32
Many of them are on my website at emanuelderman.com. Others I probably have anyway. Feel free to email me
16
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 Chapter 3 of this book. Here, $B_t=e^{rt}$ is the value of the money-market account, and $r$ is the risk-free interest rate.
On the other hand, you can create ...
12
This is a basic fact about futures trading and the storage of commodities.
The phrase that was used by futures traders in the old days (and probably still today) was "the contango is limited by the carrying cost, there is no limit to the backwardation". This means that for example if spot gold is at 1200, gold dated one year from now cannot possibly sell ...
11
I had read some of them; actually, it does not exist an on-line library that collected them (or, better, it existed here, but it seems the website does not work anymore).
I reported here below some of them that you did not find:
More Than You Ever Wanted To Know* About Volatility Swaps
Model Risk
The Volatility Smile And Its implied Tree
Enhanced Numerical ...
8
The best overview I have seen so far is this paper which lists 214 (!) factors (or anomalies if you like) on over one hundred (!) pages:
Harvey, Campbell R. and Liu, Yan and Zhu, Caroline, …and the Cross-Section of Expected Returns (February 3, 2015). Available at SSRN: https://ssrn.com/abstract=2249314 or http://dx.doi.org/10.2139/ssrn.2249314
Abstract: ...
8
I think you might find this answer in The future language of quant programming? useful.
People get this problem wrong because they always end up discussing the theoretical advantages of these languages rather than the practical uses of these languages.
Theoretically speaking:
Haskell is elegant and has many of the theoretical advantages (language ...
7
A hurst exponent, H, between 0 to 0.5 is said to correspond to a mean reverting process (anti-persistent), H=0.5 corresponds to Geometric Brownian Motion (Random Walk), while H >= 0.5 corresponds to a process which is trending (persistent).
The hurst exponent is limited to a value between 0 to 1, as it corresponds to a fractal dimension between 1 and 2 (D=2-...
6
You can find the answers here:
http://www.wiley.com/legacy/wileychi/pwiqf2/degree.html
6
C++
Think in C++ can be a starting point. This is free. And, you might study Beginning Visual C++ 2010 by Ivan Horton
Quantitative finance and C++ (if you are derivatives-oriented)
You might find Mark Joshi as well as Daniel Duffy's writings of (great) interest.
It is easy to find the references of both their books on a website such as Amazon.
You can also ...
6
For a basic introduction, the three chapters in Hull's Options, Futures, and Other Derivatives on Binomial Trees, Wiener Processes and Ito's Lemma, and The Black-Scholes-Merton Model helped me start to understand the basic concepts within a broader context.
After that, Shreve's two books seems to be pretty popular (see here and here). He explains things ...
5
Quantopian provides both the fundamental data (from Morningstar), as well as the backtest platform to reproduce results from the books you mentioned. Here's the introduction to our fundamentals offering: https://www.quantopian.com/posts/fundamental-data-from-morningstar-now-available-for-backtesting
(disclosure: I'm the ceo of quantopian)
5
A detailed description of the Hurst Exponent can be found here. A further (rather short search of Google) turned up this site claiming to provide an Excel Workbook with, among other things, Hurst Exponent estimation.
5
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 combination of them), if the correlation of the two assets is equal to the ratio of Sharpes (smaller to larger), there is zero diversification benefit.
For ...
5
You have started a huge job, an enormous number of anomalies have been reported. The web site quantpedia.com has a list, here for example is their writeup on momentum effect in stocks
5
Unfortunately, there is no correct answer for this question, it's like what car you should drive on your weekend.
C++ is a popular language in quantitative finance, but it's usually (but not always!) only used to build the application backbone, such as derivative pricing. Why C++? C++ is a good choice because C++ is platform independent, we can natively ...
5
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 education, go look up the course listings of any reputable MFE program, and then look into the sites for those (past) classes and see the recommended readings and ...
5
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 of a random $X$ variable with values $v_j$ such that $P(X=v_j)=p_j$.
