In what follows (Bt), t 0 denotes the Brownian motion process started at zero. The terms...

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In what follows (Bt), t≥ 0 denotes the Brownian motion process started at zero. The terms "option", "claim" and "contract" mean the same, and are inter-changeable. Each question is worth 20 points. 1. Let the stock price over two time periods be modelled by So = 1, S₁ = $1, S₂ = S12, where $1, §2 are identically distributed random variables taking two values d and u with P(§1 = $2) < 1. The savings account pays 3 > 1 over one period. The parameters of the model satisfy d < ß < u. You need to price an option that pays X = (S2 S₁) at time t = = 2. (a) Describe the Equivalent Martingale measure Qin this model. (b) Give the price of the contract Co at time t = 0 by using the EMM. (c) Derive the replicating self-financing portfolio for this contract at t = 1, 2. (d) Suppose that the market price of the contract Po is less than the arbitrage- free price Co, Po < Co. Show how to make a risk-free profit by providing a trading strategy. In what follows (Bt), t≥ 0 denotes the Brownian motion process started at zero. The terms "option", "claim" and "contract" mean the same, and are inter-changeable. Each question is worth 20 points. 1. Let the stock price over two time periods be modelled by So = 1, S₁ = $1, S₂ = S12, where $1, §2 are identically distributed random variables taking two values d and u with P(§1 = $2) < 1. The savings account pays 3 > 1 over one period. The parameters of the model satisfy d < ß < u. You need to price an option that pays X = (S2 S₁) at time t = = 2. (a) Describe the Equivalent Martingale measure Qin this model. (b) Give the price of the contract Co at time t = 0 by using the EMM. (c) Derive the replicating self-financing portfolio for this contract at t = 1, 2. (d) Suppose that the market price of the contract Po is less than the arbitrage- free price Co, Po < Co. Show how to make a risk-free profit by providing a trading strategy.

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A a The equivalent martingale measure Q in this model is a measure which corresponds to the probabil... View the full answer