Hi everyone,I have a Convertible model and have made the following change, i believe sometimes known as a Catz:When the stock price is above a certain value and between certain dates there is an addition to the conversion Ratio of X share per bond.This change was (i think) fairly easy to make to the model however i am still trying to understand some of the results:My delta now decreases (negative gamma) after the strike price for the additional conversion. From a model perspective i can make sense of this (i will discribe as a binomial tree for simplicity, although my model does the same for binomial/trinomial/Finite difference) If we imagine the whole tree is converted then when we increase the stock price we would normally see a delta of 100%, however with this model there is an increased chance the additional conversion ratio will be used, hence we see a delta of more than a 100%. This theory predicts the delta would then decrease down to 100% as the stock price increases, which happens in my model.However this means sometimes i have a negative gamma on a CB.This means you would be expecting to short fewer shares as a hedge as stock price increases, which seems wrong....In advance, thanks for the help,David

It usually helps to take a simplified case. I have a security that converts to either:(a) $100(b) 2 shares of stock if the stock price is under $100 (if it's under $50, I won't convert)(c) 3 shares of stock if the stock price is over $100If the stock price is very low, well under $50, the delta will be smallIf the stock price is around $75 the dollar delta will be near $2If the stock price is very high, well above $100, the dollar delta will be near $3This is all smooth. But what happens if the stock is at $100 very near expiry? If the stock price falls $0.50, the security is worth $199. If the stock price goes up $0.50, the security is worth $301.50. So the security goes up $102.50 for a $1 change in stock price. If you are in the unfortunate position of trying to hedge this, you will have to short a lot of stock near $100 near expiry. Any move away from $100 will make you reduce your hedge dramatically.

are you talking in cb delta terms?would be better to look at the number of shares as this will show you aren't really short gamma