Question

Binomial Model

The current price of a stock is $16. In 6 months, the price will be either $20 or $11. The annual risk-free rate is 5%. Find the price of a call option on the stock that has an strike price of $14 and that expires in 6 months. (Hint: Use daily compounding.) Round your answer to the nearest cent. Assume a 365-day year. Do not round your intermediate calculations.

$   

Answer 1

Answer :

P= $16

P(u)= $20

P(d)= $11

r_RF= 5%

X= $14

C_u ending up option payoff = Max(20-14) = $6

C_d ending down option payoff = Max(11-14) = $0

Share of stock (N_s)= C_u– C_d/ P(u) – P(d)= $6 - $0 / $20 - $11

Share of stock= 0.6667

Hedge portofolio’s payoff if stock is up = N_sP(u) - Cu

=0.6667($20) - $6

= $7.3333

Hedge portofolio’s payoff if stock is down= N_sP(d) – Cd

= 0.6667($11) - $0= $7.3333

PV of riskless payoff= $7.3333/ (1+r_RF/365)^365(t/n)

= $7.3333 / (1+0.05/365)^365(0.5/1)

= $7.1523

Option’s Value (VC)= NsP - Present value of riskless payoff =

= 0.66667 x $16 - 7.1523

= $3.514

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