You are given the following information about the S&P500 index: Current price = $1000 Risk-free rate = 4% convertible semiannually Price for 6-month options: Strike Call Put $950 $120.405 $51.777 1000 93.809 74.201 1020 84.470 84.470 1050 71.802 101.214

(i) Which of the following spot prices at expiration has the largest loss for a purchased straddle created with at-the-money options?

A. $950

B. $980

C. $1000

D. $1020

E. $1050

(ii) The spot price at expiration is $1020. What is the profit for a purchased $950-$1050 strangle?

(iii) The spot price at expiration is $1020. What is the profit for a purchased $950-$1000-$1050 buttery?

(iv) A $950-$1020-$1050 asymmetric buttery is created by selling 10 call options at $1020-strike plus buying or selling the necessary options at $950-strike and $1050-strike. The spot price at expiration is $960. Calculate the buttery's profit.