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The best paper is probably Relative Volume as a Doubly Stochastic Binomial Point Process - James Mcculloch. In this paper the volume is modelled via a Point Process, and theoretical laws are derived (with confident intervals, etc). And if you can wait few days (it will be available very soon), we put elements about this in Market Microstructure in Practice, ...

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I would like to add a few more points to @Phun's already very good answer: The question is interesting because generalized Brownian motion already covers a lot of cases: This example includes all possible models of an asset price process that is always positive, has no jumps, and is driven by a single Brownian motion for each asset. (Shreve, ...

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To recover the Black-Scholes pricing equation, you should first express the standard normal cdf in terms of its characteristic function analogous to the Heston solution: $$N(x) = \frac{1}{2} - \frac{1}{\pi} \int_0^{\infty} Re [\frac{e^{-i\phi x} f(\phi)}{i\phi}] d\phi$$ where $f(\phi)$ is the characteristic function of the standard normal distribution: $$... 4 I have honestly not come across a good book (or good enough review to make me buy the book) on Fund Transfer Pricing. While it is not my career focus, I had to familiarize myself a bit with the topic because of certain requirements involving funding trading operations and the performance of funding specific operations. Personally I would recommend the ... 3 One approach is to include the nominal rates, real rates and inflation in the model and then represent the inflation as a kind of exchange rate between nominal and real rates. Jarrow and Yildrim presented such an approach in their paper "Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model" (2002). The definitive ... 3 I have asked myself the very same question when I first read the book. As far as I can tell, the "scalability" condition is only imposed for technical reasons. It simplifies the subsequent proof of the Fundemental Theorem of Asset Pricing in constrained markets. There are several papers that have shown that the theorem is valid for conic constraints. ... 3 You could read it like this: The typical change in equity value is equal to the typical change in asset value, adjusted for the probability of the assets surviving. Note that the formula is not specific to Merton models, it's also true for regular options and their underlyings. It's just that volatility of option prices isn't typically a concern in ... 3 Well, the main intuition of the Merton model is that a company's equity can be treated as a call option on its assets, thus allowing for the application of Black-Scholes option pricing methods. Let's consider a company that has assets A_{t} financed by equity E_{t} and a zero-coupon debt B_{t} with face value K, and maturity T. At time of maturity T, ... 3 I deal recently with some analysis of the Volume time series, daily volume in € for European stocks. I found out that an ARIMA model works well. But, some EWMA could also provide good forecast if it's well parameterized. You can also face some seasonality effect due to macroeconomic events, some you may need to clean you data and treat these days in a ... 3 There is the white paper "New volatility conventions in negative interest environment - Current developments and necessary adjustments of IT systems in trading, risk management and accounting" by M. Beinker and H. Planck (2013), which discusses recent developments and also gives an introduction to the displaced diffusion model, which can handle negative ... 2 Try the following : perform the logarithmic transformation of the volume data. check if the transformed data fits the normal distribution nicely. if you are working with intraday volume, then adjust for the seasonality for time of the day effect, if using daily data, in some cases some special seasonalities like expiry day, etc might be applied but it may ... 2 Estimation of the initial states of R and particularly Q is indeed more of an art than science. The task at hand is to estimate the covariances. You have basically two main choices: Live with the fact that you will never be able to exactly pinpoint the covariance of noise in financial time series. The most often used approach is to pose the coveriance ... 2 My answer will be very non-quantitative but the resulting models are actually quite mathematical but I like to stick to a general overview because of the proprietary nature of those models. Here couple thoughts though: You can't just try to explain market moves by a few indicators or a single Fed speech (by the way, the market hugely misread those ... 2 The equation stated in the question is not at the core of Merton's credit model, (Not saying you claimed it is) but is a simple device in helping to solve the system of linear equations. The equation given simply establishes a relationship between the volatility of equity and the volatility of the assets and it follows from the application of Black Scholes ... 2 Well, typically in the process of coming up with a model you are supposed to understand the assumptions that you're making and the circumstances(preferably quantifiable) under which your assumptions will hold/break. No model is infallible and it is how well the assumptions are stated and understood that will determine if your model is acceptable. I can't ... 2 I dont know what you want to hear, but i have several points for you: The main driver of uncertainty is a Wiener process, which goes back to the discrete binomial model for stock prices. In reality the main stochastic source could be something completly different. \alpha and Vola \sigma are depending directly on your stockprice. Why should they? the ... 2 From my point of view, dynamic models like the one developped in Relative Volume as a Doubly Stochastic Binomial Point Process - James Mcculloch to provide a dynamic forecast of the volume does not improve significantly the forecasting comparing to a static volume curve forecast using historical data (last month intraday data, and an EWMA algorithm). I've ... 1 Assuming the underlying mortgages that have been pooled into a Mortgage-Backed Security (MBS) are freely prepayable, the notional of the interest swap is unknown at inception. Therefore, you have two options - estimate a notional schedule to the best of your ability assuming some future evolution of interest rates (which are an important driver of ... 1 UK(IFRS) and the US(GAAP) use different accounting standards - off the top of my head you're likely to have differences at least in the Receivables Index, Margin Index, Asset Quality index due to inventory and costing differences. For example LIFO isn't permitted under IFRS, which is going to affect COGS and Inventory. It doesn't mean it's unusable, you'll ... 1 As @Rustam notes, "correlation" of deterministic functions in the sense you describe is a special case of allowing \mu and \sigma to have a term structure of arbitrary shape. Since the latter is easy to treat, no one bothers with restricted forms of it. Now, there quite a few people who deal with models that let \sigma change with S. I am thinking ... 1 it was meant to be a comment, so please don't treat it like an answer, just suggestion. I think every department has its own standards. and if you want to constitute your model somehow, then you can just compute R^2 between real and fitted values, RMSD, information capacity criteria (AIC/BIC) or you can use any from tens other measures. you can also state ... 1 In my experience with forecasting, you could try a model of the form$$ X_ t = cycle_t + seasonality_t + residuum_t.  Sometimes it is hard to find the cycle but the seasonality could be doable if it has some natural structure (something happening in a certain month each year e.g.). Rob Hyndman explains all these things (and provides an R package) in his ...

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Nobody assumes the market is right. The issue with Libor was that nobody could do much about it. Well, not 100% correct, you had the following 3 choices: Participate in the scheme and benefit (monetarily) Be on the receiving end and despite you knowing the rate is not what it should be you have no choice, you gotta borrow/lend your funds at the end of the ...

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I think most models failed in the 2008 crisis. Historical simulation and e.g. a value-at-risk calculated from it is designed for normal to "medium" market behavior. To account for crisis scenarios stress tests should be in place. This what is done e.g. in the USCITS framework. However, after the crisis your model should keep this history "in mind".

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