# LO 11.6: Define option-adjusted spread (OAS) and apply it to security pricing.

LO 11.6: Define option-adjusted spread (OAS) and apply it to security pricing.
The option-adjusted spread (OAS) is the spread that makes the model value (calculated by the present value of projected cash flows) equal to the current market price. In the previous CM T example, the model price was equal to $1,466.63. Now assume that the market price of the CM T 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 CM T 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: ($2,500 x 0.6) + ($0 x0.4) + 0.0745 1 +$1,250
$2,696.13 ($ 0 x 0 .6 )+ (-$2 ,5 0 0 x 0 .4 ) t | 0.0695 2$1,250
-$2 ,2 1 6 .4 2 2018 Kaplan, Inc. Page 141 Topic 11 Cross Reference to GARP Assigned Reading – Tuckman, Chapter 7 Notice that the only rates adjusted by the OAS spread are the rates used for discounting values. The OAS does not impact the rates used for estimating cash flows. The final step in this CM T swap valuation is to adjust the interest rate used to discount the price back to today. In this example, the discounted rate of 7% is adjusted by 20 basis points to 7.2%. The updated initial CM T swap value is: ($2,696.13 x 0.76) + (-$2,216.42 x 0.24) + 0.072 1$1,464.40
Now we can see that adding the OAS to the discounted risk-neutral rates in the binomial tree generates a model price ($1,464.40) that is equal to the market price ($1,464.40). In this example, the market price was initially less than the model price. This means that the security was trading cheap. If the market price were instead higher than the model price we would say that the security was trading rich.
T i m e S t e p s