Survival Function

The notary’s pen dies halfway through my last name. The bank’s closer hands over another one without looking up. She does not congratulate us. She does not tell us what a nice street 137th is. She points at the signature lines and then she says the number, four hundred eighty, which is how many monthly payments we owe. The last one comes due the year I turn seventy-four.

The rate is six point one percent. I remember it because of my job. I am a medical coder at the hospital on Kendall. All day I take what doctors write and turn it into numbers, and the numbers decide whether a family gets a bill that ends them. Every chart has one figure that carries the whole thing, and after a few years you learn to find it before you read anything else. So I watch digits. Six point one. Four hundred eighty. Some charts also carry a curve, a line that runs flat for a long time and then drops off a shelf. The doctors call it a survival function. It tells you the odds a person is still here at any point you care to name.

Beto signs after me. The pen works for him. In the car he says cuarenta años like it is a joke he is trying on for size. I tell him we will be old. He says he plans to be.

A week later the paper comes out.

It is from a cosmology group in Chile, three authors, in one of the letters journals. I read the abstract at work between charts. It says the universe cannot end within the next thirty years. That is the finding, and it is meant to be a comfort. They used fifty years of laser ranging to the Moon and the tracking data from the orbiters at Mars. If space were about to fold or tear, the orbits would already be drifting, and they are not drifting. So nothing ends before thirty years. After thirty years the data goes quiet. The paper cannot say. There is a floor and there is no ceiling.

I do not understand most of it. I understand the floor.

By Friday the big lenders have posted new rules. No mortgage longer than thirty years. No life policy longer than thirty. A judge in the Southern District commutes a man’s forty-five-year sentence down to thirty, because the state cannot promise a punishment longer than the world can hold. The cryonics companies send letters. My aunt Nereida paid into cryonics since 2011, and her contract now covers thirty years, and past that there is no guarantee and no refund. The wedding chapels start selling thirty-year vows with a renewal option. I am not making that up. Renewal option.

I keep thinking about my own paper, signed nine days before any of it, forty years, four hundred eighty payments, on a house whose sky just got a deadline.

I call the servicer. I ask if they will rewrite me to thirty, to match. The woman on the phone is patient with me. She says her system will not generate a term past thirty, so she cannot generate mine. Mine already exists, is the thing. There is no button for mine.

So I start pulling documents. I am not a lawyer, but I can file a records request. I ask the bank for the underwriting policy that was in effect the week I signed, and for the revision history, because the disclosure law says they have to give me what they used to decide me. Six weeks later a PDF arrives, forty pages long. On page nine there is a field with a name I do not know yet. Expected cash-flow horizon. Beside it the number runs forty years, then thirty-nine, then thirty-eight, then thirty-seven, each with a revision date.

I copy it onto the back of a chart I was going to throw away. Dates on the left. Horizon on the right. It reaches back to 1989. Horizon forty-five. Then forty. Then thirty-nine in 2019, thirty-eight in 2021, thirty-seven in 2023. The notes say the model has been learning. Every revision cites a parameter update.

The last revision is dated nine days after my closing. Horizon thirty-six. So the week I signed, this bank’s own model had already decided the world was worth thirty-seven more years. Later I find the desk rule. Never write a term longer than the horizon minus one, a buffer of a year. The week I signed, the longest mortgage that desk should have written was thirty-six years. My broker wrote forty because the new policy had not reached his screen. A paperwork lag. Nine days, and I am holding the last forty-year mortgage in the bank’s book.

I print page nine and put it in my bag.

The name on the revision notes is Arun Vasudevan, and his office is in a glass building in Brickell with a fountain in the lobby and a security guard who does not want to let me up. I tell the guard I have an appointment. I do not. I wait three hours. When Arun comes down for lunch I stand in front of him and say his name.

He is holding a sandwich from a place that charges sixteen dollars for a sandwich. He looks at me like a collections call. I say, expected cash-flow horizon. I say, page nine. I say, thirty-seven.

He stops chewing.

He takes me up to a conference room that looks at the bay. He sets the sandwich down and does not pick it up again.

He says banks have priced mortality since banks have existed. Life expectancy, prepayment, default, every risk is a curve of how likely a flow is to arrive. He says this bank carried one more curve than people knew about, and it has been in the models since the eighties. He calls it the cosmic hazard.

I ask what feeds it.

He stands at the whiteboard and draws a line. It runs flat for a long time and then it falls off a shelf. He says the expansion of the universe was supposed to be a constant, a number that never moved. It is not constant. The newer measurements say it is changing. If it keeps changing in the direction the data leans, the gentle push becomes a tear, and the tear works from the outside in, clusters first, then galaxies, then solar systems. It depends on the masses of the top quark and the Higgs, and on other things nobody has measured. The measured part says the rate is small but not zero. You compound it, he says, year after year, across a whole book of thirty-year loans, and at some horizon the expected value of the last payment goes to nothing. The model finds the year where the tail stops being worth pricing.

I ask him which year.

He says, for the version that was in force when you signed, thirty-seven.

I ask why nobody here is running around. Why he can eat a sixteen-dollar sandwich.

He says the number did not change for him. The paper did not tell him anything that was not already a column on his screen. He says the whole street had been pricing the same horizon for years. The paper just put it in the newspaper. The calm is not confidence. His book is hedged to the horizon, and past the horizon the hedge does not exist, so there is nothing to do but wait.

I ask if he owns a house.

He says he refinanced to a fifteen.

I go home and sit at the kitchen table with the actuarial table from work, the one I use to code hospice. I am thirty-four. A woman like me, with my blood pressure and my mother’s chart, has a median of forty-one more years. I do the arithmetic twice because the first time I do not believe it. The universe’s line falls at thirty-seven. Mine falls at forty-one. The universe is going to end before I do, or the median says so, which is a strange thing to find on the back of a chart at midnight with the tree dropping fruit outside.

I read survival curves all day. My mother is seventy-one and in a home in Hialeah, and her curve has the same shape as Arun’s whiteboard, flat and then a cliff, and the only difference is the axis. I have been looking at one for a year without knowing it, and I recognized the other in an afternoon. I do not tell Beto about the forty-one. He has enough.

Before I leave the building, I ask Arun one more thing. If the model prices the last three years of my loan at nothing, can the bank cancel them for nothing. He says no. He says the model prices the whole book at once, and then my contract gets collected from me one month at a time. Two systems, and they do not talk. He sounds tired when he says it, and I believe him. He is not a bad man. That is what I keep coming back to.

The statement comes on the fourth. Total due, one thousand eight hundred forty-seven dollars and twelve cents. Principal, four hundred twelve dollars and sixty cents. The rest is interest. The principal is the only number on that page I can move, so I move it.

I put page nine in the drawer with the deed and close it. Then I go to work and code the next chart, and I enter the code.