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B2- There are a ton of other things that go into asset swap pricing that you're not accounting for at all, either. The most salient issue is the fact that capital is a scarce resource and asw's allow for convert arbs to get the bonds off their books; since arb funds carry at different rates, each fund will have a different value for the swap.Couldn't you use exactly the same reasoning when pricing a straight bond or in fact any asset?nb. there is a bug in the edit message function that switches the HTML characters for italics, bold etc. to regular brackets.

asset swaps are special in that they swap the physical. no other swaps do that.and yes, you're right that the carry issue pops up in all other sorts of physical assets. but people put long/short into those other assets when they price them.asset swaps aren't simple transactions because at contract initiation the physical transfer removes a lot of your carry. stoeve: you also have to allow the credit spread to be time-dependent. the monis model you're talking about is a mess because the credit spreads are:1. time homogenuous2. exogenously specified by the user. what's the point? it's not modeling anything. if i knew enuf to give a decent set of credit spreads to the "model", i wouldn't need to use the thing. having to specify the spreads yourself defeats the entire purpose of running a FV model.honestly if you ever have to exogenously specify more than about 3 parameters in a model you should probably throw it out, go back to the three parameter case, and look at payoff distributions. this is why of the extant FV models that have been published I like Leland 96 the best.

hi, i thought the blended discount rate methodogy is introduced by the Goldman Sachs paper, can anyone share the pdf file that i cannot find it, thanks!

In Monis XL v4.10, 5 different options are allowed (if one factor model is selected, i.e. only stock price is stochastic). As stated in the manual, Bond and put option cash flows are always discounted at the risky rate. But one could choose the setting for the share growth rate and the payoff discounted rate:i) Grow risk free, discount composite - payoff arising from conversion are discounted at the risk free rate, and contributions from other sources e.g. redemptions, puts, calls for cash, are discounted at the risky rate (this is the default setting)ii) Grow risk free, discount risk free - payoff is discounted at the risk free rateiii) grow risk free, discount riskyiii) grow risky, discount risk freeiv) grow risky, discount riskyThis is quite confusing. I think the simple method (e.g. Hull) corresponds to (ii) - grow risk free, discount risk free. But is there any reason why the others should be used?

A short intro to this can be found in Mark Davis article "Taking convertibles for a spin", Derivatives eek V9, May 2000.I attached the file. If you need something more basic, let me know. Apologies for the format.

Thanks for the reference, but there is no attachment ; I don't achieve to find it.

yes, I apologise for this...somehow you can't attach Docs in this thread...if you private message me I'll E-mail it to you.Two other points of reference are Number Sixes paper "The Valuation of Convertible Bonds With Credit Risk" http://www.scicom.uwaterloo.ca/~paforsyt/convert.pdfas well as Mark Davis paper "Convertible bonds with market risk and credit risk http://www.defaultrisk.com/pdf__files/C ... sk.pdfHere is also a somewhat ad hoc argument for the full discounting. If you look at the usual binomial tree pricing without credit (i.e. the stock S goes to S(up) resp. S(dn) after 1 time step), thenCV - D*S (D = (CV(S(up)) - CV(S(dn)))/(S(up) - S(dn)), CV(S(up)) resp. CV(S(dn)) are the value of the convertible in the up- resp. dn scenario) is risk free. Thus CV - D*S = exp(-rt)*(CV(S(up)) - D*S(up)) = exp(-rt)*(CV(S(dn)) - D*S(dn)). If the issuer can default this is no longer risk free. The amount we stand to loose is E[(CV(S(up) - D*S(up))*{1, if issuer has defaulted during time t, 0 otherwise}]. If we assume that the stock price-process and the default process are uncorrelated,E[(CV(S(up) - D*S(up))*{1, if issuer has defaulted during time t, 0 otherwise}] = E[CV(S(up)) - D*S(up)] * p where p is the default probabilty of the bond. As usual p = (1- exp(-ht)), where h is the credit spread of the bond. Hence the above is equal to exp(-rt)*(CV(S(up)) - S(up))*(1-exp(-ht)).Further assuming for the time being that there is no recovery (it is not hard to include that as well), means that CV - D*S + exp(-rt)*(CV(S(up)) - D*S(up))*(1-exp(-ht)) is now risk free, hence has to be equal to exp(-rt)*(CV(S(up)) - S(up)). So if you rearrange terms you come up withCV = D*S - exp(-rt)*(CV(S(up)) - D*S(up))*(1-exp(-ht)) + exp(-rt)*(CV(S(up)) - S(up)) = P*CV(S(up)) + (1-P)*CV(S(dn)) where P = (S*exp((r+h)*t - S(up))/(S(up) - S(dn)).The interpretation of the higher growth rate in the stock is what the traders have been doing all along, viz. that you can hedge part of your credit by overhedging your delta.

