# Quantitative Finance Stack Exchange Community Digest

## Top new questions this week:

### If arbitrage can happen exactly at one moment, is it really arbitrage?

There are many "interpretations" of what no-arbitrage means in mathematical finance, the most well known is no free lunch with vanishing risk: If $S=\left(S_{t}\right)_{t=0}^{T}$ is a ...

stochastic-processes risk-neutral-measure arbitrage probability martingale

### forward variances under rough bergomi

I have seen in several papers on rough volatility using the following expression for the forward variances $$d\xi_t(u) = \xi_t(u) \eta \sqrt{2H} (u-t)^{H-1/2}dW_t$$ Can anyone explain to me how this ...

volatility finance finance-mathematics stochastic-volatility quantitative

### How does the underlying get delivered for electricity market derivatives?

I have been reading around energy markets recently and recent schemes such as Voluntary Carbon Markets, similar to the 'cap and trade' style of the Kyoto Agreement in 1997. I have been reading in ...

futures derivatives commodities

Is it correct to write $$E_t \int_0^{X_T} f(z) dz = \int_0^\infty \left(\int_0^x f(z) dz \right) p(x)dx \,\,?$$ Here $X_T$ is a positive random variable with density $p(x)... stochastic-calculus random-variables integral  asked by Frido Rolloos 4 votes  answered by Brickcity 0 votes ### Some basic questions using consumption CAPM Say we are in a world described by the consumption CAPM. All investors in this world have quadratic utility. Also, assume that consumption is as follows: $$c_{t+1} = (1+m_t)c_t + s_t c_t e_t$$ where ... asset-pricing capm  asked by elbarto 3 votes ### What is the Q-dynamics of affine bond prices when r is described by the given model? Assuming an Affine term structure model, where bond prices arebe defined as: $$P(t,T)=\exp({A(t,T)-B(t,T)r_t)}$$ and describing the Q-dynamics of the short rate according to the Dothan model:$$dr_t=... interest-rates bond short-rate term-structure affine-processes  asked by Mr Frog 3 votes  answered by fesman 1 vote ### Are there any studies on the link between energy markets and hedging-strategies for Cryptocurrency mining? Full Disclaimer: I first asked this question on Bitcoin.SE, however I feel like my question is more relevant to this site as there would be wider knowledge and insight of some better sources or ... derivatives hedging commodities expected-return bitcoin  asked by Hamish Gibson 2 votes ## Greatest hits from previous weeks: ### How to calculate historical intraday volatility? Sorry for what must be a beginner question, but when I went to write code I realized I didn't understand exactly how historical volatility, or statistical volatility, is defined. Wikipedia tells me "... volatility high-frequency market-microstructure tick-data high-frequency-estimators  asked by Darren Cook 32 votes  answered by LazyCat 14 votes ### How exactly do I calculate and interpret factors in Fama-French model? Could anyone explain me how to interpret factors and what kind of regressions I should run? I have already calculated the factor returns as well as 6 Fama-French portfolio returns, the only problem ... regression factor-models fama-french  asked by Eimantas 4 votes  answered by vonjd 6 votes ### Digital Signal Processing in Trading There is a concept of trading or observing the market with signal processing originally created by John Ehler. He wrote three books about it. Cybernetic Analysis for Stocks and Futures Rocket Science ... trading digital-signal-processing  asked by ali_bahoo 33 votes ### Is R being replaced by Python at quant desks? I know the title sounds a little extreme but I wonder whether R is phased out by a lot of quant desks at sell side banks as well as hedge funds in favor of Python. I get the impression that with ... time-series statistics r python quants  asked by Matthias Wolf 69 votes  answered by statquant 47 votes ### Are there any good tools for back testing options strategies? There are all kinds of tools for backtesting linear instruments (like stocks or stock indices). It is a completely different story when it comes to option strategies. Most of the tools used are ... backtesting option-strategies software  asked by vonjd 39 votes  answered by Shane 16 votes ### Calculate theoretical forward price of a stock The current price of a stock is USD400 per share and it pays no dividends. Assuming a constant interest rate of$8% $compounded quarterly, what is the stock's theoretical forward price for delivery ... forward  asked by Samyak Choudhary 4 votes  answered by wsw 4 votes ### Bachelier model call option pricing formula Does anybody have the Bachelier model call option pricing formula for$r > 0$? All the references I've read assume$r = 0. I don't speak French, so I can't read Bachelier's original paper. option-pricing call  asked by Galsunja 11 votes  answered by Gordon 13 votes ## Can you answer these questions? ### Implementing a Variance Swap Hedging in R I am trying to compute a hedge for a variance swap, in a simulation. Fo that I am using the following equation:\begin{align*} E^Q\bigg(\sum_{i=1}^n \bigg(\frac{S_{t_{i}}-S_{t_{i-1}}}{S_{t_{i-1}}}\bigg)... option-pricing volatility programming  asked by Pedro Gomes 2 votes ### Likelihood ratio and pathwise sensitivity method for coupled SDEs I have two coupled SDEs \begin{align*} dS_t=rS_tdt+V_tdW_t^{(1)},\\ dV_t=aV_tdt+b(V_t)dW_t^{(2)},\\ \end{align*} whereW^{(1)}$and$W^{(2)}$are independent Brownian motions, initial input are$S_0\$ ...

option-pricing monte-carlo brownian-motion numerical-methods