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VALUATION OF FORWARDS

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VALUATION OF FORWARDS
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Sunanda K. Chavan
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VALUATION OF FORWARDS - October 8th, 2010

Let us take a simple example of a fixed deposit in a bank. Rs. 100 deposited in the bank at a rate of interest of 10% would become Rs. 110 after 1 yr. Based on annual compounding; the amount will become Rs. 121 after 2 yrs.

Thus, we can say that the forward price of the fixed deposit of Rs. 100 is Rs. 110 after 1 yr. and Rs. 121 after 2 yrs.
As against the usual annual, semi-annual and quarterly compounding, continuous compounding are used in derivative securities. In terms of annual compounding, the forward price can be computed through the following formula:
A = P (1 + r / 100)t

Where A is the terminal value of an amount P invested at the rate of interest of r % p.a. for t years.
Now, if compounding was done twice a year, the amount at the end of 2 years can be calculated as follows:

Beginning of period Principle Interest Amt. at the end
I Half–year 1000 1000 x 0.05 = 50 1050
II Half-year 1050 1050 x 0.05 = 52.50 1102.50
III Half-year 1102.50 1102.5 x 0.05 = 55.125 1157.6254
IV Half-year 1157.625 1157.625 x 0.05 = 57.881 1215.51

It is observed that with all the inputs being the same, the amount is a little higher when the frequency of compounding is increased from one to two in each year. With the still greater compounding frequency, the amount at the end of the 2 yr period would increase. For instance, for different compounding period at the end of 2 yrs are given below:

Compounding Amount (Rs.)
Quarterly 1218.40
Monthly 1220.39
Weekly 1221.17
Daily 1221.37
In general terms,
A = P (1 + r / m)m n
where r is the per annum rate of interest, m is the number of compoundings per annum and n is the number of yrs. For quarterly compounding, for eg. m = 4, while for daily compounding, m = 365.

To carry the idea further, if the number of compoundings per annum increases more and more, the time period between successive compoundings would steadily fall. In the extreme case, the compounding may be thought to be continuous. In such an event, it can be shown mathematically that the amount may be calculated as follows:
A = Pen r

Where all symbols carry the same meaning as before, and e is a mathematical constant whose value is 2.7183.
Since the compounding is continuous, the amount is likely to be the largest. To know the exact amount, we make the following calculation:

A = 1000 x 2.71832 x 0.1
= 1000 x 1.22140
= Rs. 1221.40

In case there is a cash income accruing to the security like dividends, the above formula will read as follows:
A = (P – I) em r
Where I is the present value of the income flow during the tenure of the contract.

-----------------------
Example

Consider a 4 month forward contract on 500 shares with each share priced at Rs. 75. Dividend @ Rs. 2.50 per share is expected to accrue to the shares in a period of 3 months. The CCRRI is 10% p.a. the value of the forward contract is as follows:
Dividend proceeds = 500 x 2.50 = 1250
Present value of Dividend = 1250e- (3/12) (0.10)
= 1219.13
Value of forward contract = (500 x 75 – 1219.13) e(4/12) (0.10)
= 36280.87 x e0.033
= Rs. 37498.11

----------------------------
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Re: VALUATION OF FORWARDS
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Rose Marry
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Re: VALUATION OF FORWARDS - April 15th, 2016

Quote:
Originally Posted by sunandaC View Post
Let us take a simple example of a fixed deposit in a bank. Rs. 100 deposited in the bank at a rate of interest of 10% would become Rs. 110 after 1 yr. Based on annual compounding; the amount will become Rs. 121 after 2 yrs.

Thus, we can say that the forward price of the fixed deposit of Rs. 100 is Rs. 110 after 1 yr. and Rs. 121 after 2 yrs.
As against the usual annual, semi-annual and quarterly compounding, continuous compounding are used in derivative securities. In terms of annual compounding, the forward price can be computed through the following formula:
A = P (1 + r / 100)t

Where A is the terminal value of an amount P invested at the rate of interest of r % p.a. for t years.
Now, if compounding was done twice a year, the amount at the end of 2 years can be calculated as follows:

Beginning of period Principle Interest Amt. at the end
I Half–year 1000 1000 x 0.05 = 50 1050
II Half-year 1050 1050 x 0.05 = 52.50 1102.50
III Half-year 1102.50 1102.5 x 0.05 = 55.125 1157.6254
IV Half-year 1157.625 1157.625 x 0.05 = 57.881 1215.51

It is observed that with all the inputs being the same, the amount is a little higher when the frequency of compounding is increased from one to two in each year. With the still greater compounding frequency, the amount at the end of the 2 yr period would increase. For instance, for different compounding period at the end of 2 yrs are given below:

Compounding Amount (Rs.)
Quarterly 1218.40
Monthly 1220.39
Weekly 1221.17
Daily 1221.37
In general terms,
A = P (1 + r / m)m n
where r is the per annum rate of interest, m is the number of compoundings per annum and n is the number of yrs. For quarterly compounding, for eg. m = 4, while for daily compounding, m = 365.

To carry the idea further, if the number of compoundings per annum increases more and more, the time period between successive compoundings would steadily fall. In the extreme case, the compounding may be thought to be continuous. In such an event, it can be shown mathematically that the amount may be calculated as follows:
A = Pen r

Where all symbols carry the same meaning as before, and e is a mathematical constant whose value is 2.7183.
Since the compounding is continuous, the amount is likely to be the largest. To know the exact amount, we make the following calculation:

A = 1000 x 2.71832 x 0.1
= 1000 x 1.22140
= Rs. 1221.40

In case there is a cash income accruing to the security like dividends, the above formula will read as follows:
A = (P – I) em r
Where I is the present value of the income flow during the tenure of the contract.

-----------------------
Example

Consider a 4 month forward contract on 500 shares with each share priced at Rs. 75. Dividend @ Rs. 2.50 per share is expected to accrue to the shares in a period of 3 months. The CCRRI is 10% p.a. the value of the forward contract is as follows:
Dividend proceeds = 500 x 2.50 = 1250
Present value of Dividend = 1250e- (3/12) (0.10)
= 1219.13
Value of forward contract = (500 x 75 – 1219.13) e(4/12) (0.10)
= 36280.87 x e0.033
= Rs. 37498.11

----------------------------
Hi friend,

I am also uploading a document which will give more detailed explanation on Study on Detecting Spot Price Forecasts In Futures Prices.
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