# OAS & Interest Rate Volatility

CFAI Vol 4 Page 172

Volatility Risk

…“OAS tends to widen when expected volatility increases and narrow when expected volatility declines”

As I understand it, OAS is that portion of the total spread that is left over after discounting option risk i.e. OAS compensates investors for risks other than option risk. Hence if expected volatility increases then option risk increases and more of the total spread is captured by the option risk. Therefore OAS (portion of the total spread available to compensate for other risk factors) should narrow. This would contradict the text.

Thanks!

When volatility increases - Price of the Prepayment Option increases. So Price of the MBS security DROPS. When Price drops - this means the Yield increases (Price and Yield move in opposite directions). and this would mean the OAS increases.

what you wrote makes no sense. you’re mixing OAS and option value. I agree with the O/P that this is not correct in the text. The HIGHER the volatility the LOWER the OAS all else equal. For example, when volatility increases the value of an option increases to the option holder (i.e. borrower) while concurrently the cost of providing the option increases to the lender (i.e. bond holder) Z-Spread = OAS + option cost holding Z-spread constant (because we have no other reason to believe is has changed) if the option cost increases 50bps then by default the OAS is assumed to decline by 50bps. Therefore as a lender I’m going to charge a greater yield for the option to call.

Option cost in your formula is a yield not a price paid for the option. True - the price of an option increases with volatility This means that yields fall and since your option cost is a yield it would be lower when volatility is higher. Holding the Z-Spread constant as you said means that the OAS would be wider when expected volatility is higher

understood, of course it’s yield… as is OAS - hence the equation equaling a “spread” value the z-spread is the yield charged to lend to a borrower above and beyond the risk-free rate… if the probability of the call option being exercised increases so will the yield a lender charges for that option. These are embedded options so don’t confuse this with a call or put option that trades as a derivative on the CBOE. There is no price increase for an embedded call option (because there is no option to price)- only a change spread.

I’m going to look in the book - I don’t have it with me right now

thanks for your responses. cpk - agree that price of the MBS drops and total yield increases. but still not clear why the OAS should increase. Char-lee - as FinNinja says, option cost can be translated into a yield equivalent i.e. its that portion of the total spread that is captured by the issuer not the bondholder. the bondholder gets only the OAS. total yield = treasury yield + z-spread = treasury yield + (OAS + option cost) given that bond price drops and total yield rises, can’t the increase in yield be attributed to higher option cost ? why should OAS increase? according to the CFAI text, OAS compensates for credit risk and liquidity risk. not sure how these risks are impacted by interest rate volatility.

oz001, did you not read a word i wrote? “given that bond price drops and total yield rises, can’t the increase in yield be attributed to higher option cost ?” yes, in this case OAS doesn’t change “why should OAS increase?” I never said this. I suggested it is implied that OAS DECREASES assuming the z-spread stays the same (remember credit spreads, liquidity spreads, interest rates are staying the same only volatility is changing in turn widening option cost) “OAS compensates for credit risk and liquidity risk. not sure how these risks are impacted by interest rate volatility.” in theory they are not related… in practice though some markets will demonstrate changes in liquidity spread in very volatile markets.

So I’ve read a lot on this topic and I’m now undecided, but here is what I know: Level III book says: OAS tends to widen when expected volatility increases. Level II books says (Repeatedly): Reducing the volatility assumptions increases the OAS so let’s follow the effects of volatility on an MBS security assuming volatility increases: 1. option prices increase (whether seprately traded from MBS or not) this means Option cost (in terms of yield) decreases (since yield moves inversely from prices.) 2. MBS price declines which means the MBS yield increases 3. if MBS yield increases then the z-spread increases since there would be no change in the spot rate curve (right?) 4. if z-spread and option cost (yield) are moving in opposite directions, the logical assumtion is that OAS is getting larger since z-spread = OAS + Option cost. I’m unsure why Level III contradicts Level II but I am unable to find a reason why OAS moves opposite to volatility.

1. When volatility increases, option cost increases and OAS decreases and vice-versa 2) Reading 26, page 172 “… OAS tends to widen when expected volatility increases and narrow when expected volatility decreases.” I believe the distinction here is that statement one refers to CURRENT volatility and statement 2 refers to EXPECTED volatility. Reverse engineered statement 2 matches statement 1 conclusions: When expected volatility increases ==> future volatility is expected to increase ==> current volatility is low ==> OAS is or tends to be wide When expected volatility decreases ==> future volatility is expected to decrease ==> current volatility is high ==> OAS is or tends to be narrow

My views : 1. Total spread is constant = Zero-volatility spread is constant (not explictly indicated in the text, I think) 2. Zero-volatility spread = OAS + Option cost 3. Volatility increases => Option value increases => Option cost (spread) decrease => OAS increase (widen)

I have just tested on OAS1 function on Bloomberg with a callable bond: Braskem 1/8 07/41 Z-spread = 488.8 bps for a Vol of 27.5 bps --> OAS = 483.8 bps for a Vol of 100 bps --> OAS = 480.9 bps It seems to me the text is actually wrong: when volatility rises OAS goes down to callable / prepayable securities.

I’ve seen so many different definitions of OAS that I always ask what someone means when they say OAS. Here I think they mean “It is the difference between the price of a security with embedded options and the price of the same security without options” http://www.wisegeek.com/what-is-an-option-adjusted-spread.htm Using that definition it’s pretty clear why OAS widens when expected volatility goes up.