Question

The current price of a stock is $35. It can either go up to $65 with probability 0.5 or it can go down to $25 with probability 0.5.

The risk free rate of interest is 6%.

1. What is the value of a call on the stock with an exercise price of $35 which expires in 1 year's time?

2. What is the value of a put with an exercise price of $30?

Answer 1

Let us calculate the binomial perameteres first.

Su= upside potential of stock =65

Sd= downside potential of stock = 25

S0= current price = 35

U= Su/S0= 65/35 = 1.857

D= Sd/S0= 25/35 =.7143

P= probability of price going up= .50

q= probability of price going down =.50

Call payoff if price goes above the exercise price= Cu = 65 - 35= $30

Call payoff of price goes below the exercise price = Cd =0 as the call lapses.

Price of call today = C0 = (Cu * P + Cd * q)/(1+r)

r = risk free rate =6%

C0= (30 * .5 + 0 * .5)/1.06 = $14.15

Part b

With similar process we can calculate the price of put

Let us first calculate the payoff of put

Put payoff if price goes up = Pu =0 as the put lapses

Put payoff if the price goes down = Pd = $30 -$25 =$5

Price pf put P0= (Pu * p + Pd * q)/(1+r)

P0= ( 0 * .5 + 5 * .5)/1.06 = $2.36