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F0 Ft (1 + R)T t in .NET Make bar code 39 in .NET F0 Ft (1 + R)T t barcode for visual C#

F0 Ft (1 + R)T t using none toinclude none in asp.net web,windows applicationbarcode image generator class file using c# when R is compounded annually Developing with Visual Studio .NET Today is 8 March. ULS shares are selling today at 10.75.

The share pays a dividend of 6% per year in two equal dividend payments, made on 8 April. Forward contracts and 8 October. Stella wants to enter a forward contract to buy 1000 shares on 8 November. She can borrow money at 5% per year, compounded annually.

(i) Find the eight-month forward price on ULS shares. (ii) On 8 May, the share price has fallen to 9.25.

On this day, what is the value of Stella s forward contract . Solution Dividends are paid. The divi dends are discrete. The interest rate is compounded annually.

So Ft = (St Dt ) (1 + R)(T t) (i) S0 = 10.75 8 T = 12 R = 0.05 Two dividends are paid before maturity.

Dividend 1 = 0.3225 Time to payment = 0.08333: Present value = 0.

3225 (1 + 0.05) 0.08333 = 0.

3212 Dividend 2 = 0.3225 Time to payment = 0.5833: Present value = 0.

3225 (1 + 0.05) 0.5833 = 0.

3135 Present value of dividend payments (D) = 0.3212 + 0.3135 = 0.

6347 S0 D = 10.75 0.6347 = 10.

1153 8 8 F0 = (S0 D)(1 + R) 12 = 10.1153 1.05 12 = 10.

4497 The eight-month forward price of the share is 10.45. On 8 May: (ii) St = 9.

25 6 There are six months to maturity: T t = 12 R = 0.05 One dividend payment is made before maturity. Dividend 1 = 0.

3225 5 5 Time to payment = 12 : Present value = 0.3225 (1 + 0.05) 12 = 0.

3160 St Dt = 9.25 0.3160 = 8.

9340 6 Ft = (St Dt )(1 + R)T t = 8.9340 1.05 12 = 9.

1546 This is a long forward contract. Hence: ft = Ft F0 (1 + R). 6 12. 9.1546 10.4497 = 1.

2639 1 .050.5.

If the interest rate R (in t none for none he example, 5% per year, compounded annually) had in fact been a continuously compounded rate, we would have used the. Financial Products form: Ft = (St Dt ) e R( none for none T t) and Dt would be calculated using the continFt F0 uously compounded rate, R. Also, ft = R(T t) . e If R was a continuously compounded interest rate and the asset paid a continuous dividend Q, we would have used: Ft = St e (R Q)(T t) with t F 0 ft = eFR(T t) .

See Exercise 21. Finally, as time passes, what is the relationship between the value of an asset, the forward price of the asset and the value of a (short) forward contract based on that asset If we know, or can project, future values of the asset, then a succession of forward prices and forward contract values can be calculated. We illustrate this for Example 12 in the spreadsheet shown in Figure 2.

10. The interest rate is entered in B3 with the cell name rate. Column A gives the time, in months, after 8 March.

Column B gives the value of the asset in succeeding months (entered with range name assetval). Column C shows the two dividend payments made by the asset (entered with cell names div1 and div2)..

Forward contracts Asset price and forward price 11 10.5 Price 10 9.5 9 0 2 4 6 Time (months) 8 10 Series 1 Series 2 Asset price and value of forward contract 12 10 8 Price 6 4 2 0 2 0 2 4 6 Time (months) 8 10 Series 1 Series 2 Column D shows the present v none none alues of the dividend payments (entered with range name presvaldiv). Column E shows successive forward prices (range name forwardval). E8 shows the eight-month forward price (10.

45). E9 shows the seven-month forward price one month later (9.80).

E10 shows the six-month forward price two months later (9.15). Column F gives the values of a long forward contract at the times given in column A.

In Figure 2.11 we show graphs, over time, of the asset price and the forward price (through to maturity). Note the high correlation between these values and the fact that at maturity, the forward price coincides with the asset value.

In Figure 2.12 we plot, over time, the asset price and the corresponding value of the (long) forward contract. The graphs indicate a strong positive correlation in these two sets of values.

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