Assume I have a firm-value credit model in which the default time [$]\tau^*[$] is subject to the evolution of the assets [$]X[$]. Also assume that the default time is defined as [$]{\tau ^*} = \inf \left\{ {t \in {\mathbb{R}^ + }:X(t) \le h} \right\}[$], where [$]h[$] is the default barrier. This is...

Cuchulainn : The figures that I posted show [$]\theta[$] after I imposed some restrictions on it. If I didn't, it would explode. Without the restrictions the sequence of [$]\theta[$] in time would be e.g. like [$]\theta ({t_0}) = 0.1,\theta ({t_1}) = 0.2,\theta ({t_2}) =  - 0.3,\theta ({t_3}) = 0.8...

Bearish -  You are right, the model is inappropriate for continuous time modeling. I think some explosion discussion when using the (continuous?) BDT are provided by Clewlow and Strickland [1998] but I no longer have the book so I can not check it. In my case I just needed to verify some special tre...

Finally got it. It's tricky. Here is the BDT-fitted vs observed discount curve: https://s14.postimg.org/y4uoj8k29/BDT_vs_observed_png.png The function [$]\theta[$] (notice that I had to limit the range of [$]\theta(t)[$] to prevent 'explosions'): https://s14.postimg.org/3oorl3yj5/BDT_theta_t_png.png...

I did some analysis now and it looks that the problem is surprisingly complicated. I did the analysis on one-factor Hull-White model where [$]\theta(t)[$] has an explicit form and thus can be compared with the numerically obtained [$]\theta(t)[$] through the PDE. The main issue here is that [$]\thet...

I'm having a difficulty with calibrating the drift of the continuous version of the BDT to the yield-curve. I have first calibrated a discrete constant-volatility BDT (tree) to a set of interest-rate derivatives, this gave me a reasonable value of the log volatility [$]\sigma(t)=\sigma = 0.59[$].  I...

Alan,  thanks, this is complete and clear to me. I'm familiar with the infinitesimal generators so it was easy to understand for me.  So in this case (based on the dynamics of [$]X[$] that you use), [$]N[$] is one-dimensional Poisson process. In turn, the convolution integral captures a jump in [$]f...

Alan: 1) You are right with the [$]J[$]s in the integral. I corrected several typos in the formula shortly after I posted my question but I forgot to correct this one. In the Merton model it was correct so I hope you don't think it was a mistake but rater a typo. I now corrected this. 2) Yes, I'm aw...

Hi,  I'm looking for an analogy of Feynman-Kac (but ideally a fairly general) that would be able to incorporate the jump processes. I.e. Feynman-Kac analogy for  [$]dx(t) = \mu (t,x(t))dt + \sigma (t,x(t))dW(t) + dJ(t,x(t))[$], where [$]J[$] is some sort of a pure jump process. Also, I'm interested ...

Great, thanks a lot.

<t>I have two questions about iTraxx single tranche deal mechanics. To make my questions more accurate, let's work with some actual data.Today's on-the-run iTraxx series is S25 and let's focus on the 5Y index. This 5Y index has the effective date Mar 21, 2016 and Maturity Jun 21, 2021. Q1: If an inv...

<t>What do you mean by the 'mark-to-market leg'?The standard mechanics of a plain CCS is that it works like an IRS just with every leg being denominated in a different currency and also with the possibility that both legs earn floating or fixed interest. Thus, you just price a CCS as a short and lon...

<t>I have done a small exercise - I downloaded CDS quotes for all the names in the basket (both iTraxx and CDX) and computed the fair upfront on the equity tranche by allowing every name to retain its default probability implied by its CDS, with the implied correlations for the equity tranche. This ...

<t>I agree with what you say and now a question appears in my mind: if an implied correlation is quoted for a tranche, does this correlation apply to (i) a model in which all the credits are assumed to be equal, or (ii) to a model in which the credits are allowed to be different in terms of the CDS-...

<t>What do you mean by the "spread dispersion"? Do you mean the relative variability (or non-homogeneity) in CDS spreads of the credits in the basket? I don't think this should be a problem. If I'm not wrong, the index quote is not a simple average of the CDS spread of the credits in the basket but ...