In announcing its 80/20 negative equity insurance scheme, Nama management could have, but did not, provide estimates of the implicit cost of the insurance component of the package product. The cost is hidden in the package sales prices, which Nama management describe as “fair value prices” for the property.  With a bit of work, it is possible to reverse-engineer the insurance-component cost from the scanty information provided by Nama. 

This breakdown of the package price into its two components is important for getting the true sales price of the property-only component of the package, and for inferring the profit/loss (net of the cost of providing the insurance) that Nama incurs on each package sale. With reasonable assumptions I get that the insurance component is 7.5% of the package value and the property itself is 92.5%.

The required inputs (in order to use the Black-Scholes options pricing model) are the time to maturity (5 years), risk free rate of interest, implicit rental yield (equivalent cash value of residing in the property), and property price volatility. For convenience the package price is fixed at 100 and therefore the insurance floor price at 80, so that the results are in percentage of total value.

I used 4% per annum as the appropriate risk-free rate of interest. To calibrate the implicit rental yield I used a quote from Ronan Lyon’s blog on Irish property,

“Figures on rents are even harder to get than figures in household income and I’ve only been able to get numbers back to 1996. Nonetheless, over the period 1996-2002, the average yield was about three quarters of a percentage point above the average mortgage interest rate, which was 6%. By coincidence, 6% is the ballpark long-run rate of interest that I think will prevail in Ireland over the coming generation. Thus, we can use that 6.75% yield – and figures on rents up to this year – to calculate an alternative equilibrium house price from 1996 on.”

Hence I use an implicit rental yield of 4.75% which is three-quarters of a percentage point above the calibrated risk-free rate of 4% that I use.

The sample quarterly volatility of log-changes to the Permanent TSB house price index is 0.045153 which implies annualized volatility of .063855.  Index volatilities are lower than the volatilities of individual components of the index (single properties) and the Nama insurance option is written against the single-property-specific price.  Hence this volatility estimate is biased downward. On the other hand, the sample period includes a property bubble which might bias the volatility estimate upward.  Treating these two biases as roughly offsetting, I use .063855 as the annualized volatility of log property price changes. 

The excel spreadsheet performing these calculations can be downloaded from the following url:
http://dl.dropbox.com/u/36105182/namaoption.xlsx