athos
• Member for 9 years, 10 months
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• Singapore

My understanding is because the Ito's integration definition keeps the martingale property. With Brownian motion $W(t, \omega)$ defined, to define stochastic integration in a Riemann–Stieltjes style:...

Is this the proof you are looking for? -- from Shreve, S. E.'s book "Stochastic calculus for finance II, continuous-time Models", chapter 5.

thanks for all answers above. William's answer is more direct. actually i was quite new to the calibration area one year ago, so my question is quite simple but that simplicity might mislead others ...

So far I only know that SunGard has a product named "Ambit Focus", where its module "Liquidity Risk" supports the LCR and NSFR reports according to Basel III liquidity rules.

let me try answer my own questions, partially, from below that are exerpted from FRM exam notes. So actually the K above, is UL, though it derives only from PD and maturity, but the G, N and 0.999, ...

In my opinion, risk free rate is not necessarily positive and not so important to pricing theory. It happened to be positive in most cases, but imagine a planet using Uranium-235 instead of gold as ...

American options pricing (swaption is just a kind of option) is a bit tricky due to the early exercise. Here is a page listing possible approaches, including some numeric methods, and some close form ...

OK, I think now I got the point, after comparing to Shreve's "Stochastic calculus for finance I, The binomial asset pricing model", the simpler case. The pricing theory in continuous time is: Defi ...

Just to answer my own question. Discrete variates' quantile, could be modelled and tested. I followed this paper: "Discrete Quantile Estimation", Halina Frydman and Gary Simon, New York University, ...

Pls check Shreve‘s Theorem 9.2.2 Change of risk-neutral measure . Is this what you are looking for?

I think I got the quantitative explanation in Steven E. Shreve's "Stochastic calculus for finance II":

to answer my own question, there's no popular model for the question, that $dS/S=\mu(t)dt+\sigma(t)dW$, and $\sigma(t)$ is correlated with $\mu(t)$. the general framework should be stochastic ...