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  3. 4 consider a continuous time model on 0 t...

Question: 4 consider a continuous time model on 0 t...

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4. Consider a continuous time model on 0 t 1 in which the savings account rt rt

is given by βt =e^(rt) and the stock price is given by St =S0e^(rt) . The model also includes another random variable X that takes values from {0, 1}, indicating whether an earthquake has occurred at time 1. It is known at time 0 that the probability of the earthquake occurring at time 1 is strictly between 0 and 1. Only the stock and the savings account are traded.

  1. (a)  Does this model have arbitrage opportunities?

  2. (b)  Find two different equivalent martingale measures (EMMs) for this model. Using the fundamental theorems of asset pricing, what can you conclude about the model?

  3. (c)  Find a contract that cannot be replicated in the market.

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