Consider a two-period binomial market model for an underlying asset with price process St at each time t. Branching from t to t+1 results in St+1 and St+1 = dS; in case of a downward price move. You are asked to input values So d = 1/2, r = 0.1, and & = 0 to price a European put option with strike price 3. uS; in case of an upward price move, 2, u = 2, a. Write down the evolution of the underlying stock and the payoff of the option along the tree. b. Determine the structure of the replicating portfolio at times 0 and 1 in every node. c. Determine the price of the option at time 0. d. Explain how the price computed at point (c) would change if the option were of American type.
Consider a two-period binomial market model for an underlying asset with price process St at each time t. Branching from t to t+1 results in St+1 and St+1 = dS; in case of a downward price move. You are asked to input values So d = 1/2, r = 0.1, and & = 0 to price a European put option with strike price 3. uS; in case of an upward price move, 2, u = 2, a. Write down the evolution of the underlying stock and the payoff of the option along the tree. b. Determine the structure of the replicating portfolio at times 0 and 1 in every node. c. Determine the price of the option at time 0. d. Explain how the price computed at point (c) would change if the option were of American type.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:Consider a two-period binomial market model for an underlying asset with price process S; at
each time t. Branching fromt to t+1 results in St+1
and St+1 = dS; in case of a downward price move. You are asked to input values So = 2, u = 2,
d = 1/2, r = 0.1, and 8 = 0 to price a European put option with strike price 3.
uSt in case of an upward price move,
a. Write down the evolution of the underlying stock and the payoff of the option along the tree.
b. Determine the structure of the replicating portfolio at times 0 and 1 in every node.
c. Determine the price of the option at time 0.
d. Explain how the price computed at point (c) would change if the option were of American
type.
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