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  
asked by W. Volante 4 votes

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  
asked by Daan 4 votes
answered by Quantuple 3 votes

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  
asked by Hamish Gibson 4 votes

Expectation of integral where one of limits of integration is a random variable

Is it correct to write \begin{equation} E_t \int_0^{X_T} f(z) dz = \int_0^\infty \left(\int_0^x f(z) dz \right) p(x)dx \,\,? \end{equation} 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 ...

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*} where $W^{(1)}$ and $W^{(2)}$ are independent Brownian motions, initial input are $S_0$ ...

option-pricing monte-carlo brownian-motion numerical-methods  
asked by user107224 1 vote

Value of continuously rebalanced stock portfolio

I'm thinking about what a theoretical continuously re-balanced stock portfolio could look like, in which the portfolio is uniformly distributed over a selection of stocks at all times. For example, if ...

portfolio-optimization differential-equations  
asked by JMC 1 vote
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