By now, you've probably seen Tom Sargent's great Ally Bank TV spot.

But, were I to needle Tom just a bit, I might ask, "Tom, the Ally Bank CD allows you the option of raising your CD rate once over its two-year life. Can you explain when to optimally exercise that option?'' Or (second beer), "Tom, to what portfolio optimization question is the answer, combine a two-year CD with an American option to raise the rate once? You must have some great robust-control result here about parameter uncertainty in dynamic interest-rate models."

My question for today is why are long term rates so low. I reject Fed manipulation as an explanation. In years past, they were unable to bring long rates down. Are the rates a warning of Japanization?

ReplyDeletethey are swapping long term bonds with short ones

DeleteWE ARE JAPAN

Japan had their crash in 1990 and they never fixed their banks and now their market is down 80% in 22 years

We are copying their stupidity.

Bernacke caused this housing boom and is making us pay for it for generations.

It is a great ad but there is nothing in there that says that Sargent had anything to do with the design of the product or advocates the product in any way.

ReplyDeleteAssuming markets are basically efficient, you'd want to exercise the option as soon as possible. Rates would be just as likely to go up as down, and you don't want to lose time at the better rate.

ReplyDeleteActually that's not right. If it goes up very little relative to the annual standard deviation you probably want to hold off. There's gotta be a formula based on the change relative to the chance it will go up to a % that will beat the current value over the remaining time.

ReplyDeleteIsn't that as late as possible?

ReplyDeleteI found the ad appropriately ironic as Sargent seems to recognize the difficulty of forecasting, while the Fed is happy to publish 17 mutually conflicting estimates of future rates even though future rates clearly depend on the policy decisions made by them between now and then. That is absurdly unrealistic and not useful.

ReplyDeleteHowever, it is an implicit endorsement of the product, which is odd since its a fairly complicated product that is targeted at rather unsophisticated consumers. Presumebly few of them would claim to understand the pricing of the option and judge it to be fairly priced. The presumption that Sargent has done the analysis. Hope is contract indemnifies him against claims.

Reminds me of a quote (over 2 decades ago, if my fallible memeory is approximately correct) by John Kenneth Galbraith when a reporter was pestering him for his interest rate forecast. His reply was (approximately): "People forecast interest rates simply because they are asked." The implication was that it wasn't because they knew anything.

ReplyDeletet*=argmax_{t in (0,2]} E[ exp{int_{0}^_{t}(r_{u})du}*exp{-y_{0}*t}+exp{int_{t}^_{T}(r_{u})du}*exp{-y_{t}*(T-t))*exp{-y_{0}*t} |F_{0}]

ReplyDeletewhere y is the rate on CD's

Rght. Now we need an interest rate process, with market prices of risk (I think you have risk neutral expectations here), take the integral, do the max...pause,... Sargent says "when rates hit 2.35%"

Deletehaha. Pardon my sloppy notation and pretend I put a Q next to the expectation operator

DeleteI'd say build a binomial tree for the (risk neutral) short term interest rate, then solve it backwards, evaluating the decision of exercising the option at each node of the tree. That is not easy but it ain't difficult either (one can set it up on a Excel sheet).

ReplyDeleteOccam's Razor: Simply ask Mr. Bernanke. He can tell you and make it happen.

ReplyDeleteYou lose the option once you exercise it, so you should exercise when the value of the option is lower than the benefit of exercising (the PV of the increase in the spread is greater). This is how exercise decisions in Bermuda Bonds are made.

ReplyDeleteThe data you need for that calculation is mostly OTC and banks have access to it, I have no idea how an average Joe buying a CD would get it. You need a vol structure of interest rates and an interest rate model for inputs. Assuming they can do the math - which for Bermudans is done by a posse of quants at the bank.

And after all that, your calculations (based as they are on models with lots of assumptions) can still be wrong and you can lose to the exercise. But, hey, it's because we don't know the future that all decisions are probabilistic.