Question

For a non-dividend paying company. The current spot price of the company’s equity is $50 per share. The value of the stock will be at least $100 in 12 months.

S₀ = $50

T = 12 months

r = 30 basis points per month

u=1.1 per month

d = 1/u= 1.1^-1 per month

1. Apply the binomial tree model to value a 12-month European style call with a strike of $100. What is the call premium?
2. Use put-call parity to value the put on the same asset, for the same expiration, and with the same strike. What is the put premium?
3. The investor is considering two other calls. One with a strike of $200. Another with a strike of $0. What is the premium on the call with a strike of $200? Why? What is the premium on the call with the strike of $0? Why?

Answer 1

Call Premium is $0.18

Value of Node at T=12 = Max (stock price - strike price, 0)
Value of Node at T=11 = [(Prob of Up Move * Value of call option on up move) + (Prob of Down Move * Value of call option on the down node)] / (1 + Rf)

Probability of Up Move = [(1 + Rf) - d] / (u - d)
where u = up move
d = down move

  

2) Put-Call Parity

Stock + Put Option = Call Option + X/(1+Rf)n
50 + x = 0.18 + 100/(1+0.3%)12
50 + x = 0.18 + 96.47
x = 46.65

Put Option Premium is $46.65

3) Value of Call option if the strike price is $200 = $0. This is because the option is Out of the Money till expiry i.e. the price of the stock doesn't move more than the strike price of $200. The maximum the stock price can go at the end of 12 months is $156.92

Value of Call Option if the strike price is 0 = $50. This is because the option is In the Money throughout its life i.e. Price of stock at all the nodes is more than $0 and the least price of the stock at the end of 12 periods is $15.93 (which will still be in the money)