Consider the following structured note: It pays the principal amount P = $1,000,000 with certainty, and also the participation rate of r = 50% of the upside of the S&P500 from its current level over the next 1 year, where the participation rate is calculated on the principal amount P = $1,000,000, but the upside is capped at a 20% increase in the level of the S&P500, so the maximum upside is (20%)r = (20%)0.5 = 10% of the S&P500. For example, if the S&P500 increases by 30% from its current level (i.e. it goes from 1,900 to 2,470), then the total payoff will be: P (principal) + minf (30%r; 10%) P (equity participation coupon) = $1,000,000 + min (15%; 10%) ($1,000,000) = $1,000,000 + 10%($1,000,000) = $1,100,000. In order to construct that structured note, you need to trade three assets: buy a zerocoupon bond with face value equal to P = $1,000,000 that matures 1 year from now, buy some at-the-money call options on the S&P500 with expiration in 1 year, and sell (write) the same number of out-of-the-money call options on the S&P500, with strike price equal to the cap, i.e. K = 1.2(1900) = 2280 and expiration in 1 year. How many options do you need to buy and sell? Working as before, the principal amount of $1,000,000 corresponds to $1,000,000/1900 = 526.3158 units of the index. However, you only participate r = 50% to the upside, so your position is equivalent to only (0:5)526:3158 = 263:1579 units of the index. Therefore, you need to buy 263.1579 at-the-money call options and sell 263.1579 out-of-the-money call options.

Answer the following question:

What is the price of the zero-coupon bond, and what is the price of each at-the-money call option that you need to buy?