Option Close-out Reserve

We present a model to calculate the monthly Close-Out Reserve of the structured interest rate derivatives. Products cover vanilla swaptions, Bermudan swaptions, callable swaps, variable notional swaptions, cap and floor and Treasury bond options.

The M×N Vega matrix has to be bilinear projected into a smaller-sized 4×4 Vega matrix, and then the netted positions of this smaller-sized matrix are applied to the quoted bid/offer spread.

We can price all kinds of options and get the corresponding Vegas based on the above volatility matrices.

Let us consider an option (vanilla or non-vanilla). Given a swaption term, an underlying term and a strike price, if we change the volatility from the above volatility cubic, we can get one Vega by using the definition of Vega.

Given a M× N Vega matrix obtained from the above methods and a same-sized M×N Volatility Spread matrix, the option Close-Out Reserve can be calculated. However, Broker only offers a smaller-sized quoted bid/offer Volatility Spread matrix, which usually has a minimal dimension of 4×4.

To obtain better accuracy, this matrix can be expanded along with the option terms and underlying terms, so currently a 6 x 7 matrix has been proposed. However, below we use a 4×4 dimension matrix as an example. For instance, a 4×4 Volatility Spread matrix is given with option terms of 1y, 5y, 10y and 20y, and underlying terms of 1y, 5y, 10y and 20y.

In order to calculate the Option Close-Out Reserve, the M×N Vega matrix has to be transformed into a smaller-sized 4×4 matrix, and then the netted positions of this smaller-sized matrix are applied to the quoted bid/offer spread. We have used bilinear projection to transform the Vega matrix. Let us review the algorithm of the bilinear projection. Given M× N Volatility Spread matrix, we will transfer it to be a 4× 4 Volatility Spread matrix and calculate the total Close-Out reserve.

Firstly, for each column, we project the value at the underlying term=1M, 3M, 6M and 1Y into the value at the underlying term=1Y, the value at the underlying term= 5Y into the value at the underlying term=5Y, the value at the underlying term=10Y into the value at the underlying term=10Y, the value at the underlying term= 20Y, 25Y and 30Y into the value at the underlying term=20 Y.

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