Financial engineering deals with the design of new assets. Draw the payoff (at t1) of the following bull butterfly spread: (a) Purchase 1 call with exercise price a Sell 2 calls with exercise price (a+b)/2 Purchase 1 call with exercise price b as a function of the underlying stock price S at t 1 where a-120 and b 140. [4p] b) An individual agent thinks that there is a high probability that the Dow Jones will have a payoff (or points) between a-20,000 and b-24,000 at t Design a digital option (see Figure 1) as a sequence of calls on the Dow that converges to a pure bet on getting $1 on the interval [20,000, 24,000], i.e. if the Dow lies between Se120,000, 24,000] at t1, then the portfolio of calls pays off exactly $1. The payoff is 0 otherwise. [6pl Figure 1 (Digital option) payoff a-20.000 b 24,000 Hint: You have to modify the sell strategies of a bull butterfly spread to obtain a payoff as given in Figure 2 and then adjust n and appropriately. Figure 2 payoff of portfolio Financial engineering deals with the design of new assets. Draw the payoff (at t1) of the following bull butterfly spread: (a) Purchase 1 call with exercise price a Sell 2 calls with exercise price (a+b)/2 Purchase 1 call with exercise price b as a function of the underlying stock price S at t 1 where a-120 and b 140. [4p] b) An individual agent thinks that there is a high probability that the Dow Jones will have a payoff (or points) between a-20,000 and b-24,000 at t Design a digital option (see Figure 1) as a sequence of calls on the Dow that converges to a pure bet on getting $1 on the interval [20,000, 24,000], i.e. if the Dow lies between Se120,000, 24,000] at t1, then the portfolio of calls pays off exactly $1. The payoff is 0 otherwise. [6pl Figure 1 (Digital option) payoff a-20.000 b 24,000 Hint: You have to modify the sell strategies of a bull butterfly spread to obtain a payoff as given in Figure 2 and then adjust n and appropriately. Figure 2 payoff of portfolio