You want to use the binomial tree analysis to value a 6-month call option with a
ID: 2614105 • Letter: Y
Question
You want to use the binomial tree analysis to value a 6-month call option with a $65 strike price on Lupin Corporation. The shares are currently trading for $70. The annualized continuously compounded risk-free rate is 3%. The volatility of the stock is 51%. You will use the Cox Ross Rubenstein method for computing the binomial tree.
a)Draw the binomial tree and find the value of the option using a time step of 3 months (n=2).
b) Draw the binomial tree and find the value of the option using a time step of 2 months (n=3).
Explanation / Answer
(a) Strike Price = $ 65, Current Stock Price = $ 70, Option Tenure = 6 months, Annualized Constinuously Compounded Risk-Free Rate = 3 % per annum, Volatility = s = 51 %, Time step = 3 months
Upward Movevement Factor = u = EXP[0.51 x 0.25] = 1.136 and Downward Movement Factor = d = 1/u = 0.8803
Risk Neutral Probabilty of Up Movement = p = [EXP(0.03 x 0.25) - d] / [u-d] = (1.00753 - 0.8803) / (1.136-0.8803) = 0.4976 and (1-p) = 0.5024
PV of Expected Payoff at node 2 = 0.4976 x 25.33472 + 0.5024 x 5.001456 / EXP[0.03 x 0.25] = $ 15.0063
PV of Expected Payoff at node 3 = 0.4976 x 5.001456 + 0.5024 x 0 / EXP[0.03 x 0.25] = $ 2.4701
PV of Expected Payoff at node 1 = Call Option Value = 0.4976 x 15.0063 + 0.5024 x 2.4701 / EXP[0.03 x 0.25] = $ 8.643
(b) Strike Price = $ 65, Current Stock Price = $ 70, Option Tenure = 6 months, Annualized Constinuously Compounded Risk-Free Rate = 3 % per annum, Volatility = s = 51 %, Time step = 2 months
Upward Movevement Factor = u = EXP[0.51 x 0.167] = 1.089 and Downward Movement Factor = d = 1/u = 0.918
Risk Neutral Probabilty of Up Movement = p = [EXP(0.03 x 0.167) - d] / [u-d] = (1.005- 0.918) / (1.089 -0.918) = 0.509 and (1-p) = 0.491
PV of Expected Payoff at node 4 = 0.509 x 25.40275783 + 0.491 x 11.20728346 / EXP[0.03 x 0.167] = $ 18.341
PV of Expected Payoff at node 5 = 0.509 x 11.20728346 + 0.491 x 0 / EXP[0.03 x 0.167] = $ 5.676
PV of Expected Payoff at node 6 = $ 0
PV of Expected Payoff at node 2 = 0.509 x 18.341 + 0.491 x 5.676 / EXP[0.03 x 0.167] = $ 12.062
PV of Expected Payoff at node 3 = 0.509 x 5.676 + 0.491 x 0 / EXP[0.03 x 0.167] = $ 2.875
PV of Expected Payoff at node 1 = Call Option Value = 0.509 x 12.062 + 0.491 x 2.875 / EXP[0.03 x 0.167] = $ 7.513
t = 0 months t = 3months t = 6 months Payoff $ 90.33472 (node 4) $ 25.33472 $ 79.52 (node 2) $ 70 (node 1) $ 70.001456 (node 5) $ 5.001456 $ 61.621 (node 3) $ 54.2449663 (node 6) $ 0Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.