3. (20 marks) Use the Principle of Mathematical Induction (PMI) and the recursive formula V(i, j)...
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3. (20 marks) Use the Principle of Mathematical Induction (PMI) and the recursive formula V(i, j) = eV(i + 1, j + 1)q + V(i + 1, j)(1 q)], 0 i N-1, 0 j i where j is the number of up-jumps up to time t = ih, to derive the formula for the price V(0) of a European option with payoff g(ST) under the binomial tree model N V(0)=e -rNh (M) q (1 q)g(Soui). "Mara- (6) (7) (8) 3. (20 marks) Use the Principle of Mathematical Induction (PMI) and the recursive formula V(i, j) = eV(i + 1, j + 1)q + V(i + 1, j)(1 q)], 0 i N-1, 0 j i where j is the number of up-jumps up to time t = ih, to derive the formula for the price V(0) of a European option with payoff g(ST) under the binomial tree model N V(0)=e -rNh (M) q (1 q)g(Soui). "Mara- (6) (7) (8)
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