Stochastic Interest Rate Models Flashcards
In this chapter what have we changed in our cash flow model
We are now modelling the interest rate stochastically. There is no uncertainty around the amount of cash flows just the interest rates
What are two areas of variability in a cash flow model
The cash flow amounts and the assumption of a fixed i
Why can we not discuss the present value or accumulated value of a set of payments and what do we instead examine?
W will not know for certain what actual interest rates
will apply over the time carrying out the discounting or accumulation steps
Instead we use methods of probability theory to calculate the expected value and the
standard deviation of the present and accumulated values of the set of payments
What does FIRM stand for
Fixed interest rate model
What is the concept of FIRM
We assume there is exactly one random event which occurs immediately before the start of the
first year and such that the effective annual rate of interest applying in every future year is
determined by this single random event. I is fixed after this random event
What is the significant of spread in finance
Spread is the risk
What is the caveat with FIRM
The fixed interest rate model is very unrealistic: interest rates tend to vary quite a lot over the investment term and are rarely, defined at the outset by one single random event. At the same time, the fixed interest rate model is simple and easy for us to apply.
What does VIRM stand for
Variable interest rate model
What are the assumptuions under VIRM?
Assume there are n random events at the start of each one of the n years in question during the investment term. Each of these events define the effective annual
rate of interest applying for the corresponding year alone. The effective annual rate
of interest varies each year in line with the statistical distribution. We also assume that the random events are pairwise independent of each other.
How realistic is VIRM?
It is more realisatic than FIRM - allows interest rate to vary each year according to an assumed distribution.
We could always re-scale VIRM to work for shorter time periods, per month per day etc
Unrealistic assumption is successive interest rates are independent as successive interest rates are high correlated - markets are dependent on events an dinterconnected
In result A what does j stand for
Expectation of the interest rate distribution
In result A what does s^2 stand for
Variance of the interest rate distribution
In result A what does Sn stand for
Accumulated value of a UNIT sum of money at the end of the n year period
What is the purpose of Result A and its limitations
Result A allows us to calculate statistics for the particular variable interest rate model much more
quickly and efficiently than if we had to project forward each possible outcome under that model. However it does not allow for working out probabilities or cut off points.
What is the log normal interest rate model
Special case of the variable interest rate model where we make the
additional assumption that each annual (random) growth or scale factor (1+i) has a certain log-normal distribution. Continuing to assume growth factors are pairwise independent of each other.
Describe the properties of the log normal distribution
Replicated under multiplication: the product of log-normal random variables is a log-normal random variable
Heavy tailed distribution
Positively skewed (makes sense with more small claims)
Very sensitive
Flak peak
Log(Log normal RV) = Normal RV
Why is it useful the log normal distribution is heavy tailed
When modelling interest rates and stock prices as markets and interest rates go through periods of low crashes and high gains much more frequently than would be implied if a normal distribution was
underlying such prices and rates.
What is the scale factor
1 +i
What are the parameters of the log normal
NOT THE EXPECTED VALUE AND THE VARIANCE. They are mew and sigma squared but they are not the mean and variance of the distribution
What property of log normal distribution is useful to calculate tail probabilities
If X log normal then log(X) is normal
What makes log normal distribution ideal for equity and property
These are volatile funds and the log normal distribution is very sensitive
Drawback of log normal model
Independence assumption still stands and is unrealistic
