 days of gap (from 

March 22 to May 12) made the high impact in 

prediction as our simulation model is unknown 

of the sudden close of market. 
 

Then the line plot for the predicted index and actual 

NEPSE Index along with best-fit as shown in Fig. 6. 

Although the plot has the best- fit to second degree 

polynomial, the R-squared value is not as close as 

that in the year 2003/2004 which can be accounted 

by the fact the market remained closed for about 50 

days which has affected the consistency of having 

R-squared value nearly equals to one as seen 

previously in 2003/2004. 
 

Complete Scenario of market in 2020 
 

From Fig 4, we can plot the complete scenario of 

NEPSE Index up to 12 May 2020 including also the 

weekend. As we already know that decreasing 

predicted index is conveying the actual NEPSE 

Index we can have all the decreasing predicted 

indices to represent the gap of 50 days when the 

market was closed. The predicted indices from the 

date 22 March 2020 to 12 May 2020 is represented 

Table VI along with line plot in Fig 6. 

 

Fig 6: Comparison between selected predicted index 

and actual index along with best-fit  

 

 

Now for reliability of prediction we take a look at R-

squared value and best fit to two degree polynomial 

Fig 7 as done for stable market prediction. From the 

Fig 7 it is clear that the model we have proposed for 

the stable market scenario is also applicable for other 

aspects when the market is random. The R-squared 

value which is 0.936 is nearly equals to 1 meaning 

the consistency of the model to adopt in stable and 

non–stable market year.  
 

So far as the part of result and discussion, we have 

taken two scenarios for stock market analysis; one 

being the stable stock market (year 2003/2004) and 

another being the present stock market (year 2020). 

y = -1.434x2 - 4.1213x + 1403.6

R² = 0.7843

1200

1250

1300

1350

1400

1450

3
/1

1

3
/1

2

3
/1

5

3
/1

6

3
/1

7

3
/1

8

3
/1

9

3
/2

2

5
/1

2

N
E

P
S

E
 I

n
d
ex

Prediction Days (D/M)

Decreasing Predicted Index

Actual NEPSE Index



PrabinThapa and Binil Aryal / BIBECHANA 18 (2) (2021) 50-60  

57 
 

Table VI: Predicted index for 50 days gap in 2020. 

Prediction Days 
Predicted 

Decreasing Index 

Sunday, March 22, 2020 1314.952 

Monday, March 23, 2020 1312.675 

Tuesday, March 24, 2020 1311.187 

Wednesday, March 25, 2020 1292.008 

Thursday, March 26, 2020 1294.899 

Friday, March 27, 2020 1287.029 

Saturday, March 28, 2020 1287.194 

Sunday, March 29, 2020 1289.939 

Monday, March 30, 2020 1286.990 

Tuesday, March 31, 2020 1281.568 

Wednesday, April 1, 2020 1275.187 

Thursday, April 2, 2020 1277.795 

Friday, April 3, 2020 1267.111 

Saturday, April 4, 2020 1269.603 

Sunday, April 5, 2020 1264.057 

Monday, April 6, 2020 1256.732 

Tuesday, April 7, 2020 1246.317 

Wednesday, April 8, 2020 1247.575 

Thursday, April 9, 2020 1251.434 

Friday, April 10, 2020 1249.477 

Saturday, April 11, 2020 1250.117 

Sunday, April 12, 2020 1245.852 

Monday, April 13, 2020 1236.393 

Tuesday, April 14, 2020 1238.411 

Wednesday, April 15, 2020 1240.697 

Thursday, April 16, 2020 1239.029 

Friday, April 17, 2020 1239.146 

Saturday, April 18, 2020 1233.699 

Sunday, April 19, 2020 1233.995 

Monday, April 20, 2020 1225.443 

Tuesday, April 21, 2020 1214.978 

Wednesday, April 22, 2020 1220.616 

Thursday, April 23, 2020 1222.788 

Friday, April 24, 2020 1217.785 

Saturday, April 25, 2020 1223.197 

Sunday, April 26, 2020 1226.043 

Monday, April 27, 2020 1225.471 

Tuesday, April 28, 2020 1239.949 

Wednesday, April 29, 2020 1232.231 

Thursday, April 30, 2020 1234.737 

Friday, May 1, 2020 1232.025 

Saturday, May 2, 2020 1223.204 

Sunday, May 3, 2020 1217.290 

Monday, May 4, 2020 1207.588 

Tuesday, May 5, 2020 1198.191 

Wednesday, May 6, 2020 1188.459 

Thursday, May 7, 2020 1205.884 

Friday, May 8, 2020 1209.662 

Saturday, May 9, 2020 1201.972 

Sunday, May 10, 2020 1193.005 

Monday, May 11, 2020 1209.513 

Tuesday, May 12, 2020 1208.813 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig 7: Line plot for predicted (decreasing index) for 

