Can someone please help explain why a payer swap can be replicated using a long receiver swaption and a short payer swaption with the same exercise rates?
Extremely lost here…thanks
stock = long call + short put
With these it helps to keep in mind that only one of the two swaptions can be in the money.
S2000magician, can you please elaborate on your explanation? Not sure how these are analogous/synonymous still with your answer…thank you.
put call parity : p + s = c + x
the payer swap is similar to holding stock
the long receiver swaption is similar to a long call,
the short payer swaption is similar to a short put
How can you replicate the payoff on a stock? With a long call on that stock (whose strike price is the spot price of that stock) and a short put on that stock (same strike price).
How can you replicate the payoff on a commodity? With a long call on that commodity (whose strike price is the spot price of that commodity) and a short put on that commodity (same strike price).
How can you replicate the payoff on any asset? With a long call on that asset (whose strike price is the spot price of that asset) and a short put on that asset (same strike price).
How can you replicate the payoff on a . . . wait for it! . . . swap?
And what to you call puts and calls on swaps?
Voilà.
Actually now that I think about it, isn’t the OP reversed?
The long receiver swaption and a short pay swaption is equivalent to a receive fixed swap and NOT a pay fixed swap.
This thread pretty much sums what I just said above: https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91362914
Also, one of the mock solutions I just did says: “A long position in the payer swaption and a short position in a recieve swaption with the same exercise is equivalent to a receive floating [aka pay fixed] swap.” which is consistent with the OP being reversed.
Therefore, the ops comment “help explain why a payer swap can be replicated using a long receiver swaption and a short payer swaption with the same exercise rates?”
should read as
“help explain why a payer receiver swap can be replicated using a long receiver swaption and a short payer swaption with the same exercise rates?”
Yup.
I was thinking about it generically; I didn’t consider that the options were reversed.
Good eye!
Is this because stock prices are lognormally distributed? Ie the short put covers the side of stock ownership that places the theoretical limit of losses at zero.
Nope.
You’re thinking way too deeply on this.
I’m talking about the payoffs. If you plot the payoff of a long call and a short put (each with a strike price equal to today’s spot price on the stock), then combine those payoffs, the payoff diagram you get is the same as the payoff diagram on a share of stock: a straight line with a slope of 1 passing through today’s spot price.
Put call parity is independent of the modeling assumptions of the asset, and only depends on a no arbitrage argument.
I know this is stupid question after stupid question, and thanks for your help, but how is a payer swap equal to owning a stock, if payer swap = pay-fix, rec-floating. A payer swap = payer swaption?
A payer swap isn’t equal to owning a stock.
I was offering an analogy:
stock : (long call + short put)
as
swap : (long receiver swaption + short payer swaption)
But to your point(s) above, can’t you use the put/call parity here too? This is how I’m thinking about it, but could be totally off, so feel free to eviscerate my response as needed, Magician…
Okay, here it goes: for example, if you’re the long in an IR swap, you would pay fixed and receive floating (payer swap). This is effectively equivalent to being long a stock if using the stock analogy. If you’re short the IR swap, you’re the receiver (receive fixed, pay floating). If you’re long a payer swaption, you’re basically buying a call on the IR (if market rate > strike rate, you exercise and pay the fixed strike rate, otherwise you don’t and the swaption expires worthless) and if you’re long a receiver swaption, you’re basically buying a put on the IR. So, using put/call parity where S + P = C + PV(x) (we can ignore the PV(x) here), if you’re trying to replicate a receiver swap (i.e., short IR) the put/call parity looks like this: P - C = -S, where S is the swap, P is receiver swaption, and C is payer swaption. So you would be long a receiver swaption and short a payer swaption to get a receiver swap.
Thanks
Nothing could have been simpler than this…I regret not reading this in L2…I have one doubt in one equivalence that was included in L2 but not explained. And we have the same in L3 in one of the Blue Box Examples in FI.
Long a callable fixed rate bond is equivalent to long a straight fixed rate bond and short a receiver swaption. This is very confusing. Any intituitive way to see this?
What happens when you exercise the call option on the bond you issued?
When rates decrease, issuer will exercise the call option and raise debt at lower rates.
In particular, the issuer will call the old bonds and (likely) issue new ones with a lower coupon.
When rates decline and you exercise a receiver swaption, you receive the higher fixed rate and pay the lower floating rate, effectively lowering the coupon rate on the bonds you’ve issued.
yes makes sense now…I wasnt understanding this lowering of coupon rate…Thanks a lot yet again Sir…
My pleasure.