Pricing a callable bond

Question

I have read the Lehman Brother's paper on OAS which I mostly understand, they outline how to find the OAS for a callable bond of which the formula is effectively (ignoring refinancing costs):

Market Price Callable = Value of Stripped Bond - Value of Option

They proceed to simulate a number of interest rate paths using zero coupon interest rates from the treasury curve and then pricing the stripped bond and the option they arrive at a price which is too high, thus we need to add the OAS spread in order to discount the price to the market price of the callable. The spread value that achieves this is the OAS.

My question therefore is, how do you price the callable bond in the first place if I was the issuer before having the OAS, I think my confusion is that the calculated price in this case is too high and therefore adding the OAS discounts further to equal the market price but if we don't know the OAS surely calculating the price of the stripped bond minus the price of the option will not equal that of the market price.

Answer 1

A common approach is to build a credit curve from noncallable issues if available, and then run your lattice or monte carlo on that using volatilities from interest rate derivatives market possibly adjusted. I have heard however that that approach doesnt do a great job hitting market prices, and there are more complex models which involve more explicit representation of the credit process and its interaction with the call option. Seems like most traders just accept that there is a market implied OAS, and dont worry so much about how it relates to noncallable credit spreads.