50 days gap in 2020 along with best-fit  

 

We tested our Brownian motion model for the stable 

market at first and after checking its viability shifted 

to its application in the present date. On doing so we 

found that the model is applicable to all the scenarios 

with less than 10% error in each prediction which 

makes our model more accurate and consistent. The 

error greater than 3% is accounted by the un-

uniformed opening of the stock market like someday 

y = 0.0334x2 - 3.8005x + 1314

R² = 0.9362
1180

1200

1220

1240

1260

1280

1300

1320

3
/2

2

3
/2

9

4
/5

4
/1

2

4
/1

9

4
/2

6

5
/3

5
/1

0

N
E

P
S

E
 I

n
d
ex

Prediction Days (D/M)

Predicted Decreasing Index

Poly. (Predicted Decreasing Index)



PrabinThapa and Binil Aryal / BIBECHANA 18 (2) (2021) 50-60  

58 
 

the market has opened in Sunday which is globally 

one of the weekdays when the market should be 

closed. Moreover, the error in the year 2020 is by the 

un-uniformity as well as due to the pandemic 

scenario by COVID-19. 

 

Daily Return Index Analysis 

 

 
Fig 8: Histogram plot of Daily Returns in terms of 

NEPSE Index for year 2020 using 10 bins. 

Table VII: Table for the Daily Return Calculation 

of Predicted and Actual NEPSE Index for year 2020. 

(Refer Table V). 

NEPSE Index 
Daily Return of 

NEPSE Index 

Predicted Actual Predicted Actual 

1423.09 1423.09 - - 

1384.84 1377.18 -0.03 -0.03 

1348.07 1313.04 -0.03 -0.05 

1346.43 1316.40 0.00 0.00 

1342.36 1272.07 0.00 -0.03 

1337.62 1255.80 0.00 -0.01 

1332.03 1269.31 0.00 0.01 

1314.95 1251.46 -0.01 -0.01 

 

From Table VII it can be annotated that the trend for 

the daily return between the predicted NEPSE Index 

and Actual NEPSE Index for the year 2020 is merely 

the same indicating better viability of our 

simulation. Moreover, from Fig 7 it can be seen that 

the plotting of relative frequencies of daily return of 

Index making 10 bins, the Gaussian distribution is 

followed. The histogram for predicted index has half 

Gaussian as we are selecting only the decreasing 

predicted index for the year 2020. 
 

Quartile Risk Analysis or Value at Risk (VaR) 

Table VIII: Table for the calculation of VaR or 

Quartile Risk. 

Days 

Daily Return of 

Predicted NEPSE 

Index 

Variance 

Standard 

Deviation 

(b) 

3/11 - 

0.18 0.42 

3/12 -0.03 

3/15 -0.03 

3/16 0.00 

3/17 0.00 

3/18 0.00 

3/19 0.00 

3/22 -0.01 

5/12 -0.08 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-0
.0

8
1

-0
.0

7
2

-0
.0

6
3

-0
.0

5
4

-0
.0

4
5

-0
.0

3
7

-0
.0

2
8

-0
.0

1
9

-0
.0

1
0

-0
.0

0
1

R
el

at
iv

e 
F

re
q
u
en

cy

Daily Return ( Predicted NEPSE 

Index)

0

0.05

0.1

0.15

0.2

0.25

0.3

-0
.0

4
7

-0
.0

4
0

-0
.0

3
4

-0
.0

2
7

-0
.0

2
1

-0
.0

1
5

-0
.0

0
8

-0
.0

0
2

0
.0

0
4

0
.0

1
1

R
el

at
iv

e 
F

re
q
u
en

cy

Daily Return (Actual NEPSE Index)



PrabinThapa and Binil Aryal / BIBECHANA 18 (2) (2021) 50-60  

59 
 

From Table VIII it can be seen that the predicted 

NEPSE Index for the year 2020 has the volatility of 

0.42.  

