5. Consider a market with one factor (i.e. an asset that is not traded), and a...

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5. Consider a market with one factor (i.e. an asset that is not traded), and a traded riskless asset. (a) Discuss why this market is not complete. (b) Given that there is a active market where derivatives on the factor are actively traded, show how a external parameter called the market price of risk can be used to price the derivatives. (c) Given that the factor can be represented by a Geometric Brownian Motion with constant coefficients, in the objective space, what is its dynamics in the risk neutral space. (d) Write out the PDE which gives the price a call option, and compare its closed form solution to that of the Black Scholes formula in a complete market. (Hint: use the Feynman-Kac theorem) 5. Consider a market with one factor (i.e. an asset that is not traded), and a traded riskless asset. (a) Discuss why this market is not complete. (b) Given that there is a active market where derivatives on the factor are actively traded, show how a external parameter called the market price of risk can be used to price the derivatives. (c) Given that the factor can be represented by a Geometric Brownian Motion with constant coefficients, in the objective space, what is its dynamics in the risk neutral space. (d) Write out the PDE which gives the price a call option, and compare its closed form solution to that of the Black Scholes formula in a complete market. (Hint: use the Feynman-Kac theorem)