Top new questions this week:
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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 ...
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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 ...
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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 ...
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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)...
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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 ...
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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=...
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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 ...
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Greatest hits from previous weeks:
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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 "...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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.
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Can you answer these questions?
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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)...
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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 $S_0$ ...
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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 ...
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