Question

you have chosen a binomal tree to model the price dynamic of a stock. the probability of an up move is 0.60. if the stock mives up, it earns a 5% return. if the stock moves down, it loses a 5% return. The current stock price is $100.

A.) compute the possible stock prices after two periods (based on the binomial tree for the stock price dynamic change).

B.) compute the corresponding probabilities for each possible price.

C.) compute the expected value of the stock price at the end of two periods.

Answer 1

A)

Given The current Stock price is $100

Movement in stock price

If stock moves up Stock price is 100 + 100*0.05 = 105

From Here again for second period the stock can either move up or down

If it Moves up then price will be 105+105*0.05 = 110.25

If the stock moves down the 105 - 105.0.05 = 99.75

If the stock Moves down the price is 100 - 100*0.05 = 95

From here again for the second period the stock can either move up or down

If it Moves up then price will be 95+95*0.05 = 99.75

If the stock moves down the 95 - 95 * .0.05 = 90.25

B)

Given Probabilty of Up move is 0.6

Now for second period there are two probabilities

Up move - 0.6*0.6 = 0.36

Down Move - 0.6*0.4 =0.24

Hence the probability of down move will be 1-0.6 = 0.4

Now for second period there are two probabilities

Up move - 0.4*0.6 = 0.24

Down Move - 0.4*0.4 =0.16

It is to be noted that the sum of all probablities will be equal to 1

C)

Expected value of Stock price is

Price of stock at each possible outcome multiplied by its probability

Price	Probability	Outcome
110.250	0.36	39.69
99.750	0.24	23.94
99.750	0.24	23.94
90.250	0.16	14.44
Total two period price	102.01