(a) Financial engineering deals with the design of new assets. Draw the payoff (at t=1) of the following bull butterfly spread: 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 Satt-1 where a-120and b=140. [4] (6) An individual agent thinks that there is a high probability that the Dow Jones will have a payoff (or points) between a=26,000 and b=28,000 at t=1 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 [26,000, 28,000), i.e. if the Dow lies between Se[26,000, 28,000) at t=1, then the portfolio of calls pays off exactly $1. The payoff is 0 otherwise. [op] Figure 1 (Digital option) 1 payoff a=26,000 b=28,000 S 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 8 appropriately. Figure 2 payoff of portfolio 1=ni aa- 8b- 66