More More More Convertible Bonds

[John Maiden]

Still playing around with the convertible bond class...

This is a problem I've noticed for a while and wasn't sure where it was coming
from, but I think I've isolated it. When I would model certain callable
convertible bonds at high spreads, I would get a higher value for the callable
convert than for an identical non-callable convertible bond. I also tried taking
out the put, and found that its value was higher than an equivalent convertible
bond with no calls or puts.

I had the program print out data at each step, and have isolated the problem to
the TsiveriotisFernandesLattice class, where the
TsiveriotisFernandesLattice::stepback function is producing a SpreadAdjustedRate
that is higher for the non-callable convert versus the callable convert, and
thus discounting the callable convert value more.

For those not familiar with the TsiveriotisFernandesLattice class, the way that
the program calculates the SpreadAdjustedRate is that it blends the risk-free
rate and the credit spread. If the stock price is low, then the convert should
grow like a corporate bond, and should be discounted at the risk-free rate +
credit spread. If the stock price is high and conversion is very likely, then
the convert should grow like the stock and be discounted at the risk-free rate.
At each step in the program, the program considers whether conversion is likely,
and assigns a conversion probability. This probability is then blended in
TsiveriotisFernandesLattice::stepback, and used to weigh the SpreadAdjustedRate.

The problem with this approach is that during the callable period, a convert
with calls will have lower values at every time step than a similar convert
without calls (obviously). Because of how the program assigns conversion
probability, the callable convert will have more values with high conversion
probabilities. Since these values are blended, when comparing callable versus
non-callable converts at a specific stock price and time, the callable convert
will have a higher conversion probability and thus a lower SpreadAdjustedRate
(which means it will be discounted less).  

So finally, this is my problem. At present my idea is to simply turn off the
blending, but the SpreadAdjustedRate won't be smooth. Any ideas on how to create
 a SpreadAdjustedRate that will make sure that a non-callable convert is more
expensive than its callable equivalent?


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