Derivatives of the Black-Scholes equation give us delta, IV, and other "greeks" for each individual options contract ( aka the equations to derive implied volatility for an option are very easy to come by ).
Question:Q1: How do brokerages combine the IV readings of all the individual options in a chain for an expiration cycle, weigh them properly, account for things like Volatility skew, and come up with an overall implied volatility for the expiration that represents the Implied volatility of the entire chain?
Q2: Are there any common methodologies?
If by "chain" you mean all the actively traded options of the same type across all strikes / maturities, then what you are asking is how banks / brokers fit an entire volatility surface to all the observed prices. Which accounts for both the vol smile and vol skew.
Generally you need to extend the black scholes model with additional degrees of freedom to produce the smile and / or skew behaviour commonly observed. One common model is the SABR model which has a nice closed form relationship to the black scholes IV and reproduces vol skew not vol smile (term structure), the extension called dynamic SABR model also produces vol smiles, there is also the Heston model which exhibits both vol skew and smile.
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I am writing my master thesis and I run a generalized linear mixed regression model in SPSS (version 28) using count data.
Research question: which effect has the population mobility on the Covid-19 incidence at the federal state level in Germany during the period from February 2020 to November 2021.
To test the effect of population mobility (independent variable) on Covid-19 incidence (dependent variable) hierarchical models were used, with fixed factors:
mobility variables in 6 places.(scale)
cumulative vaccination rate (only second dose).( scale)
season (summer as the reference category) (nominal)
and random effects:
one model with days variable (Time level). (Scale)
Second model with federal states variable ( each state has a number from 1 to 16) ( place level). (Nominal)
Third model with both days and federal states (Time and place level).
First I have built intercept-only model to check which type of regression is more suitable for the count data (Possion or Negativ binomial) and to choose also the best variable as an offset from two variables..It showed that negative binomial regression is the best for this data. (Based on the BIC or AIC)
Secondly I have checked the collinearity between the original 6 mobility variables and I have excluded mobility variables that are highly correlated based on VIF. (Only one Variable was excluded)
Thirdly I have built 7 generalized linear models by adding only the fixed effects or the fixed factors which are the 5 mobility variables, the cumulative vaccination rate dose 2 and the season (with summer as a reference category) to the intercept only model gradually. From these 7 models the final model with best model fit was selected.
Finally I have built a generalized linear mixed model with the above final model and a classic random effect by adding Days variable only ((random-intercept component for time; TIME level)) and then with federal states variable only ((random-intercept component for place; PLACE level)) and finally with adding both of them together.
I am not sure if I ran the last step regarding the generalized linear mixed models correctly or not??
These are my Steps:
Analyze-> mixed models-> generalized linear mixed model-> fields and effects:
1.target-> case
Target distribution and relationship (link) with the linear model-> custom :
Distribution-> negative binomial
Link Funktion -> log
2.Fixed effects-> include intercept & 5 mobility variables & cumulative vaccination rate & season
3.random effects-> no intercept & days variable (TIME LEVEL)
Random effect covariance type: variance component
4.weight and offset-> use offset field-> log expected cases adjusted wave variable
Build options like general and estimation remain unchanged (suggested by spss)
Model options like Estimated means remain unchanged (suggested by spss)
I have done the same steps with the other 2 models except with random effects:
3.random effects-> no intercept & Federal state variable (PLACE LEVEL)
3.random effects-> no intercept & days variable & Federal state variable (TIME & PLACE LEVEL)
Output:
1.the variance of the random effect of days variable ( time level ) was very small 5,565E-6, indicating only marginal effect in the model. (MODEL 1)
2.the covariance of the random effect of the federal states was zero and the variance was 0.079 ( place level )(MODEL 2)
3.the variance of the random effect of days variable was very small 4,126E-6 and the covariance of the random effect of the federal states was zero and the variance was 0.060 ( Time and place level )(MODEL 3)
Can someone please check my steps and tell me which model from the models in the last step is the best for the presentation of results and explain also the last point in the output within the picture?
Thanks in advance to all of you...
Kademlia uses XOR metric. Among other things, this has so called "unidirectional" property (= for any given point x and distance e>0, there is exactly one point y such that d(x,y)=e).
First question is a general question: Is this property of the metric critical for the functionality of Kademlia, or is it just the thing that helps with revealing pressure from certain nodes (as the original paper suggests). In other words, if we want to change the metric, how important is to come with a metric that is "unidirectional" as well?
Second question is about concrete change of the metric: Let's assume we have node identifiers (addresses) as X-bit numbers, would any of the following metric work with Kademlia?
d(x,y) = abs(x-y)
d(x,y) = abs(x-y) + 1/(x xor y)
The first metric simply provides difference between numbers, so for node ID 100 the nodes with IDs 90 and 110 are equally distant, so this is not unidirectional metric. In the second case we fix that adding 1/(x xor y), where we know that (x xor y) is unidirectional, so having 1/(x xor y) should preserve this property.
Thus for node ID 100, the node ID 90 is d(100,90) = 10 + 1/62, while the distance from node ID 110 is d(100,110) = 10 + 1/10.
You wouldn't be dealing with kademlia anymore. There are man other routing algorithms which use different distance metrics, some even non-uniform distance metrics, but they do not rely on kademlia-specific assumptions and sometimes incorporate other features to compensate for some undesirable aspect of those metrics.
