(b) 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. [4p] Figure 1 (Digital option) payoff 1 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 appropriately. Figure 2 payoff of portfolio 1=nd a a+s b-8 S (b) 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. [4p] Figure 1 (Digital option) payoff 1 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 appropriately. Figure 2 payoff of portfolio 1=nd a a+s b-8 S