# All Questions

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In many books and derivations of the Black-Scholes PDE one sees that $$\Pi=V-\Delta F \Rightarrow d\Pi=dV-\Delta dF$$ which implicitly assumes that $d\Delta=0$. Somewhere down the road one then ...
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### Integration in the context of modelling with the Meixner Process

I failed to evaluate the integral of $\frac{e^{ax}}{x\sinh(bx)}$ with respect to $x$ from negative infinite to positive infinite, What techniques can I use to evaluate the integrals of such kind for ...
94 views

### Simple question about expected value of brownian motion

I would appreciate some help with the math in this paper : High Frequency Trading in a Limit Order Book Specifically, I would like to understand how the authors calculated the expected value of price ...
69 views

### Different range price data on one chart

I'd like to evaluate 3-4 instruments on one price chart. For example: Stock A: 90,05 90,15 90,25 90,09 Stock B: 0,0045 0,0049 0,0039 0,0040 Stock C: 1998,1 1998,7 1998,8 1997 I try to use: ...
146 views

Seeing how very few actually read the Quant Finance meta I intentionally post it here on the main site. To the more powerful admins: could you leave it here for a day or two and move it to meta ...
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### What tools exist for order book analysis and visualization?

What tools exist for order book analysis and visualization? In particular, if one wanted to examine a limit order book and understand how it changes throughout the day where would you turn for ...
27 views

### How to calculate tail exposure on a multi-product position

Let's say I have a position vector across five products: Positions <- c(40,-45,20,-32,17) How can I determine the "tail" exposure if my PCA model gives me the following loadings for the first ...
235 views

### Mean-variance portfolio & quadratic programming

I am somewhat confused when it comes to modern portfolio theory, mean-variance portfolio optimization and its quadratic programming formulation. Issue 1: Formulation of mean-variance portfolio ...
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### Incorporating a stochastic correlation structure into a multi-factor model

I am considering extending a multi-factor fixed income stochastic model (e.g. LIBOR-Market) to use stochastic correlation matrices instead of determinstic ones. For pricing instruments with short ...
730 views

### Simulating the short rate in the Hull-White model

What is the best way to simulate the short rate $r(t)$ in a simple one factor Hull White process? Suppose I have $$dr(t) = (\theta(t)-\alpha r(t))dt+\sigma dW_t$$ where $\theta(t)$ is calibrated ...
156 views

### Options with a stochastic strike

Do options where the strike itself is a stochastic process exist? If they do - what are the motivations for such a product and where is it used ? Example: Call-Option with stochastic strike: ...
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### backward Kolmogorov equations - Markov properties

I'm a physicist who's research has lead him into the theory of stochastic differential equations. If this question is not appropriate for this forum, please feel free to delete it. So I've been ...
59 views

### Log returns vs. prices

I am currently working on a stat arb that is giving me a little bit of trouble. I'm under the impression that most stat arbs are going to use prices such that we can choose a ratio N such that: Price ...
257 views

### Obtaining a consistent covariance matrix for stochastic volatility processes

What is the condition for underlying stochastic volatility processes to give a consistent covariance matrix? I read in Hull that in order to have a consistent covariance matrix, volatility parameters ...
320 views

### Practical Usage of Wavelets with Real Time Data

There are a lot of papers out there which make attempts to forecast or discuss the benefits of wavelets for frequency decomposition. Oddly, very few discuss the huge boundary effects that are present ...
255 views

### On the interface between Quant finance and actuarial-science/insurance-math

Actuaries (at least in Europe) are frequently severily lacking in quant finance topics. At best they are familiar with B&S model. People going into quant finane or striving to become a quant on ...
118 views

### Where does this copula come from?

In a paper I encountered the following notation $$P(Z\leq z,u\leq Y\leq v)=C(F_{Z}(z),F_{Y}(v)-F_{Y}(u))$$ However I don't see why this holds in relation to uniform random variables. Usually ...
345 views

### Are PX_BID and PX_ASK on Bloomberg closing bid/ask? or are they daily averaged?

Bloomberg provides PX_BID and PX_ASK on a daily basis, but it's not clear exactly where these numbers come from. Are they closing bid and ask prices, or are they averaged over the entire day? For ...
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### What impact does arbitrage have on realised volatility estimates?

Doing some research modeling/estimating volatility in the bitcoin market. There is quite a bit of scope for arbitrage within crypto-currency markets. Wonder if this has any impact on my volatility ...