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55

Visualization should lead to truth and understanding. As such, I find that simple visualizations tend to be the best. My favorite visualization for showing relationships is the scatterplot. Once you start to even introduce a line plot, you are implying continuities between data that may not exist. And trying to introduce more advanced visualizations like ...


24

The risk-neutral measure $\mathbb{Q}$ is a mathematical construct which stems from the law of one price, also known as the principle of no riskless arbitrage and which you may already have heard of in the following terms: "there is no free lunch in financial markets". This law is at the heart of securities' relative valuation, see this very nice paper by ...


23

The Google Motion Chart is a particularly elegant visualization for 'replaying' time series data. There is also an R package to interface with it.


20

Nanex has an interesting way of showing the order-book: The following images show CME's emMni future (S&P 500) depth of book and trades. The images are rainbow (ROYGBIV) color coded by the relative size at each depth level. Red indicates a lot of size, violet indicates size approaching 0. Note that a full minute before each event, the depth starts ...


12

Shane's advice is good. I think it's worth adding the following two techniques not already mentioned: Self-Organizing Maps (SOMs) Seriation (pdf pertaining to R package seriation, but great intro to the topic). They are not explicit visualize techniques, per se. Instead, they are algos that transform underlying data in ways that aim to lead to greater/...


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 feel that the best way to answer your question is to first quote your problematic idea and then carefully explain the subtle alternative. :) The derivation of the Black-Scholes PDE is based on the assumption that the price of the option should change in time in such a way that ... And my question is: Why do we assume that the price of the option has ...


11

Market makers, obviously, have to be willing to short an option. They will delta hedge their positions to limit risk. As for investors, they can aim for a buy-write strategy to collect extra income in lieu of unlimited upside. And lastly, someone who owns a stock he can't sell right away (such as an entrepreneur still under a vesting period after his firm ...


10

Here's a research note devoted to pricing of CMS by means of a stochastic volatility model. The authors indicate in the Introduction that an analysis of the coupon structure leads to the conclusion that CMS contracts are particularly sensitive to the asymptotic behavior of implied volatilities for very large strikes. Market CMS rates actually drive the ...


10

That's a complicated question. There are many paths. One path is to build a model of the underlying supply/demand relationships. For example, the sudden loss of a power supplier (or transmision corridor) shifts the supply curve to the left spiking the price. The key to the game is data, data, and more data (price, weather/wind, season, power loads, ...


8

Here are a few recent examples: https://stackoverflow.com/questions/4951193/find-largest-5-value-less-than-1-lowest-5-values http://tables2graphs.com/doku.php?id=04_regression_coefficients#figure_6 http://tables2graphs.com/doku.php?id=03_descriptive_statistics#figure_5 http://chartporn.org/category/innovative/


8

Although quite simple connected scatterplots can give interesting new insights on how time series perform together: http://steveharoz.com/research/connected_scatterplot/ As an example: Gold vs. S&P 500 from 1970 till today: The green point marks 1970, the red point is today. Every point is a year, moving vertically upwards means rise in the S&P ...


8

Just take something like $$ \frac{\log{\frac{F_j}{F_i}}}{t_j - t_i} \times 365 $$ where $t_i$ denotes the expiry (or alternatively delivery) date of future $i$. The annualization is so you can compare different futures.


8

You may want to consider splitting two important, yet very different concepts: Pricing a derivative security with contingent payoff and forecasting an asset. Pricing a derivative can be achieved through setting up a hedge portfolio and track its evolution and "value" at any point in time before the derivative security pays off. Risk-neutral pricing is a ...


8

FO is shrinking across the large investment banks. The market is not developing new products that will need new pricing formulas, if anything it is reverting to more vanilla structures. Nowdays FO quants typically hack existing models around the corners to manage new market conditions (change Sabr a bit to deal with negative rates, refine the treatment of ...


8

The interviewer meant that he's smart. Quoting Senior VP of People operations at Google, On the hiring side, we found that brainteasers are a complete waste of time. How many golf balls can you fit into an airplane? How many gas stations in Manhattan? A complete waste of time. They don’t predict anything. They serve primarily to make the interviewer ...


