CONTROL of financial mathematics

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Description

Tests on financial mathematics
Contents:
Task 1
Task 2
Activity 3
References

Task №1
Quarterly data on loan from a commercial bank for housing (in arbitrary units) for 4 years (a total of 16 quarters).
Required:
1) Build a model of adaptive multiplicative Holt-Winters with the seasonal factor, taking smoothing parameters α1 = 0,3; α2 = 0,6; α3 = 0,3.
2) Evaluate the accuracy of the model constructed using the average relative error of approximation.
3) Assess the adequacy of the model constructed on the basis of the study:
 residual component of chance on the criterion of the peaks;
 level of independence of a number of residues of d-criteria (critical-parameter values \u200b\u200bd1 = 1,10 and d2 = 1,37) and the first autocorrelation coefficient at the critical value r1 = 0,32;
 normality residual components of R / S-criterion with the critical values \u200b\u200bof 3 to 4.21.
4) Construct a point forecast of 4 steps forward; 1 year.
5) To reflect on the actual chart, calculated and forecast data.

Task number 2
Given the prices (opening, high, low and close) for 10 days. Interval Smoothing taken equal to five days. Estimate:
- Exponential moving average;
- The time;
- The rate of change in prices;
- Relative Strength Index;
-% R,% K,% D.
The calculations were performed for all the days for which this calculation can be made on the basis of available data.

Days Prices
Max. Min. Close.
1858785804
2849781849
3870801806
4805755760
5785742763
6795755795
7812781800
8854791853
9875819820
10820745756

Additional information

Task №3
Run various commercial calculations using the data in the table. The subject task parameters are given as variables. The names of the variables from the table, select the corresponding numerical values \u200b\u200band perform calculations.

1. The Bank issued a loan of 5 000 000. Date of issue of the loan - 26.01.2009, return - 14.03.2009. The day of issue and date of return assumed for 1 day. Interest is calculated on a simple interest rate of 12.5%
2. Within 90 days after signing the contract, the debtor will pay 5 million rubles. The loan bears interest at 12.5% \u200b\u200bper annum (interest ordinary). What is the initial amount and the discount?
3. After 90 days, the company should receive a bill 5 000 000 rubles. The bank purchased the promissory note at a discount. The bank has considered the bill at a discount rate of 12.5% \u200b\u200bper annum (the year is 360 days). Determine the amount received by the enterprise and a discount.
4. In the loan agreement in the amount of 5 000 000 rubles. and for a period of 6 years, fixed rate of compound interest, equal to 12.5%. Determine the amount accrued.
5. A loan of 5 000 000. provided 6 years. Interest complex rate - 12.5% \u200b\u200bAPR. Interest is accrued 4 times a year. Calculate the accrued amount.
6. Calculate the effective interest rate if the bank pays interest four times a year, based on the nominal rate of 12.5% \u200b\u200bper annum.
7. Determine what should be the nominal rate for calculating the interest to 4 times a year to ensure the effective rate of 12.5% \u200b\u200bper annum.
8. After 6 years, the company will be paid the sum of 5 000 000 rubles. To determine its present value, provided that the applicable interest rate complex 12.5%.
9. After 6 years under the bill should be paid the sum of 5 000 000 rubles. The bank has considered the bill on a difficult discount rate of 12.5% \u200b\u200bper annum. Determine the discount.
10. ...

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