Question

Financial QUESTION # 3 What is a Binomial Tree? How many terminal stock prices would it be if the binomial tree has 30 time steps? Max. Marks 3-1.5x2] ANSWER [Max. Marks 3] QUESTION # 4 Suppose that put-call parity exists for the call and put prices of $3 and $2.5 respectively. The options are of same maturity of 9 months on the stock with spot price of $45. If the available 6- month and 9-months risk-free interest rates are 5% and 6% respectively, what will be strike price(s) for the Put and Call options? ANSWER

Answer 1

Question 3:

Binomial tree is a option valuation method which shows graphical representation of stock prices at different nodes in the future. Option prices is decided based on stock prices at these nodes and probability of increase or decrease. As per Binomial tree, there will be 2 stock prices in one time step (up and down). Other assumption includes no dividend paid on underlying stock and interest rate is constant.

There will be 31 terminal stock prices for 30 time steps model

Assume 60% probability of 25% increase in stock price and 40% probability of -20 decline in stock price on $100 stock

At first time step Stock will either increase to $125 or decrease to $80 (2 terminal stock price)

At second step, stock price at $125 will either to increase to $156.25 or decline to $100 and at $80 will either increase to $100 or decline $64. There will be 3 terminal stock price.

As there are 3 terminal stock prices for 2 time period, similarly there will 31 terminal stock prices for 30 time periods

Question 4:

Value of call option = $3 ; Value of put option= $2.5

Stock spot price = $45

Assume Strike price = X

Since both call and put options are 9 months, we will take 9 months risk free interest rates of 6%

As per Put - Call parity

Value of call option + Present value of exercise price = value of put option + stock spot price

3 + X / (1+6%)^(9/12) = 2.5 + 45

X / 1.04467 = 47.5 -3

X= 44.5 * 1.04467

X = $46.5

Strike price = $46.5