7

The SABR model has an overly fat right tail. If you do the CMS replication using cash-settled swaptions you find that you need ridiculously high strikes.


7

To me, coloring by data value is a great way to bring applications alive. If traditional ways are not enough, probably taking 3D in use would be a way: And of course 2D heatmap is a very handy for sure. I'm developing data visualization software components with 3D technologies, so definitely all feedback and ideas are welcome :-)


7

And then music... Victor Neiderhoffer, in a 2001 interview: The market plays music all the time. The problem is you never know how the music of the market is going to end. But a good framework is that it will end on the tonic. Consonance to dissonance back to consonance. And whenever there's tremendous dissonance, strident moves in one direction, a good ...


7

A general hedging strategy Let assume that $S_1(t)$ and $S_2(t)$ are the price processes of your 2 stocks and that they follow a Geometric Brownian Motion (GBM): $$\forall \, i \in \{1,2\}, dS_i(t) =\mu_iS_i(t)dt + \sigma_iS_i(t)dW_i(t)$$ We assume both stocks have an instant correlation of $\rho$: $$dW_1(t)dW_2(t)=\rho dt$$ Let also $V(t)$ be the value ...


6

There are many price driven financial data finsualization concepts are available such as candle stick stock charts. However, there is an advanced charting concept, Mano Stick which is supply & demand driven charting concept. Mano Stick is a multidimentional charting concept which is able to display price information along with volume information to show ...


6

A swap does not require a model because its price can be derived from the yield curve without any assumptions about how the yield curve may move in the future. The PFE however is an indication of by how much the swap's mark-to-market may move between now and a moment in the future. It is of course influenced by how volatile rates are. The more volatile ...


6

I will refer to "Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit" by Damiano Brigo and Fabio Mercurio. In chapter 3 (One-factor short-rate models) they have a very nice table which lists some of the properties of instantaneous short rate models. In both of your models you know the distribution of $r_t$. The huge difference ...


6

It is incorrect to use 1m euribor or O/N euribor in a 6m Euribor forward curve. You should only use instruments based on 6M euribor, such as 1x7 FRA, 6x12 FRA or swaps v 6m Euribor, as you have done in your second example. The actual 6m euribor fixing itself can be thought of as a 0x6 FRA out of spot. Before the financial crisis basis between different ...


6

A constant maturity swap (CMS) rate for a given tenor is referenced as a point on the Swap curve. A swap curve itself is a term structure wherein every point on the curve is the effective par swap rate for that tenor. This is analogous to a 3m LIBOR curve represents 3m forward rates for a given tenor. A swap rate can be considered as a weighted-average of ...


6

It is hard to imagine why a trader would want to buy a forward start option to express a market view, unless there is a one-off event like an election which they don't want to have as part of the live period for the volatility. A forward start option is mainly exposed to the volatility relating to the period after the strike is set. Forward start options ...


6

The CMS represents the value of a swap rate for any point in time, i.e. we are interested in extrapolating the density of the swap rate in a similar way as the IBOR rate. Let us start with the fair value of a swaption under the annuity measure $\mathcal{A}$ with tenor at time $\tau$: $$\mathcal{A}(t)\mathbb{E}^\mathcal{A}_t[(\mathcal{S}(\tau)-k)^+]$$ Instead ...


5

Specifically, we have a generic conditional claim, $C$, that is a function of the diffusion process for the underlying, $S(t)$, and time $t$ so $C = C(S(t), t)$. As you pointed out, $C$ is an Ito process becuase it is a function of a stochastic process so we use Ito's Lemma to determine how the contingent claim varies as a function of the diffusion process $...


5

The common approach to temperature derivatives in their first run of popularity (in the late 1990's) was to use an Ornstein-Uhlenbeck process to describe deviations of temperature from a seasonal average. So far as I know, no major innovations have arisen since then. Calibrating such a model is very simple, and so is valuing certain quantities such as ...


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