Tuckman : The art of TSM: Volatility & Distribution
4 important questions on Tuckman : The art of TSM: Volatility & Distribution
What are the (dis)advantages of time dependent volatility models?
Useful for quoting fixed income option price that are not easily observable. Useful to interprolate from known option prices.
However, less useful to value and hedge fixed income securities:
1. Mean reversion is based on economic intuition; time dependent volatility assumes that the market has a forecast of short-term volatility in the near future
2. The downward sloping factor structure and term structure of volatility in mean-revering models caputre the behavior of interest rate movements better than parallel shifts and a flat term structure of volatility
What does the Cox-Ingersoll-Ross (CIR) model add to the term structure models?
Also includes level of the interest rate.
How does a lognormal (model 4) model for short term interest rate prediction look like? And how is it different?
in the lognormal model, basis-point volatility is proportional to the level of the rate
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What is the Black-Karasinski model?
A model to predict short term interest rates that allows for:
- time dependent volatility
- mean reversion that is a function of time
- central tendency of the short rate that also depends on time
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