 

Table IX: Table for calculation of VaR at different 

confidence level. 

For  

Initial NEPSE Index (a)= 1423.09 

Standard Deviation (b) = 0.42 

Trading Days (c) = 8 (at May 12,2020) 

Confidence 

Level 

Stress 

Event 

(d) 

VaR 

(a*b*d*sqrt(c/252) 

0.99 2.33 250.02 

0.95 1.64 176.78 

0.90 1.28 137.73 

 

From Table VII the Value at Risk (VaR) at different 

confidence level can be seen. At 0.99 confidence 

level the initial index has the risk of 265.19 giving 

out (1423.09-250.02) = 1173.07 NEPSE Index (at 

May 12, 2020) which on comparison to Actual 

NEPSE Index gives an error percentage of 4.33% 

which is again consistent with the table of forecast 

Table I. 
 

4. Conclusion 
 

The simulation of thousands possible scenarios of 

stock market on the basis of NEPSE index has been 

carried out using python simulation. On doing so the 

proposed model is found to be consistent for the 

analysis and prediction of Nepal Stock market 

scenario with error persistent with standard table of 

forecasting. 
 

The conclusions that can be drawn from the results 

encountered are enlisted as: 

1. The predicted model for the stable period of 

market (2003/2004) shows two degree 

polynomial fit with R-squared value nearly 

equals to one. From this it can be known that the 

proposed model incorporates the changing 

nature of stock market. 

2. Comparison of predicted indices and actual 

indices shows the error less than 10 percentages 

which define the accuracy (highly accurate) of 

proposed model for the year 2003/2004 and year 

2020. 

3. As for the error analysis, errors greater than 3 

percentage in the year 2020 is due to the 

irregularities in market like opening of the 

market in weekends and closing in business 

days, dealing a greater number of trades due to 

pandemic situation which is merely the case in 

the year 2003/2004. 

4. The prediction of indices for 50 days gap in the 

year 2020 shows the trend of stock market if it 

was opened during that period of time resulting 

to latest published index at 11 May 2020 (actual 

NEPSE index 1226.16, predicted NEPSE index 

1208.81 with error of 1.415%); the positive error 

representing presence of randomness in market. 

5. Brownian motion model is found to be more 

accurate than other stochastic processes like 

random walk, Wiener process, Levy process etc. 

as it incorporates the diffusion and drift along 

with the properties of Wiener process 

incorporating both the deterministic parameter 

from historic data and the randomness by 

generating diffusion σBk. 
 

Acknowledgements 
 

I would like to acknowledge NEPSE database center 

for conveying data needed. Moreover, I would like 

to thank Central Department of Physics (CDP) for 

all the support. 
 

References 
 

[1]. W.J. O’Neil, How to make Money in Stocks, 4th 

ed., The McGraw-Hill Companies, New York, 

2009. 

[2]. D. Owen and R. Griffiths, Mapping the Markets: A 

guide to Stock market Analysis, The Economist, 

London, 2006. 

[3]. G. Sãvoiu, Econophysics: Background and 

Applications in Economics, Finance, and 

Sociophysics, Academic Press, Waltham, 2012. 

[4]. C. Blomberg, 1st ed., Physics of Life: The      

Physicist’s Road to Biology, Elsevier, 

Netherlands, 2007. 



PrabinThapa and Binil Aryal / BIBECHANA 18 (2) (2021) 50-60  

60 
 

[5]. I. Karatzas and S. E. Shreve, 1st ed., Brownian 

motion and Stochastic Calculus, Springer, New 

York, 1987. 

[6]. K. F. Vajargah and M. Shoghi, Simulation of 

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115-125 

 https://doi.org/10.1007/s40096-015-0158-5 

[7]. G. Dhesi et al., Modified Brownian motion 

Approach to Modeling Returns Distribution,  

 

 

 

Wilmott. 82 (2016) 74-77. 

 https://doi.org/10.1002/wilm.10494 

[8]. S. N. Z. Abidin and M. M. Jaffar, A Review on 

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 https://www.researchgate.net/publication/325986

792 

[9]. V. Singal, Beyond the random walk: A guide to 

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https://doi.org/10.1007/s40096-015-0158-5
https://doi.org/10.1002/wilm.10494
https://www.researchgate.net/publication/325986792
https://www.researchgate.net/publication/325986792