Hi, I’m finding the Derivatives topic pretty challenging. How do you break these questions down? 1. What is the value of a LIBOR-based payer swaption (expiring today) on a $10M 1-yr 4.8% swap? LIBOR yield curve 180-days = 5.2% 360-days = 5.4% A) $0 B) $50,712 C) -$50,712 or D) $25,356 2. Consider a 3-yr quarterly-pay bond to be issued in 180 days w/ a 7% coupon. A 180-day put option on this bond, w/ an exercise price rate of 7%, has a payoff equal to that of a: A) receiver swaption B) payer swap C) payer swaption D) receiver swap Please explain your answer. The answers to Q1 and Q2 are B and C, respectively. Thanks!
I didn’t do the math on this one, but for #1, you can rule out A automatically as even a far out-of-the money option has value. Also, since this is a payer swaption, that is, this option gives the purchaser the right to enter in to a pay fixed rate swap at 4.8% (and receive LIBOR), it would have positive value to the payer as LIBOR is higher than the fix rate, so C can be ruled out immediately as well. So that leaves B and D. Finally, quick and dirty math on this shows that the expected payout based on these LIBOR rates is over 25k (5.2-4.8)/2*10M+(5.4-4.8)/2*10M = 50k, so B.
My first thought was that it should be (B). The correct answer is ©, of course. An investor would exercise the put if the rates go *UP* (the price of the bond goes down). Therefore, the investor wants to pay the FIXED at 7%, but receive the LIBOR. I’m just now sure why it’s © over (B). I can’t tell you the difference, except a swaption is the OPTION to enter a contract. 2. Consider a 3-yr quarterly-pay bond to be issued in 180 days w/ a 7% coupon. A 180-day put option on this bond, w/ an exercise price rate of 7%, has a payoff equal to that of a: A) receiver swaption B) payer swap C) payer swaption D) receiver swap
Say what? Principle #1: An option (including a swaption) can never be worth less than 0. The most OTM option on the entire planet right now is worth about 0.
Edit and for #2 - a swaption has to have a similar payout to a bond option as they are both ‘ptions’ and all ‘ptions’ have similar payout profiles. So now it’s just a matter of deciding whether a receiver swaption is more like a put or a payer swaption is more like a put. I use a alliterative mnemonic that cause maximal spitting.
For Q 1: the value of a LIBOR-based payer swaption (expiring today) on a $10M 1-yr 4.8% swap = option to enter a swap as the fixed rate payer. So value the swap first. discount rates Z180 = .9747, Z360 = .9488 fixed side value = .024 in 180 days 1.024 in 360 days = .9949 * 10M = $9,949,288 var side value = 1.026 in 180 days = 1 * 10M = $10,000,000 so pay fixed rec var = -9,949,288 + 10,000,000 =+50,712. payer swaption value = Max (0, Value of swap to fixed payer) = B) $50,712 For Q2: A put option on a bond, gives you the option to sell someone a bond which is to have them loan you principal and you pay them interest. In this case the option is to loan at a fixed rate rate of @ 7% so you have the option to be the fixed rate payer. So the payoff is the same as C) payer swaption
Thanks everyone - you guys make this look so easy, hopefully soon i can say it is! Good luck on test day and thanks again.