Question

A tree is constructed to value an option on an index which is currently worth 100 and has a volatility of 25%. The index provides a dividend yield of 2%. Another tree is constructed to value an option on a non-dividend-paying stock which is currently worth 100 and has a volatility of 25%. A. The parameters p and u are the same for both trees B. The parameter p is the same for both trees but u is not C.The parameter u is the same for both trees but p is not D. None of the above

Answer 1

A. The parameters p and u are the same for both trees

Step-by-step explanation:

Calculation of parameters of u(upper limit) and p(lower limit) for both index and stock:

1) INDEX

Current Value: 100

Volatality : 25%

Value can increase upto 100+25% = 125

Value can decrease to 100-25% = 75

U = Value after increase/current value = 125/100 = 1.25

P = Value after decrease/ current value = 75/100 = 0.75

2) STOCK

Current Value: 100

Volatality : 25%

Value can increase upto 100+25% = 125

Value can decrease to 100-25% = 75

U = Value after increase/current value = 125/100 = 1.25

P = Value after decrease/ current value = 75/100 = 0.75

---> The parameters U and P for both index and stock are same. This is because both the index and stock has same value and same volality rate. Therefore, stock move according to the index.

if index changes by certain percentage the stock also changes. Here in this case, volatality rate is same for both index and stock. Hence Parameters U and P are same for Index and Stock.