P2.T5.302. Term structure models with and without drift

Suzanne Evans

Well-Known Member
AIM: Describe the process and effectiveness of the following models, and construct a tree for a short-term rate using the following models: A model with normally distributed rates and no drift (Model 1); A model incorporating drift (Model 2)

Questions:

302.1. Analyst Greg is constructing an interest rate tree with monthly time steps; i.e., (t) = 1/12. The current short-term rate is 4.0%. His term structure model assumes an annual basis point volatility of 180 basis points. He employs Tuckman's Model 1 which assumes normally distributed rates and zero drift. Here is his rate tree:

T5_302.1_model1.png

(Source: Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011))

What is the undisplayed missing value at node [2,2]; i.e., the rate in the tree not the realized process?

a. 4.20%
b. 4.83%
c. 5.04%
d. 6.59%

302.2. Analyst Barbara constructed an interest rate tree with monthly time steps, where (t) = 1/12. The current short-term rate is 3.0%. Her term structure model assumes an annual basis point volatility of 200 basis points with an annual (lambda) drift of 50 basis points. She employs Tuckman's Model 2 which assumes normally distributed rates and incorporating drift. Here is her rate tree:

T5_302.2_model2.png

(Source: Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011))

What is the undisplayed missing value at node [2,0]; i.e., the rate in the tree not the realized process?

a. 1.93%
b. 2.17%
c. 2.38%
d. 3.01%

302.3. Tuckman's Model 1 assumes zero drift and is also called a normal model. His Model 2 adds a term for drift. Each of the following is true about these two models, according to Tuckman, EXCEPT for:

a. A weakness of Model 1 (normal model) is that the short-term rate can become negative
b. Model 1 implies a term structure that is perfectly flat at the current rate for all maturities, including the long-term rates
c. Model 2 is more capable of producing an upward-sloping term structure, which is often observed
d. Model 2 is an equilibrium model, rather than an arbitrage-free model, because no attempt is made to match the term structure closely

(Source: Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011))

Answers:
 
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