Question 5 (a) Suppose the stock price s follows geometric Brownian motion with expected return u and volatility rate o such that ds = uSdt + o Sdz . (i) Determine the process followed by the variable Vs. [8 marks] (ii) State the distribution of In(VS) with parameters. [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] Question 5 (a) Suppose the stock price s follows geometric Brownian motion with expected return u and volatility rate o such that ds = uSdt + o Sdz . (i) Determine the process followed by the variable Vs. [8 marks] (ii) State the distribution of In(VS) with parameters. [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]