THE PROBLEM
Option, option everywhere - Option Risk everywhere. The current low-interest rates have significant repercussions on capital markets. For example, many banks experienced a torrent of residential mortgage prepayments and called bonds during the third quarter of 2019, lowering financial income significantly. Regulators call such prepayment spikes "option risk". The Asset-Liability Committee (ALCO) has to manage option risk, especially when there are many options embedded on the balance sheet.
The specifications and explanations should include the following:
1. Local Volatility Model
The model specification is relatively simple and robust. There are only five parameters to specify the model. (i) Parameter [a] specifies the short term volatility. (ii) Parameter [b] specifies the short-term increase or decrease of volatility. (iii) Parameter [c] specifies the decay of the volatilities over time; (iv) [d] in the long term volatilities. (v) Parameter [p] is the skewness of the binomial distribution.
2. Historical Trends
To underscore the transparency of the Local Vol model, a historical trend of the term structure of volatilities is provided. The graph depicts the projected one-month interest rate volatilities of the Local Volatilities Model.
3. Rate Distribution
The Rate Distribution presents the capital market relative pricing of rates rising vs falling.
4. Out-of-the-Money (OTM) Impact on Rate Distribution
Many interest rate models are calibrated with only At-the-Money Options. But when interest rates are low, the Out-of-the-Money options can have a significant impact on the Rate Distribution, and hence the pricing of caps and floors.
In Summary
- The term structure of volatilities identifies the market perceived uncertainties of short term and long term events
- Rate Distributions identify the two side tail distributions of rates
- Calibration should use both OTM and ATM options to correctly price the cap/floor structures embedded in loans.
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