20
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Black Scholes differential
In general, you won't be able to replicate the option by a portfolio of the form $\Delta_t S_t + B_t$, though it is possible to do so with a portfolio of the form $\Delta_t^1 S_t + \Delta_t^2B_t$; see ...
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8
votes
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Algorithmic Trading: Python vs SQL
Python has lots of excellent libraries to compute Technical indicators for you, ta and ta-lib are great. These libraries have ...
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7
votes
Where can I find detailed information of famous quant companies such as Renaissance Technologies?
Most RIAs have to file a Form ADV, through which some information is publicly available via SEC's website.
Further, large RIAs are sometimes involved in high profile civil lawsuits through which ...
- 2,705
7
votes
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Explanation for Different Piecewise Yield Term Structures from QuantLib Python
When you bootstrap a curve, you get discount factors/zero rates for the maturities of the instruments you supplied. So in practice, you get points, and not a "curve".
After you have built ...
- 5,895
7
votes
Probability of success given expected return and volatility
It's probably a simple textbook example to illustrate Taleb's point. Suppose $\text{d}S_t=\mu S_t \text{d}t+\sigma S_t \text{d}W_t$ with $\mu=0.15$ and $\sigma=0.1$.
By Itô's lemma, the log return ...
- 16.3k
6
votes
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CAPM and factor modeling: Machine learning
1) In an academic sense could it be enough to use ML to create a new factor portfolio?
The original FF papers (92,93) said something deep because they contradicted the dominant theory of the day. ...
- 468
6
votes
Differencing vs Detrending financial time series
Hi: It depends on what the DGP of the original process is. Is the process trend stationary or difference stationary ? If it's trend stationary then de-trending is the way to go. If it's difference ...
- 1,178
5
votes
Method to combine trading signals to achieve higher sharpe
There is no guarantee you can improve the Sharpe in this case, depending on the correlation of the returns streams. For the two asset case (you can model your strategies as assets and take a linear ...
- 547
5
votes
Step by Step Guide to Learn Quantitative Finance
This thread will inevitably close because it doesn't meet community guidelines, but I respect your passion in this field and my best suggestion for you is that if you're trying to emulate a MFE ...
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5
votes
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Mark Joshi Quantitative finance numerical techiniques, writting an algorithm that produces a random variable
Yes. Mark Joshi's book is a good preparation.
For this question you are given some function random() yielding a uniform random number and what we want is a function next() which yields realizations ...
- 164
5
votes
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Who trades exchange options in practice (Margrabe's formula)?
Yes, you can say they are traded on listed options, but only for a few limited markets, and not that liquid relative to options on a single asset.
For instance, the commodity futures space, there ...
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5
votes
Curve fitting under different regions and stitching
I hope I understood you correctly and that the following thoughts help you a bit.
Reference point: Univariate curve fitting using splines
With a univariate function $f(x)$ you can perform 1D spline ...
- 7,140
5
votes
Reflection principle of the Brownian motion
I'll only show it for $M_T = \max_{u\leq T} B_u$ and $(x,h)$-domain
$$ \{ h> 0, h > x \}. $$
By the reflection principle we have:
$$ P\left( B_T < x, M_T > h \right) = P\left( 2h - B_T &...
- 5,173
4
votes
Accepted
Disadvantages of large panel
In general, more data is better than less data.
On the topic of your specific scenario, you want to cluster by date or use some other procedure to produce consistent standard errors in the presence ...
- 7,024
4
votes
Accepted
Barrier Option from binomial tree
I'm assuming you're talking about a European option. I did a similar problem for my homework recently, I used the in-out parity for pricing the up and in barrier option.
Basically European Option = ...
- 196
4
votes
Carry vs Roll-Down on a zero-coupon IRS
(This is my opinion; someone is likely to disagee).
I like to think of the carry as the predictable part (e.g. the coupon that accrues daily) and the rolldown as the stochastic part (the curves moved ...
- 13.2k
4
votes
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Quantitative risk management for energy markets
The book "Managing Energy Risk An Integrated View on Power and Other Energy Markets" by Burger et al. (2014) may be very helpful as it not only introduces the relevant notions, but does so directly ...
- 197
4
votes
Algorithmic Trading: Python vs SQL
You said you're developing an algorithmic trading system. First, I'd suggest maybe consider an off-the-shelf product that will let you do some trading without ...
- 141
4
votes
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How does Linear-Exponential Loss (Linex) function tend towards Quadratic Loss function?
It just needs the power series(Maclaurin) expansion: $e^{x}=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots$
Take the Linex function:
$L\left(y,\overset{\wedge}{y}\right)=\frac{2}{a^2}\left[e^{a\left(y-\...
- 6,242
4
votes
forward variances under rough bergomi
Maybe this deck by Jim Gatheral would help get the intuition, see slides 10 and following.
The dynamics you mentioned is obtained by:
Looking at the Bergomi dynamics for the forward variance process;
...
- 14.8k
4
votes
Multi-Period Contribution
Thanks for the example. It is exactly like my comment. Look at your weights after the first period. Are they really 80% and 20%?
Lets say you have £100 to invest.
£80 is invested in product A. That ...
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4
votes
Where can I find detailed information of famous quant companies such as Renaissance Technologies?
For Rentech, try the Greg Zuckerman book, "The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution".
HSBC Hedge Fund Report might be of use for other funds.
- 2,292
4
votes
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Pricing a Forward Rate Agreement using QuantLib Python
For a 3x6 FRA, you probably want to write something like:
...
- 8,008
3
votes
Accepted
Fama and French (market premium) factor
Update
I downloaded the return series for WFIVX (a Wilshire 5000 index fund) and I calculate a correlation coefficient of .9991 with the Fama-French market return series from Ken French's website (...
- 7,024
3
votes
Mark Joshi Quantitative finance numerical techiniques, writting an algorithm that produces a random variable
I am sure you have seen the $n=2$ case:
Write a program that returns "Yes" with probability p and "No" otherwise. You are given a function runif(), which returns a random number between 0 and 1.
...
- 11.8k
3
votes
Accepted
Sigma moves - annualize return or no?
This is hardly a simple dumb question. Drawdown of BM with no drift is
$ 2 \sqrt \frac{\pi}{8} \sigma \sqrt T $
see Magdon-Ismail: On the Maximum Drawdown of a Brownian Motion, Eqn. (16)
or ...
- 2,563
3
votes
Accepted
Using Normal Distribution to forecast active return
If your benchmark has a volatility of zero and return 5% then for a benchmark investment of 1.0 after 1 year it is guaranteed to be worth 1.05, or $$X_b = 1.05$$
On the other hand your second ...
- 12.1k
3
votes
Why the spread is calculated on raw prices instead on the price changes?
That is the concept of Cointegration
Regressing two non-stationary variables results in spurious regression. However, if these two variables are cointegrated, spurious regression no longer arises.
As ...
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3
votes
Accepted
Fama French sorting
Let's start replicating the Fama-French portfolio construction:*
Portfolios are created at the end of June each year $t$, based on size and book-to-market ratio (BE/ME).
The size breakpoint for year $...
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