Question

1. Consider the one period binomial model and assume 0 < So< 00, S1(H) -- uSo and Si (Τ)-dSo for some 0 〈 1 + r 〈 d 〈 u. P is an arbitrage oportunity. rove or disprove There

Answer 1

Yes, there is an abritrage opportunity

as d > (1+r)

Take S0 loan from bank/other and take long position on S

after 1 period

S1 will be S0 * d or S0 * u

Now note that

both S0*d and S0 * u > S0 (1+r)

You can repay the loan by giving S0 (1+r)

now you can have

i) S0 u - S0(1+r)

= S0 (u- (1+r)  

or ii) S0(d - (1+r) )

both are > 0

hence there is arbitrage