# One periodic binomial model

I need to look into a one-period Binomial model $$(B_t, S_t)$$ with interest rate $$r = 0.1$$ , $$S_0 = 100$$ and $$S_t= 120 \, \text{with probability}\, 0.5$$ $$S_t= 60\, \text{with probability}\, 0.5$$

a) I need to show this market has no arbitrage.

b) Find the replicating portfolio for the contingent claim $$X = S^2_T$$.

c) Find the price of $$X$$ that leads to no arbitrage.

d) Find the risk-neutral measure for this market.

Now I guess that in a) I need to show that the state-price vector is positive, but how do I do that? For the rest I have no idea and would welcome your help!

• Hint: For (b) you need a portfolio worth 14000 in the up state, 3600 in the down state. Is there any combination of stock and risk free asset that can match that? – Alex C Nov 5 '19 at 1:50
• for (d): the risk neutral measure should be $q_u=\frac{e^{-r\delta t}-d}{u-d}$ right? where $u=\frac{120}{100}$ and $d=\frac{60}{100}$? – Anon Nov 6 '19 at 8:23