There are two call options with the same underlying stock but different exercise prices. The exercise price for Option One is $100, and the exercise price for Option Two is $150. Both options have 1 year to expiration. The underlying stock pays no dividends. The underlying stock is currently trading at $150 per share. You believe it has a 50% chance of increasing by 20% and a 50% of chance of decreasing by 20% in one year. The risk-free rate of interest is 15%. The market price of Option One is $60 and the market price of Option Two is $25.

Calculate & Answer:

i). What is the hedge ratio for Option One and Option Two, respectively? (4 Marks)

Hedge ratio =

ii). Given the market conditions, is Option One underpriced or overpriced? Formulate an arbitrage strategy to exploit the mispricing and show how it provides a riskless cash flow in 1 year. (8 Marks)

iii). Given the market conditions, is Option Two underpriced or overpriced? Formulate an arbitrage strategy to exploit the mispricing and show how it provides a riskless cash flow in 1 year. (8 Marks)