Question

Consider a 3-month put option. Suppose that the underlying stock price is $25, the strike $26, the interest rate is 5% p.a., stock volatility is 6% per month. Use the same data to answer questions e) – h).

e) Build the binomial tree for the underlying asset (stock). Note: the tree nodes can be edited. Show computations for first up and first down nodes.

f) Compute the price of the European put option using a 3-step binomial tree. Show computations for terminal and two non-terminal nodes.

g) If the market price on the European put option is $1.5, what should be the price of the European call option of the same strike and maturity to prevent arbitrage?

h) Compute the price of the American put option using a 3-step binomial tree. Show computations for two non-terminal nodes.

Answer 1

Part e) and f)

The price of the 3 Step European Put option is $0.754

I have solved it in Excel. The formula used are written in the new sheet. If you still have any doubt, kindly ask in the comment section.

The formula used are:

Part g)

Exercise price: $26

Call option price: ?

Put option price: $1.5

Risk-free rate: 5%

Current market price: $25

Time to maturity: 0.25 years

Let’s plug these values in the put-call parity equation:

Call + Strike Price * e^(-R*T) = Put + Current Stock Price

C + 26* e^(-5%*0.25) = 1.5 + 25

C = $0.823

Part h)

The price of the 3 Step American Put option is $1.0

I have solved it in Excel. The formula used are written in the new sheet. If you still have any doubt, kindly ask in the comment section.

The formula used are:

Note: Give it a thumbs up if it helps! Thanks in advance!