From standard textbooks we know the following transformation: If $u_i$ are uniform random ...
5
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 are options on commodity spreads listed, and a strike of 0 would be the same as an exchange option.
These options have some liquidity in energy and grain markets,...
4
The general idea
For equity securities, a simple backtest will typically consist of two steps:
Computation of the portfolio return resulting from your portfolio formation rule (or trading strategy)
Risk-adjustment of portfolio returns using an asset pricing model
Step 2 is simply a regression and computationally very simple in Matlab. What's trickier is ...
4
If you have a fairly good model of regime separation (of course requiring a good quantitative measure of regime state classifications -- momentum and reverting) and predictive likelihood (using something like a markov state transition matrix)-- one could weight contributions corresponding to next state probabilities. Of course, you will rarely get a ...
4
I found these nice lecture note by Karl Sigman on the web. On page three you see if $X\sim N(\mu,\sigma)$ then the moment generating function (mgf) of $X$ is given by
$$M_X(s) = E(exp(sX)) = \exp( \mu s + \sigma^2 s^2 /2)$$
Thus for Brownian motion with drift $X_t$ you get
$$
M_{X_t}(s) = E(exp(s X_t)) = \exp( \mu t s + \sigma^2 s^2 t /2).
$$
Finally for $...
4
It depends the kind of information you look for.
Questions and answer.
This web site is really the best I know on quant finance. You can browse "tags" and go the the associated wiki pages to have summarized information.
Wilmott Forum is not that bad;
Nuclear Phynance is good too.
Generic knowledge.
It depends on what area on finance you are interested in.
...
4
There is not a single 'interest-rate' to reduce, there are various interest rates in play.
The central bank mandate is usually to control CPI or a similar measure of inflation (e.g. Bank of England's 2% inflation target for GBP). There are various tools for them to do this, including QE and setting the central bank rate.
However, at the moment, the central ...
4
Just an update on my playlist, It has 33 videos now, roughly 3x more vids. I have included some more general economics and machine learning and programming vids, which have relevant applications in Q finance.
https://www.youtube.com/watch?v=jXFNpDcYOxM&list=PLqMiStH7exaXmQqV7y-tg68f2ZYZK3Yur
4
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. When you say in an academic sense, you may not get much respect from serious academics if you data mine a factor these days. However, as a statistical exercise, ...
4
Another way of staying "time-varying risk-premium", is saying that the risk-premium is predictable. However, that the fact that the risk-premium is predictable does not means that you can make money out of this.
The best two references to understand this are:
Cochrane (2008) - The dog that did not bark
Goyal and Welch (2007)
The first tells you what ...
4
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 = Knock up and in Option + Knock up and out option
You can price the up and out easily using Binomial and use BS formula for pricing the European Option, then ...
4
(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 - maybe the forwards realized, maybe not. A good estimate of what it might turn out to be as to reprice for the next day assuming all forwards are realized.
I ...
3
Question 2 has a straight forward solution using a differential equation approach: $\mathbb{P}(\tau^\mu_a<\infty)=1$
The following link (pp. 21 f.) explains it nicely (and is also very detailed) - could not write it much better.
If you were to google "brownian motion linear boundary" you will get additional results.
Also if you are generally interested ...
3
We have,
$$ h(x) = x^\beta(x-K)^+ = x^\beta (x - K) \, \mathbf{1}_{[x>K]}$$
Thus we get,
$$ h(x) = x^{\beta+1}\mathbf{1}_{[x>K]} - K\,x^{\beta}\mathbf{1}_{[x>K]}$$
now $x \in [x>K]$ if and only if $ x \in [x^{\beta}>K^{\beta}]$
Therefore,
$$ h(x) = x^{\beta+1}\mathbf{1}_{[x^{\beta + 1}>K^{\beta + 1}]} - K\,x^{\beta}\mathbf{1}_{[x^{\beta}&...
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