<t>Hi,I am working on an autoregression model (with the MATLAB econometrics toolbox by LeSage) and I am wondering the following... Suppose I have a data series, for which I do not know what kind of process it represents, and find statistically significant autocorrelation. I think an average economet...

<t>I realize the term discrepancies is vague; let me try to clarify:Suppose as oversimplification that we have a linear skew for the equities imp. vol. curve. Since sticky delta can be visualized in strike-space as a (roughly) vertical shift, it is possible to include an additional up/down shift suc...

<t>Hi,just some thoughts...- if the 'level' PC is uniform over maturity, you can simply offset a long position in any maturity, by a short position in any other maturity;- if the 'steepness' PC is linear over maturity, you can use some linear weighing function to be long X in maturity 1 and short Y ...

<t>Alternatively to behavior and tradition / convention, you might consider the following argument:The FX implied vol is more of a smile;The equity(/index) implied vol is much more of a smirk;Though the definitions are often mixed-up, consider the definition for 'smile' as the curvature of the imp. ...

<t>Yes, i think you have the correct idea.Derman introduced three approximate rules for what happens with the implied volatility curve when the underlying changes. The sticky strike and sticky moneyness/delta rule are the most well-known:- Sticky strike means that the implied volatility for every ST...

<t>Hi fnisky,I wanted to reply to your question, because I have had a somewhat similar experience. Since I am now finishing my MSc applied math, I have also had a number of courses that simply assume GBM and do not discuss the validity of this assumption. Feeling not satisfied, I also read Lo and Ma...

Thanks both for your advice! (Especially moltabile for the extension to Cauchy)I have found another derivation of what I was trying to prove, so no need for any undefined ratio any more.Regards

<t>This issue popped up when I was trying to prove something from the Heston model. The derivation, I have to admit, is mathematically not fullproof (ok, this is perhaps an understatement ).I realize that it is a somewhat weird ratio to define, dW1 / dW2...However, I was hoping there was some mathem...

If possible, I would like to proof that:E [ dW1 / dW2 ] = 0,given that W1 and W2 are two uncorrelated Wiener processes. Is this possible in any way?

<t>Hi,perhaps you can explain a little further, because now I seem to be confused...I agree with you that a markov chain with non-constant expectation is not a martingale. However, I am not sure if I agree with your other argument:for a path dependent option the (discounted) current price reflects t...

<t>My apologies to all mathematicians for the rough explanation below;Intuitively, a Markov process (in discrete case often referred to as a chain) represents a process that possesses the Markov property. The Markov property can be thought of as a property such that for every future step in the proc...

<t>Hi Mixumus,I just finished some research on the calibration of the Heston model. I tried several optimizers, including ASA. Some advice:- Check your error function and your option price calculation algorithm (I suggest using the version described in [The Litlle Heston Trap] as the version that do...

<r>Jeuj! Found a correct derivation of the expression as defined in the minimum-variance delta..minimum-variance delta = total delta = dP(t)/dS(t) = dP(t)/dS(t) + dP(t)/dv(t) * dv(t)/dS(t)A paper of Carel Alexander (see section three of <URL url="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=76...

<t>Hi Alan,Thanks for your feedback. I agree with you on the existence of your expressions. However, they are not specifically useful for my needs.. What I would like to have is a difference function for the underlying S(t) and the variance v(t), such as delta_v(t)/delta_S(t)=... (or delta_S(t)/delt...

<t>Hi,Need some help with stochastic calculus...I'm currently investigating stochastic volatility models and am interested in the dynamics of the implied volatility curve that go with the model. In particular: I am looking at the Heston model and want to know the derivative of the instantaneous vari...