 This topic has 5 replies, 2 voices, and was last updated Apr17 by Sophie Macon.

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Question:
An analyst wants to explore how the OAS for callables and putables vary when he alters his assumed volatility in his models. You can assume he uses riskfree rate as his benchmark and that the callables and putables he is analysing have higher credit risk. Which of the following best explains this relationship?A. Lower the assumed volatility the lower will be the OAS for a putable and callbles.
B. Higher volatility assumption will mean the market price will be lower for a callable bond meaning the OAS will be higher.
C. OAS moves in the same direction as the model price. Therefore if his model price for a callable falls, then the OAS falls.The answer is C.
Explanation:
Given the higher credit risk, the market price will be lower than the model price using benchmark rates. The adjustment we need to make to the tree is the OAS. The bigger the difference between the model price and the market price, the bigger the OAS.If we assume a higher volatility, the market price is unaffected but our model price will be; for example our callable price will be lower. Therefore the adjustment needed to move our model price (using risk free rates) to the market price will be less since our model price is now nearer to the market price. Hence OAS will fall when our model price falls.
1. I thought the price of a callable bond = straight bond – call option value
So if the volatility increases the price of a callable bond would reduced so shouldn’t B be the right answer?2. Why will the market price be lower than the model price when there’s a high credit risk? I would assume that the market price refers to a similar bond just without the call option, so when the market price (interest rate without adding OAS) reduces the model price (which is based on interest rate + OAS) would reduce as well. On top of that shouldn’t the model price of a callable bond be less than the market price since it has a call feature?
3. Why is the model price now closer to the market price?
4. I thought when OAS falls the model price will increase, since OAS is added to the interest rates in the binomial tree by adding less the price will discount less hence should increase shouldn’t it?

Hi @vincentt:
1. OAS = Z spread – option cost.
If volatility increases, the value of call option increases,so for a given Z spread, OAS should be lower.2. Because his model is pricing a callable bond based on risk free rates, so he’s assuming for example a callable bond issued by AAA government for example. But as mentioned, in reality he is assessing a callable bond with high credit risk, and this is not taken into account in his model pricing if it’s priced on risk free rates!
3. Similar to question 1, it’s saying that if volatility increases, price of call option increases, OAS reduces (for the model price that uses risk free rate). So it brings it closer to real market price, because callable bond = straight bond – call option value. So OAS and callable bond price move in the same direction.
4. This may make more sense now given 3? Note that if it’s puttable bond then the case is different. The relationship of OAS and bond (optionembedded) price depends on whether the option is bought or sold.


Nope. Model price is basically pricing a callable bond, but using risk free rate (which is incorrect as the credit risk is higher than that). Remember that OAS reflects compensation for liquidity risk, credit risk and model risk.
Market price is the actual market price of that callable bond using the ‘real/true’ rates.

thanks @sophie got that now. One last question regarding this statement
If we assume a higher volatility, the market price is unaffected but our model price will be; for example our callable price will be lower.
Wouldn’t the market price of a callable bond falls as well when the volatility increases?
Callable bond = straight bond – call option 


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