# Derivatives help

Ok, I apologize in advance for asking such a broad question but I’m hoping someone out there can help me with this. I am having a REALLY hard time with all of the questions that ask you to determine the equivalent investment for a certain type of derivative. I get the stock options fine because I just remember C - P = S - X and I can shift the equation around to get an answer, but I just don’t seem to be able to wrap my head around the other ones (fixed rate receiver equivalency to calls/puts or FRAs, FRAs equivalent to certain calls/puts, etc.) I’m sure it doesn’t help that it’s past 3 am here but does anyone have any tricks to remembering these things? At this point I’m seriously better off taking the answer I come up with and then guessing between the two that are left. Even a list of each and the corresponding investment would be fine if that’s all anyone has, I don’t want to resort to memorization with this but I’m not sure I’ll have a choice. Thanks!!

I’m with you Aimee, I find myself guessing for the most part on these. Certain ones are easy, basically I just determine what the cash flows are and match them, but sometimes they get ridiculous and I’m totally guessing.

I really have not prepared a list. If you could start the list by giving what you wanted, that would really help. I try to work thro them based on what has been asked, and many a time get them wrong as well.

aimee- i have 100% faith that you can nail these. take, i dunno, a fixed payer interest rate swap. so you’re paying fixed, receiving floating. if you’re long then, first i like to think of when do i make money? when interest rates go up here b/c you pay fixed but you’d get a higher interest rate on the floating side. that’s good, right? cool, so with options- you’d need something that pays when the floating rate goes up. BUT on the flip side, you need something where you have to pay when the floating rate goes down. this is why it’s not just 1 option- you need to replicate both the gain and the loss. so if you go LONG an interest rate call, you make \$\$ as interest rates go up. if you SHORT an interest rate put, shorting the put is also bullish on interest rates but here you’d lose if interest rates go down. so that replicates your fixed payer swap. the bond side i think is even easier- you’re paying fixed, so that’s like issuing a fixed rate bond. you as the issuer have to pay that fixed coupon. you buy a floating rate bond- you get paid floating. that one’s not bad i don’t think. FRA’s- this one is maybe the hardest to see but maybe draw it out or check schweser (i want to say they drew a picture to show the cash flows). it’s like a series of long FRA’s- remember the long in a FRA borrows money (you’re long a loan and paying fixed rate on it)- so you want interest rates to go up. for caps, floors, etc… i dunno- i think the first and best thing to do with any of these is say to yourself- when do i make money, when interest rates or libor or whatever goes up or down? then you can figure out the rest pretty easily. take a long interest rate floor. so it says that you’ll get paid at least whatever % interest rate. i dunno, 5%. when do you make money then? if interest rates go down to 3%, your floor kicks in, you like that. if interest rates go up to 7%, who cares about your floor. ok, so we get paid when interest rates fall. got that much. so what’s that in options- it’s like buying a portfolio of puts on LIBOR or some benchmark rate. it also would be like a portfolio of call options on fixed income securities- remember, interest rates down, FI securities UP. so you benefit when interest rates go down. i might be completely rambling here, but that more or less is my process- figure out if you make \$\$ if interest rates are going down or up and then 99% of the time, the answers fall into place very nicely, no pure memorization necessary.

Ban, good post. It must of took you 1/2 hr. Doing enough exercises will help a ton. Personally I think drawing picture helps a ton. And ask urself if you u a FRA, swaption, caplet, floor etc what are you really buying? Once you understand that its a matter of interest rate saving calc and PVM. FYI I’m going to spend prob a whole day redoing these problems.

Thanks a ton Banni. I think its something where I’m just going to have to do enough of these to get some good intuition going on them, but this certainly helps!

DONT FORGET that a swap is like a set of forward rate agreements but ONE LESS than the number of payments dictated by the swap. Why? Because at the initiation of the the swap, you know current LIBOR which gives you the upcoming payment, therefore there are no payoffs based on uncertainty on the first payment.

@ban: that’s exactly what I do with these sort of questions. My advice when you get to one of these is: 1) Don’t panic! You have plenty of time on the exam, use it. 2) Look at the instrument given in the question and do a scenario analysis on it as if you’re the long (what happens when rates go up, what happens when they go down). Write this down. 3) If the scenario payoffs don’t immediately tip you off to what instruments would replicate these CFs, go through each answer one by one and replicate the scenario analysis approach used in 2), until you get properly matching CFs 4) verify that the answer you get in fact provides the right CFs and not just the same CFs. What I mean hear is that you need to make sure the CFs have the right sign, and that you don’t infact need to be entering the complete opposite position (knowing instrument payoffs helps greatly here). But again the biggest thing when facing one of these “beasts” is to NOT PANIC, just take a deep breath, calm down and take solace in the fact that you know perfectly the instruments and payoffs of the constituent instruments and move forward slowly and methodically! There is just no sense in memorizing these things if you understand what the individual instruments do and how their payoffs are structured (which everyone on here should know anyways), you should nail these questions every time if only after you spend some time on them.

bannisja & adavydov7- that’s exactly how I do it too. It takes time (who cares?) to come to an answer - but working my intuition that way, never leads me to a incorrect answer. No memorization needed - keep that for gazillion other things you also need to know for this ridiculous exam.

one thing i think i figured out about derivatives that wasn’t clear to me from the readings was deriving put call parity for forwards from put call parity from options. PCP from options says: So + Po = X/(1+Rf)^t + Co (sexy pamela is an x rated cougar) You know that a forward price is equal to the spot rate times one plus the risk free rate (Ft = So(1 + Rf))^t, so multiple everything in the options PCP by (1+Rf)^t. this results in: So(1+Rf)^t + Po(1+Rf)^t = X + Co(1+Rf)^t, or Ft + Po(1+Rf)^t = X + Co(1+Rf)^t Solving for Ft we get Ft = -Po(1+Rf)^t + X + Co(1+Rf)^t, or Ft = X + (Co - Po)(1+Rf)^t

@ridgefield: why don’t you just solve for S0 (i.e S0=Ft/(1+rf)^t) and then plug this into put call parity for S0?

doesn’t that get you to the same answer?