(a) Suppose the stock price S follows geometric Brownian motion with expected return and volatility rate...

   

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(a) Suppose the stock price S follows geometric Brownian motion with expected return and volatility rate such that dS = Sdt+Sdz. (i) Determine the process followed by the variable 5. (ii) State the distribution of In (5) with parameters. [8 marks] [4 marks] (b) Consider the combinations of the following options: long 1 call of exercise price $70, short 2 calls of exercise price $90, and long 1 call of exercise price $110. Suppose all the options are derived from the same underlying asset with same time to maturity. The price of the calls with exercise price of $70, $ 90 and $110 are $2, $3 and $4, respectively. Does arbitrage exist? Show all the trading strategies in cash flow table. [8 marks] (a) Suppose the stock price S follows geometric Brownian motion with expected return and volatility rate such that dS = Sdt+Sdz. (i) Determine the process followed by the variable 5. (ii) State the distribution of In (5) with parameters. [8 marks] [4 marks] (b) Consider the combinations of the following options: long 1 call of exercise price $70, short 2 calls of exercise price $90, and long 1 call of exercise price $110. Suppose all the options are derived from the same underlying asset with same time to maturity. The price of the calls with exercise price of $70, $ 90 and $110 are $2, $3 and $4, respectively. Does arbitrage exist? Show all the trading strategies in cash flow table. [8 marks]

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a Geometric Brownian Motion GBM is a continuoustime stochastic process used to model the behavior of ... View the full answer