**Matt Levine**, Bloomberg, It Cost JPMorgan $1.5 Billion to Value Its Derivatives Right, here.

Last quarter, JPMorgan’s financial results included a $1.5 billion loss due to implementing a funding valuation adjustment in its accounting for uncollateralized over-the-counter derivatives and — wait, where are you going? Somewhere where people don’t talk about accounting and derivative valuation? Oh, yeah, okay, that’s fair, I cannot really argue with you. Go in peace.

If you want to stick around, though, we can talk about it, because I think it’s pretty neat. Conceptually, derivatives are contracts that involve exchanging (normally uncertain) cash flows over time. So the way to value a derivative, loosely speaking, is to guess what those future cash flows are likely to be, and then discount them back to present value. But it turns out that banks mostly hedge derivatives by trading in the underlying stock or currency or commodity or whatever, or by trading offsetting derivatives in the interdealer market. What this means is that you should — in theory! — have no stock price or currency or whatever risk, and so you can guess those cash flows on a “risk-neutral basis.” Similarly, since you have no risk, you can discount your cash flows on a risk-free basis.

That’s the textbook, Black-Scholes-y way of valuing derivatives. But recent years have provided many reminders that people don’t always pay what they owe on derivatives, so your risk-free cash flows can be risky, even if they have no risk to the underlying stock or interest rate or currency or whatever. There are two main ways of dealing with that fact, which are:

- Price it, or
- Collateralize it.

Both have their points. So there has been a big push to move derivatives onto exchanges, to increase collateralization requirements, etc., etc. If all your derivatives are perfectly collateralized — with instantaneous movement of cash to cover all liabilities — then your cash flows go back to being risk-free and you can live in a Black-Scholes world.

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