HelloDid anyone has done something on including the cds spreads levels into his vol curve to price vol and variance swaps? I've done that but the problem is that for low strike level puts, as a variance swap overwieght the low strikes I end up having high levels for my variance swaps...do I need to cut the strikes below a certain level? Is there an arbitrage ? In the market, currently, variance swaps are not priced taking into account the cds spreads.Thanks in advance

Hi Multiwin,Hope I understand your question: Simplest model (I mean not talking about dividends under default risk etc)1. Take CDS curve -> get deterministic survivalprobablity SV to maturity of swap2. Get "riskfree" call/put prices Call_Risk_Less ( k ) = Call_Market( k / SV ) [if you are market badly you'll get arbitrage here:-)]3. Price the swap on riskless part (variance from that part == variance from stock up to default).4. Decide what you want to pay off in event of default \tau (clearly, if you pay log(S_\tau/S_0)^2 that is a bit expensive...) I guess the latter depends on the contract...Done.Did that help?PS I actually don't see right away why the swap would get more expensive (assuming payoff zero on default).I should have a look at that... PS2 for volswaps, that obviously depends on your model. But same approach would work to transformmarket data input.

I've done a lot of work on the links between CDS and variance swaps.First, let's be clear that there is no perfect hedge for a discretely monitored variance swap on returns. In contrast, since Neuberger 1990 and Dupire 1992, we've knownthat there is a perfect theoretical hedge for a continuously monitored variance swap on returns (log price relatives) provided that the underlying price process is both positive and continuous(other assumptions are also needed eg continuum of strikes but the vol process is arbitrary).Let's use reduced form models to handle default.The jump that accompanies default leads to hedge error.If the jump in the underlying stock price or index is to zero, thenboth the payoff on the variance swap and the hedge error is infinite.If the jump accompanying default is of a fixed finite percentage move down and is the only possible jump, then the hedge eror is constant in dollar terms. This means that a claim that pays one dollar if default occurs before T and zero otherwisecan be synthesized by a static position in a variance swap and its alleged hedgecombining static options with dynamic trading in the underlying.The good news is that the digital hedge works perfectly for arbitrary unknown stochastic vol and arbitrary unknown risk-neutral default arrival rate.The bad news is that the desired target payoff of one dollar contingent on default is missed bya lot if the stock price actually drops by a different percentage than planned.We therefore get a robust way to create extreme sensitivity to the uncertanty in the jump sizegiven default.

Hi PutorCall ...Say do you know the real contractual conditions of a std var swap? I'm more used to indicies where it doesn't matter so much (the default, I mean, not the jumps).Also, do you have an idea how big the hedging error is between daily and continousy priced swaps?I heard there's some paper on it, but did not find something..

I think that for single stocks there is usually a cap on the variance to ensure that the payout doesnt blow up in event of default, (could be a large cap)

Well i saw 2.5 VolSet a few times?

yep 2.5 times vol seems typical from what I see too.

Regarding the distinction between continuously monitored realized varaince and discretely monitored realized variance, here is what I know.First, there is no way to robustly and perfectly replicate the payoff of a discretely monitored variance swap. In contrast, there is a well known so-called robust replicaiting strategy for continuously monitored variance swaps.It is not actually robust to jumps in price.Alo bankruptcy (zero stock price) is an issue if logs are used inthepayoff.In my papers on continuously monitored variance swaps,I always assume that the price process is postive and continuous price process.Carr and Lewis Risk 2004 address the replication error when attempting to replicate thepayoff of a discretely monitiored variance swap under arbitrary price dynamics.To be precise, we assume that the increment to realized variance is the square of the percentage move not the log price relative.We show the error has a leading term which is third order in the percentage move.It's easy to show that this result is also true when squaring log price relatives but the constant changes (even in sign).The replication error can be large or small depending on the permitted jumps if monitoring were continuous, or the length of the rebalancing interval under disrete monitoring (which are observationally equivalent).Jim Gatheral's recent talk at ICBI shows that for S&P500, the expected error would be about a third of a percentagepoint for S&P500, but this depends on term. I think a paper by Jacod and Protter addresses the error that discrete monitoring of the sample path induces when trying to estimate the integrated variance i.q. quadratic variation.I don't have a terms sheet for a variance swap on a single name.I'm told that the 2.5 times cap is universal and has in fact been breached occasionally.I'm told that the cap is also apparently not priced into single name var swap quotes.Perhaps an EDS quote shoud be used to price it.

Thanks PutorPut For the other readers, the paper from Jacod/Protter is here for free download.The other one is on Carr's website.Best