Averages, volatility and european put prices

[tillemannetje]

The following is the prices of a stock (no dividend) over 12 months, starting at S0 = 50:

Month : 0 1 2 3 4 5 6 7 8 9 10 11 12
Stock price: 50 56 52 47 49 40 39 43 48 51 54 55 58

(i) What is the stocks average monthly return, average geometric (i.e. continuously compounded) monthly return, and annualized average (arithmetic and geometric) returns?

(ii) What is your estimate of the price volatility of the stock?

(iii) Suppose the continuously compounded interest rate is 2%: Based on your answer to (ii), what is the price of a one-year European put with strike price equal to 50?

(iv) Suppose you created synthetically a long position in the above put option, starting at time 0 until the end of one year. What would be your total cost? Is it higher or lower than the price in (iii)?

 

[Deleted member 4993]

The following is the prices of a stock (no dividend) over 12 months, starting at S0 = 50:

Month : 0 1 2 3 4 5 6 7 8 9 10 11 12
Stock price: 50 56 52 47 49 40 39 43 48 51 54 55 58

(i) What is the stocks average monthly return, average geometric (i.e. continuously compounded) monthly return, and annualized average (arithmetic and geometric) returns?

(ii) What is your estimate of the price volatility of the stock?

(iii) Suppose the continuously compounded interest rate is 2%: Based on your answer to (ii), what is the price of a one-year European put with strike price equal to 50?

(iv) Suppose you created synthetically a long position in the above put option, starting at time 0 until the end of one year. What would be your total cost? Is it higher or lower than the price in (iii)?

What are your thoughts?

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[tillemannetje]

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

I'm a senior student and need help with this excercise, especially part iii and iv

i've got this for i and ii:

i) Average monthly return: = 49.38

Average geometric monthly return: ((X1)(X2)(X3)……(Xn))^1/n , where X is the individual score and N is the sample size.

((50)(56)(52)(47)(49)(40)(39)(43)(48)(51)(54)(55)(58))^1/13 = 49.039

Annual arithmetic return: = 49.33

Annual geometric average: ((X1)(X2)(X3)……(X12))^1/12

((56)(52)(47)(49)(40)(39)(43)(48)(51)(54)(55)(58))^1/12 = 48.959

ii) First we calculate the average mean price for the number of periods. Then we determine each period’s deviation. Square each period’s deviation. Sum the squared deviations. Divide this sum by the number of observations and in the end the standard deviation (volatility) is then equal to the square root of that number.

 

[tillemannetje]

I've got some solutions for i and ii.
i) Average monthly return:

= 49.38

Average geometric monthly return: ((X1)(X2)(X3)……(Xn))^1/n , where X is the individual score and N is the sample size.

((50)(56)(52)(47)(49)(40)(39)(43)(48)(51)(54)(55)(58))^1/13 = 49.039

Annual arithmetic return:

=

= 49.33

Annual geometric average: ((X1)(X2)(X3)……(X12))^1/12

((56)(52)(47)(49)(40)(39)(43)(48)(51)(54)(55)(58))^1/12 = 48.959

ii) First we calculate the average mean price for the number of periods. Then we determine each period’s deviation. Square each period’s deviation. Sum the squared deviations. Divide this sum by the number of observations and in the end the standard deviation (volatility) is then equal to the square root of that number.



But i cant figure out iii and iv

 

[stapel]

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[tillemannetje]

I calculated the average monthly return by adding all the stock prices and dividing it by the number of observations and the annual arithmetic return i calculated the same only then with 12 observations instead of 13.

 

[tillemannetje]

I calculated the average monthly return by adding all the stock prices and dividing it by the number of observations and the annual arithmetic return i calculated the same only then with 12 observations instead of 13.

Anybody with an answer for iii) and iv)