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Many of them are on my website at emanuelderman.com. Others I probably have anyway. Feel free to email me


13

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 ...


11

There is certainly much more to quantitative finance than technical analysis, and a previous question does a decent job of outlining the different areas, as does the wikipedia on "quantitative analyst". Even for what wikipedia terms an "algorithmic trading quant" or what Mark Joshi terms a "statistical arbitrage quant", technical analysis is just one tool ...


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 ...


11

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 ...


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: ...


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-...


7

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 ...


6

You can find the answers here: http://www.wiley.com/legacy/wileychi/pwiqf2/degree.html


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 ...


6

Hi Quantitative Finance has in my opinion two main streams. The first is about of valuation of some derivative contracts in a consistent way. This is a theory and once paradigms accepted it is coherent, it can considered as science at the same level as economy can pretend to this kind of terminology. The second is about making (or trying to) prediction(s) ...


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 ...


5

Quant in trading creates system that can be backtested, has a certain risk valuation. It is more like playing chess when you need to calculate multistep strategy. Let say certain instrument moves 1% a day. Our goal is to create strategy for one year (250 step strategy). If we use stock + options we get 50 or more entries a day into our system for analysis. ...


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

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

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

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.


4

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)


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

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 ...


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

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 ...


4

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 ...


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 ...


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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