II. Tony, a trader who specialises in trading exotic options, has recently taken some positions in barrier options. Specifically, his portfolio consists of positions in two exotic options that he entered 2 months ago: 1. One down-and-in call option on ABC with a barrier of $25, strike price of $22 and 3 months to maturity. Tony paid a premium of $0.70 for this long position. 2. One down-and-out call option on ABC with a barrier of $25, strike price of $22, and 3 months to maturity. Tony paid a premium of $1.65 for this long position. a) How can Tony replicate his current portfolio with a single option? Explain how Tony can do so and describe this option's characteristics. (3 marks) b) What should the premium be for this single option identified? (2 marks) c) Tony's friend, Jason, holds the following portfolio of exotic options that he entered 2 months ago: 1. One down-and-in call option on ABC with a barrier of $25, strike price of $22 and 3 months to maturity 2. One down-and-out call option on ABC with a barrier of $24, strike price of $22, and 3 months to maturity. Without any calculations, explain whose portfolio would have cost more to enter? That is, would Tony have paid more than Jason in total for his positions, or vice versa? (3 marks) II. Tony, a trader who specialises in trading exotic options, has recently taken some positions in barrier options. Specifically, his portfolio consists of positions in two exotic options that he entered 2 months ago: 1. One down-and-in call option on ABC with a barrier of $25, strike price of $22 and 3 months to maturity. Tony paid a premium of $0.70 for this long position. 2. One down-and-out call option on ABC with a barrier of $25, strike price of $22, and 3 months to maturity. Tony paid a premium of $1.65 for this long position. a) How can Tony replicate his current portfolio with a single option? Explain how Tony can do so and describe this option's characteristics. (3 marks) b) What should the premium be for this single option identified? (2 marks) c) Tony's friend, Jason, holds the following portfolio of exotic options that he entered 2 months ago: 1. One down-and-in call option on ABC with a barrier of $25, strike price of $22 and 3 months to maturity 2. One down-and-out call option on ABC with a barrier of $24, strike price of $22, and 3 months to maturity. Without any calculations, explain whose portfolio would have cost more to enter? That is, would Tony have paid more than Jason in total for his positions, or vice versa
