The Art of Term Structure Models: Drift
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About the Lecture
The lecture The Art of Term Structure Models: Drift by Edu Pristine is from the course Archiv - Market Risks. It contains the following chapters:
- Short term interest Rate Models
- Interest Rate Models
- Interest Rate Models with Constant Drift
- Interest Rate Model with time Dependent Drift
- Arbitrage free Models of Interest Rates
- Interest Rate Models with Mean Reverting Drift
- Example
- Generating Recombing Trees from Non Recombing Vasicek Model
- Expected time to reach Mean Reversion level
- Vasicek Model vs. No Drift Models
Author of lecture The Art of Term Structure Models: Drift
Edu Pristine
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Excerpts from the accompanying material
... In addition to volatility, we can have interest rates with no drift, constant drift and mean reverting drift. Simplest model assumes that interest rates are normally distributed and have no drift. Continuously compounded interest rate is assumed to follow relation ...
... rates, they can be capped at zero to recreate the rate tree. Alternatively, we must change the basic assumption to distributions which are non negative like lognormal or ...
... shift which is usually not observed. Scenario II: Model with constant drift dr = dt + dw where = constant drift and = const volatility. Example: If r 0 = 6% i.e., current short term rate, = 2% and = 0.5% ...
... structure which is observed in markets. Since two parameters have to be chosen for calibration the model fitting is better. If drift is assumed to be risk premium, then ...
... allow for mean reversion. The short rate follows a normal process. Allow drift to change in each time period and also assume negative values. Drift is the sum of risk premium and expected rate change. Recombined middle node at time ...
... or illiquid. Models calibrated using market data and then used to price illiquid securities. Arbitrage models assume market prices are accurate which may not be in case of excess ...
... mean equilibrium level then positive drift will move closer to mean levels dr = m(? – r)dt +dw m = speed of mean reversion = mean reverting interest rate level r = current interest rate level. Thus, drift = m(? – r) ...
... can be recombined. ...
... of the middle two nodes to compute the middle node value. Also involves replacing the probabilities of 50% up & down with new probabilities which must ...
... = current interest rate = half life which is half the average time to reach mean reverting level from current level. Larger mean reversion ...
... hand no drift models produce a flat term structure of rates. Vasicek model does not imply parallel shift from interest rate shocks which is the case with no drift models. Long lived shocks have low ...
