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).

Answer 1

(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

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)	$ 0

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

t = 0 months	t = 2 months	t = 4 months	t = 6 months	Payoff
			$ 90.40275783	$ 25.40275783
		$ 83.01447 (node 4)
	$ 76.23 (node 2)		$ 76.20728346	$ 11.20728346
$ 70 (node 1)		$ 69.97914 (node 5)
	$ 64.26 (node 3)		$ 64.24085052	$ 0
		$ 58.99068 (node 6)
			$ 54.15344424	$ 0

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