Question is: building society offers 3 year bond providing return on FTSE100 up to max of 50% growth over 3 years and subject to gteed min return of x%. How do we hedge the position using options? My answer: Define S_t = amount invested x FTSE100 index at time t Create portfolio consisting of: a) Buy put option on index with strike x% S_0 b) Buy S_0 c) Write call option with strike 1.5 S_0 This will provide payoff: S_3 if x% S_0 < S_3 < 1.5 S_0 x% S_0 if S_3 < x% S_0 1.5 S_0 if S_3 > 1.5 S_0 so we are hedged. The money received from writing call option can be used to buy put option (at least most of it) is this an acceptable alternative solution?
I don't see why not Gareth. Put-call parity shows that P_x + S_0 = C_x + X(discounted). Therefore your portfolio provides the same payoff as a bull spread with threshold x and limit 1.5S_0 with cash invested to payoff X at T. For me, your method isn't the most intuitive as when I sketch the payoff diagram I'm immediately thinking either two calls or two puts (each with different strikes) for the spread but it's horses for courses.
thanks olly. i also confirmed it seems ok as i get same answers for numerical parts of question following.
