Question

The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European put option on the stock with a strike price of $32 that expires in 6 months with u=1.1 and d=0.9. Each step is 3 months, the risk free rate is 8%.

b) what is the value of the put if it were American style option, all else being equal to that problem.

Answer 1

The main difference between these two options is American option can be exercised before maturity also so at the end of three months the difference in the pricing of option will be there let's understand with the help of calculation.

1452al -331.21 fy?- 0.79 6y=30.6 50=30$ > Sud-30 fuc= 2 St = 32$ d = 29.4 5 = 28.82 P fa - 3.19 *t P- e- page=2 U -d = 200.02 e - 0.9% 1.) -0.9 1.02 – 0.9 1.1-0-9 = 10.6

Pax:-3 fuz ett [p. for? + <1-P)(fud) ] 500.02 [0.660.29*(0.4)(2)] = e =0.0210.494 + 0.8] = 1.248] fd2 = pot q Pcfud) + (1-P) (fa?) I - € 0.02 1 0.6127 +0.4(3.193) a ē 0.02 [ 1.2 + 1.276] a é oo [ 2.9426 - 2.427)

Now the value of fu = 1.4(32-30.6) & ta- 2.6 insteadao of albove calculated value because american put holder has a right to sells at 3-month also, which Europien put did not have. E = ert [ P. fu + (1-P). fd J = € 0.02 CO.6(14) + 0.4(2.6)] = 0 0.02 [ Poster 0.84 +1.04] = -0.02 [ 1.887 - 1.84

I hope my efforts will be fruitful to you...

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