The option-adjusted spread (OAS) is the spread that makes sure that the model value (calculated by the present value of projected cash flows) is equal to the current market price.

In the previous CMT example, the model price was equal to \$1,466.63. Now assume that the market price of the CMT swap was instead \$1,464.40, which is \$2.23 less than the model price. In this case, the OAS to be added to each discounted risk-neutral rate in the CMT swap binomial tree turns out to be 20 basis points. In six months, the rates to be adjusted are 7.25% in the up node and 6.75% in the down node. Incorporating the OAS into the six-month rates generates the following new swap values:$ V1,u= \frac{(\$2500*0.6)+(\$0*0.4)}{1+ 0.0745/2} +1250=2696  V1,l=\frac{(\$0*0.6)+(-\$2,500*0.4)}{1+ 0.0695/2}-1250=2216  V0=\frac{(\$2,696.13*0.76)+(-\$2,216.42*0.24)}{1+ 0.072/2}=1464 \$

## Why OAS is Important?

OAS tells that if the market price was initially less than the model price, the security was trading cheap. If the market price were instead higher than the model price then the security was trading rich.

Owais Siddiqui
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