Thank you all for such an interesting thread.ITO 33 is directly concerned with all the topics and issues that you raise, so I can only apologize for having not shared my thoughts with you earlier.I had previously discussed a lot of CB issues on the Wilmott forum, so by all means, try to search for the keyword "Convertible", or "credit spread", or "hazard rate".The good news is that in the next issue of the Wilmott magazine, an article I co-authored will exactly tackle the issues of full or blended discounting in the CB pricing models.All the questions, whether we should apply the credit spread to the bond component (or more generally to any cash-flows, fixed or contingent, expected from the issuer: early call, early put, etc.), or apply it to the difference between the CB price and the conversion option, or apply it to the full CB, and the question whether the share should grow at risky rate, or risk free rate, etc., all these questions are unified, and explained in the light of a general model for credit risky derivatives under default risk. Every particular model (answering yes to any of the previous questions) falls under this general umbrella. Differences are explained in terms of what different RECOVERY assumptions you make.Next, the issue of correlation of credit spread and stock.I agree, unless you want to rely on a structural model and commit to its theoretical assumptions, you have no choice but to specify exogeneously the way credit spread will depend (deterministically or stochastically) on the equity.As a matter of fact, the real function you want to model is not credit spread as a function of equity (for the notion of credit spread is instrument relative: are we talking about the credit spread of a discount bond, of a credit default swap, of an asset swap, etc. ?), but the hazard rate, or the instantaneous probability of default of the issuer, as a function of equity. The hazard rate is relative only to the issuer, therefore you have in theory to specify only one such function for each issuer. Also, it is the hazard rate function that enters explicitly in the "general pricing model under default risk" that I mention in the previous paragraph. Credit spreads are actually outputs of this model, because you will use the same model to price a CDS, a CB, a Asset swap, or a corporate bond.And now you can see that there are two things that you need to specify in my "general model above", (and this is why the difficulty of CB pricing is twofold):- your recovery assumption (this corresponds to one term in the PDE)- you hazard rate function (this corresponds to a term multiplying the previous one).So the problem is how we specify this hazard rate function.This question has been going on for some time on this forum, and there is no ready answer.True the ITO 33 tool is quite general and open to any recovery assumption and any specification of hazard rate function, but then people like B2 will complain that "if you ever have to exogenously specify more than about 3 parameters in a model then you should probably throw it out".I say: Go ahead and pick your favourite structural model if you wish...Actually, it seems that somebody has already done the job for us. CreditGrades for instance publish whole tables of CDS credit spreads (equivalently cumulative probability of default) for different maturity dates, and different equity levels. Go ahead and use this as input, and if you do not wish to use it to trade, use it to manage your risk, or to see how the greeks of the CB would look like, etc.The only problem is that CB is sensitive to credit risk anywhere, anytime, because its payoff depends explicitly on the share level, and you can convert, or be called, anytime.It is OK to use Credit Grades black box to price a CDS or a corporate bond, for a certain equity level, off the credit spread curve that they produce for that equity level. But how do you price the CB?Ho do you get from their table of credit spreads of finite maturity, to "instantaneous credit spreads" (which is what you really need for the CB)?In other words, given their table C(S,T), is there a way of differentiating it with respect to S and T ?The answer is that this "differential" that you need is not a mathematical differential. It is no other than the hazard rate function!!Indeed, the CreditGrades table is really a table of prices: prices of the CDS, or prices of risky zero coupons (roughly equivalent to cumulative probabilies of default).So the question "How we differentiate" is really a full-blown inverse problem in disguise: How do we find the hazard rate function, to go as parameter in our "general pricing model under default risk" such that the CreditGrades price table is matched?We have actually solved this problem. But you can see that all this is very quickly becoming very complex. Remember B2's complaint.Now the last question of risk neutrality.True, everything I said assumes that the hazard rate function is the risk-neutral instantaneous probability of default.But then it is OK to use it to price CBs, if you are inferring it from market prices in the first place (or what you think market prices should be). In other words, my view of the ideal CB pricing model is:- Calibrate the parameters, or the parametric functions, of your pricing equation (volatility, hazard rate) to any market data you have (or will ideally have): CDS credit spreads, vanilla options prices, and (why not?) CDS swaptions. Then have the CB pricing model tell you how to dynamically hedge with the instruments you used in the calibration...

***meant to send a PM, sorry***