Saturday, November 30, 2013

yield curve -> fwd rate, spot rate ...

This is yet another blog post about yield curve, fwd rate, spot rate etc

Let's say we have a bunch of similar derivative instruments [1] on IBM. Each has an expiry date, on each month end. For the Feb instrument, on the expiry date (end of Feb) all uncertainties would vanish and the value of the instrument would be determined/fixed. Therefore it's possible to cash settle on that day. Alternatively the contract may specify a later a maturity date (eg 3M from expiry/fixing) for the actual cashflow to occur.

Today, I can record all the current prices of this family of (eg 9) instruments. A minute later I can record their new prices... I keep doing it and get 9 (time-series) streams of live prices.

The "live yield curve" is something similar. The 9 instruments are the 9 deposit maturities we monitor, perhaps {1M, 3M, 6M, 1Y, 2Y, 3Y, 5Y, 10Y, 30Y ...} These prices, after converting to yield numbers, actually comprise a 9-point yield curve. (Better get more data points...) From this snapshot yc, we can derive many useful rates, such as (instantaneous) forward rates, spot rates, short rates... all valid at this moment only.

An additional complexity is discounting the cashflow. Either the cashflow occurs on fixing date or on maturity date, we need to discount to valuation time (moment of observation), using a discounting curve such as the OIS curve.

Every minute, we re-sample live prices, so this 9-point yield curve shifts and wiggles by the minute.

[1] Could be bunch of forward contracts, or bunch of binary put options etc

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