Question

Q8-Part I (6 marks) The current price of a non-dividend-paying stock is $42. Over the next year it is expected to rise to-$44. or fall to $39. An investor buys put options with a strike price of $43. To hedge the position, should (and by how many) the investor buy or sell the underlying share (s) for each put option purchased? (6 marks) 08-Part II (9 marks) The current price of a non-dividend paying stock is $49. Use a two-step binomial tree to value a European call option on the stock with a strike price of $50 that expires in 6 months. Each time step covers 3 months, the risk-free rate is 5.5% per annum (continuously compounded), and the volatility is 8%. + (a) Compute the up-step size (u), down-step size (d) and probability of up move (p) for the 3-month time step. (3 marks) (6) What is the value of the European call option today? (3 marks) c) Other things remain unchanged, but if it is an American call option, what will be its value today? (3 marks)

Answer 1

Datu ginen: urrent price of non-dividend paying stock = $42 Oner next year, it is expected to rise to 444 or fall to Buys put aption with strike price of $43 or sell to hedge his position shares should he buy How many we need to calculate To hedge della of put eption rus) his sey position firstly uy i. Pu=0 [ put value = max (X-5,9) x=43 42 (5) .39 (as) :P = 4 Pu-Po us-ds 0-4 -0.8 44-39 hedge so, investor should buy 0.8 shares of stock to his position. csscanned with CamScanner

coness 3 months. & Dafa ginen: (s) current price of non dividend paying stock = $49. (X) Strike price = $50 that expires in 6 months 2 step binomial free with each step (2) Risk free Rate = sl.p.a. (continuously compounded) (6) volatility = 8% a) compute u upstep 0.0853/12 d & pi OVE move = e - e - 1.04 =0.96 d cl- 1.04 하 [where Rae" 0.0583/12 = por tu R-d u-d = 1.0125 1.0125-0.96 1.04 -0.96 0.65 1-p=1-0.65 = 0.35 CScanned with CamScanner

b) Value of european call option today (025) 0.65 52.gg CV 2.99 X = 50 (us) 50.96 0.35 0.65 Cuds) 49 luda 1 49 (5). 0:35 0.35 47.04 (05) 45.12 Odd = 0 (825) [ call price may 15-2,0)] : Co - p² x Cuu tp (l-p) Cud + 11-p)² x Cdd 11.0125) ? we are [ Ao discounting for two periods - 0.65°x 2.99 + 0.65X0.35X1 + 0.352x0 (1.012572 $1.454 Ans. it was american option, then price is? sol: As we know for non-dividend paying stock =) American aption is equal to European call option =) As there is no benefit to exercise an american option before maturity Value of American Option (call) call $1.454 = Ans CScanned with CamScanner

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