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Interest Rate Models: An Introduction

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Pricing Interest-Rate Derivatives: A Fourier-Transform

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Check out these Interest Rates images:

GDP projection based on market interest rate expectations and £200 billion asset purchases, August 2011


Image by Bank of England
Source: Inflation Report, August 2011

The fan chart depicts the probability of various outcomes for GDP growth. It has been conditioned on the assumption that the stock of purchased assets financed by the issuance of central bank reserves remains at £200 billion throughout the forecast period. To the left of the first vertical dashed line, the distribution reflects the likelihood of revisions to the data over the past; to the right, it reflects uncertainty over the evolution of GDP growth in the future. If economic circumstances identical to today’s were to prevail on 100 occasions, the MPC’s best collective judgement is that the mature estimate of GDP growth would lie within the darkest central band on only 10 of those occasions. The fan chart is constructed so that outturns are also expected to lie within each pair of the lighter green areas on 10 occasions. In any particular quarter of the forecast period, GDP is therefore expected to lie somewhere within the fan on 90 out of 100 occasions. And on the remaining 10 out of 100 occasions GDP growth can fall anywhere outside the green area of the fan chart. Over the forecast period, this has been depicted by the light grey background. In any quarter of the forecast period, the probability mass in each pair of identically coloured bands sums to 10%. The distribution of that 10% between the bands below and above the central projection varies according to the skew at each quarter, with the distribution given by the ratio of the width of the bands below the central projection to the bands above it. In Chart 1, the probabilities in the lower bands are slightly larger than those in the upper bands at Years 1, 2 and 3. The second dashed line is drawn at the two-year point of the projection.

GDP projection based on market interest rate expectations and £200 billion asset purchases, May 2011


Image by Bank of England
Source: Inflation Report, May 2011

The fan chart depicts the probability of various outcomes for GDP growth. It has been conditioned on the assumption that the stock of purchased assets financed by the issuance of central bank reserves remains at £200 billion throughout the forecast period. To the left of the first vertical dashed line, the distribution reflects the likelihood of revisions to the data over the past; to the right, it reflects uncertainty over the evolution of GDP growth in the future. If economic circumstances identical to today’s were to prevail on 100 occasions, the MPC’s best collective judgement is that the mature estimate of GDP growth would lie within the darkest central band on only 10 of those occasions. The fan chart is constructed so that outturns are also expected to lie within each pair of the lighter green areas on 10 occasions. In any particular quarter of the forecast period, GDP is therefore expected to lie somewhere within the fan on 90 out of 100 occasions. And on the remaining 10 out of 100 occasions GDP growth can fall anywhere outside the green area of the fan chart. Over the forecast period, this has been depicted by the light grey background. In any quarter of the forecast period, the probability mass in each pair of identically coloured bands sums to 10%. The distribution of that 10% between the bands below and above the central projection varies according to the skew at each quarter, with the distribution given by the ratio of the width of the bands below the central projection to the bands above it. In Chart 1, the probabilities in the lower bands are slightly larger than those in the upper bands at Years 1, 2 and 3. See the box on page 39 of the November 2007 Inflation Report for a fuller description of the fan chart and what it represents. The second dashed line is drawn at the two-year point of the projection.

Question by Capitalist_pig: What are some typical relationships between different interest rates?
Are there any well known relationships between different interest rates?

For example: The 20-year T-Bond rate is usually 2% above 3-month T-Bills.

Stuff like that. Is there a website that would have things like that? It doesn’t have to be just treasury security rates, it can be inflation rates, Federal Reserve interest rates, whatever.

Thanks
Are there some ratios between rates that indicate things about an economy?

Best answer:

Answer by Bored Goblin
they tend to go up and down together, longer maturities tend to have higher rates, but not always. A plot of rates against maturities is known as yield curve, and can be used to infer things about economy:

http://en.wikipedia.org/wiki/Yield_curve

What do you think? Answer below!