Kiwiakos
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Difference between GARCH and Heston Volatility model
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14 votes

Heston gives an expression for the characteristic function, from which option prices can be computed. Therefore it can be calibrated (statically) on a set of vanilla option prices with different ...

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Does it make sense to refer to a forex pair as a 'financial asset'
1 votes

Financial asset is the Aussie dollar bill or coin. If your numeraire happens to be the US dollar, then the FX rate is the market value of the financial asset denominated in units of the numeraire.

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Historical calibration of Hull-White model
1 votes

You can find Matlab code in these notes: http://cosweb1.fau.edu/~jmirelesjames/MatLabCode/Lecture_notes_2008d.pdf I wrote them 10 years ago and have not revisited since, but it should work.

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Why is Yahoo finance's historical prices so high
2 votes

Prices (and potentially volumes) have been adjusted for historical corporate actions. For example, if there was a 10:1 split in the past, then todays share is equivalent to 1/10th of a share before ...

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Correlation of Asynchronous Brownian Motion
0 votes

Have you tried to simulate both processes together from US close -> JP close -> US close -> JP close and so on? Where the correlation is fixed, but the volatility of each step is proportional to the ...

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Why " Even if the underlying asset price remains unchanged, the option delta for an in-the-money option increases as expiration nears"
2 votes

If the call is ITM, ie $K<S$, as expiry approaches the likelihood that the option will be exercised increases, as there is now less time for it to go OTM. Delta is the position that the hedger is ...

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How can risk-neutral pricing find the right price for securities if it doesn't account for risk premia?
4 votes

The price of a derivative does not explicitly depend on the expected return of the underlying, however the price change or return of the derivative depends on the return of the underlying. Hence the ...

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Portfolio Theory: Why is so much effort put into the reduction of estimation errors?
3 votes

In MPT investors maximize ex ante expected return for a given level of ex ante variance. Gaussian-ity or iid-ness of returns are not requirements. The problem is estimating these ex-ante quantities ...

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Black Scholes biases
3 votes

Perhaps they mean that if you use the ATM implied volatity as an input to price ITM and OTM options, then some will be underpriced and some overpriced compared to the true price observed in the market....

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In portfolio theory, has volatility a logical place as an asset class?
4 votes

IMO: Volatility is a risk factor not an asset class. Asset classes are collections of assets and volatility is not one. Options, volatility derivatives, etc, are asset classes which might offer ...

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How is this SDE interpreted?
1 votes

Looks like jump diffusion. You can take $f(t,T)=\log F(t,T)$, apply Ito's formula for jump diffusions and take it from there. I cannot see how taking integral directly can lead you anywhere.

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Volatility in short-rate models and vol practical issues
1 votes

The model has effectively two free parameters, and therefore one cannot expect it to match bonds of different maturities. Typically this is how you 'get the parameters' by solving to match a given set ...

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How can the market price of a stock be significantly lower than its Bid and Ask?
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8 votes

I don't see this issue in Bloomberg, therefore I would assume it is just bad data in your source. Based on my snaps I suspect that your bid-ask is 15 min delayed. This stock is very active today, ...

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What just happened in the market?
5 votes

What happened was the BoJ announcement. Such large scale news are well covered in mainstream media (ft, bloomberg, etc) and also mainstream anti-media (eg zerohedge).

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How to adjust regression for rolling returns?
1 votes

It depends how large the overlapping interval is. Conceptually an infinite rolling window is equivalent to the level, and no one would suggest to 'regress on levels and apply Newey West'. I think NW ...

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James Simons (Renaissance Technologies Corp.) and his model
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11 votes

In 1983 he was using Hidden Markov Models. Now he employs 100+ PhDs, therefore I expect he will have 50+ strategies using 200+ predictors. And set up as a production line, from the teams importing and ...

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Is there a stochastic equation which can model returns according to its four moments?
0 votes

Levy models do that to some degree. They have the iid look and feel of the standard Gaussian models, but allow for higher moments. You can check the papers of Dilip Madan on Variance Gamma as a ...

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Sharpe Ratio and your annualization
1 votes

Sharpe ratio behaviour reflects the diversification over time. I can diversify using a large number of stocks (ie toss 10 coins simultaneously) or by holding for a large number of periods (ie toss ...

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Mix of Arithmetic and Geometric Brownian Motion
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0 votes

Are you talking about something like this? $$dx(t)=\ldots\ dt+[x(t)]^\gamma\ dW(t)$$ If $\gamma$ is zero then you've got BM, if it's one you get GBM, inbetween you have a 'mix'.

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Heston Model Integration Oscillations
4 votes

I'd use FFT or similar rather than direct integration. Here is an old paper with Heston example: Option pricing using fractional FFT

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I need a low volatility asset that gives an interest/dividen
0 votes

Have you looked at money market ETFs? Something like Pimco's MINT http://finance.yahoo.com/quote/MINT

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Convergence of the distribution of 0.05 quantiles through Monte-Carlo simulation
2 votes

Two comments: Normal returns should always be in $[-1,+\infty)$. I believe that the way you sample $R_i$ from Stable directly violates that. You might want to sample $\log (1+R_i)$ from Stable ...

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Find the parameter $d$ of the Affine Option Pricing Model in Duffie, Pan and Singleton (2000)
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3 votes

$d$ is a vector that collapses the $n$-dimensional vector into a real number. In the BS case $d=1$. There is nothing to be estimated. Also not that in practice affine pricing is done through FFT (and ...

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SABR Model Closed Form Solution
1 votes

The derivation is in "Managing Smile Risk" by Pat Hagan et al. A copy is here: http://www.math.ku.dk/~rolf/SABR.pdf It is not closed form, but rather an approximation based on expansions.

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Is there a way to meaningfully generate daily returns from monthly?
3 votes

Kalman filter (or similar methods) are quite well suited to deal with observations that are of different sampling frequencies and/or asynchronous.

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SVI negative rates
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7 votes

I would say that $\log K/F$ points towards a log-normal type model. If I were you I would experiment with the moneyness defined as $K-F$ instead. This would make it consistent with normal dynamics. ...

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Interpret simulation results ($P$ and $Q$ measures)
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6 votes

I believe that the confusion arises because of the wrong treatment of NIG. The answer to the question you link is misleading, as it simulates under P which is not appropriate for option pricing. None ...

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how to derive critical values for augmented Dickey–Fuller test (ADF) using Monte Carlo method?
4 votes

The ADF test assumes the DGP $$ \Delta y_t = \alpha +\beta t +\gamma y_t +\delta_1 \Delta y_{t-1}+\cdots +\delta_k \Delta y_{t-k}+\epsilon_t $$ The parameters are estimated using OLS on a sample of ...

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Why aren't econometric models used more in Quant Finance?
16 votes

I think you need to differentiate between Q-quants vs P-quants. The former might not use Econometrics, but P-quants use them a lot.

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Correlation: Use Price or Return? Return doesn't make sense
0 votes

I suspect that you are mixing correlation and cointegration. What you describe as the co-movement of prices sounds like cointegration.

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