Since there can be ties in the metric (two candidates for each point), lookups could no longer converge on a precise set of closest nodes.
Bucket splitting and other routing table maintenance algorithms would need to be changed since they assume that identical distances can only occur with node identity.
I'm not sure whether it would affect Big-O properties or other guarantees of kademlia.
Anyway, this seems like an X-Y problem. You want to modify the metric to serve a particular goal. Maybe you should look for routing overlays designed with that goal in mind instead.
d(x,y) = abs(x-y) + 1/(x xor y)
This seems impractical, division on integers suffers from rounding. and in reality you would not be dealing with such small numbers but much larger (e.g. 160bit) numbers, making divisions more expensive too.
I am a master student working with localization in VANEts
in this moment I am working on a trilateration method based on RSSI for
Cooperative Positioning (CP).
I am considering the Analogue Model : Simple Path Loss Model
But I have some doubts in how to calculate the distance correctly for a determined Phy Model.
I spent some time (one day) reading some papers of Dr. Sommer about the PHY models included in veins.
Would anyone help-me with this solution?
I need a way to:
1) Measure the power of an receiver when its receive a beacon (I found this in the Decider class).
In the Decider802.11p the received Power can be obtained with this line in method Decider80211p::processSignalEnd(AirFrame* msg):
double recvPower_dBm = 10*log10(signal.getReceivingPower()->getValue(start));
2) Apply a formula of RSSI accordingly the phy model in order to achieve a distance estimation between transmiter and receiver.
3) Asssociate this measure (distance by RSSI) with the Wave Short Message to be delivered in AppLayer of the receiver (that is measuring the RSSI).
After read the paper "On the Applicability of Two-Ray Path Loss Models for Vehicular Network Simulation"
and the paper "A Computationally Inexpensive Empirical Model of IEEE 802.11p Radio Shadowing in Urban Environments"
and investigating how it works in the veins project. I noticed that each analogue model have your own path loss model
with your own variables to describe the model.
For example for the SimplePathLossModel we have these
variables defined on AnalogueModels folder of veins modules:
lambda = 0.051 m (wave length to IEEE 802.11p CCH center frequency of 5.890 GHz)
A constant alpha = 2 (default value used)
a distance factor given by pow(sqrDistance, -pathLossAlphaHalf) / (16.0 * M_PI * M_PI);
I found one formula for indoor environments in this link, but I am in doubt if it is applicable for vehicular environments.
Any clarification is welcome. Thanks a lot.
Technically, you are correct. Indeed, you could generate a simple look-up table: have one vehicle drive past another one, record distance and RSSIs, and you have a table that can map RSSI to mean distance (without knowing how the TX power, antenna gains, path loss model, fading models, etc, are configured).
In the simplest case, if you assume that antennas are omnidirectional, that path loss follows the Friis transmission equation, that no shadow fading occurs, and that fast fading is negligible, your table will be perfect.
In a more complicated case, where your simulation also includes probabilistic fast fading (say, a Nakagami model), shadow fading due to radio obstacles (buildings), etc. your table will still be roughly correct, but less so.
It is important to consider a real-life application, though. Consider if your algorithm still works if conditions change (more reflective road surface changing reflection parameters, buildings blocking more or less power, antennas with non-ideal or even unknown gain characteristics, etc).
I have a continuous dependent variable polity_diff and a continuous primary independent variable nb_eq. I have hypothesized that the effect of nb_eq will vary with different levels of the continuous variable gini_round in a non-linear manner: The effect of nb_eq will be greatest for mid-range values of gini_round and close to 0 for both low and high levels of gini_round (functional shape as a second-order polynomial).
My question is: How this is modelled in Stata?
To this point I've tried with a categorized version of gini_round which allows me to compare the different groups, but obviously this doesn't use data to its fullest. I can't get my head around the inclusion of a single interaction term which allows me to test my hypothesis. My best bet so far is something along the lines of the following (which is simplified by excluding some if-arguments etc.):
xtreg polity_diff c.nb_eq##c.gini_round_squared, fe vce(cluster countryno),
but I have close to 0 confidence that this is even nearly right.
Here's how I might do it:
sysuse auto, clear
reg price c.weight#(c.mpg##c.mpg) i.foreign
margins, dydx(weight) at(mpg = (10(10)40))
marginsplot
margins, dydx(weight) at(mpg=(10(10)40)) contrast(atcontrast(ar(2(1)4)._at) wald)
We interact weight with a second degree polynomial of mpg. The first margins calculates the average marginal effect of weight at different values of mpg. The graph looks like what you describe. The second margins compares the slopes at adjacent values of mpg and does a joint test that they are all equal.
I would probably give weight its own effect as well (two octothorpes rather than one), but the graph does not come out like your example:
reg price c.weight##(c.mpg##c.mpg) i.foreign
I need to write an algorithm in any language that would order an array based on 3 factors. I use resorts as an example (like Hipmunk). Let's say I want to go on vacation. I want the cheapest spot, with the best reviews, and the most attractions. However, there is obviously no way I can find one that is #1 in all 3.
Example (assuming there are 20 important attractions):
Resort A: $150/night...98/100 in favorable reviews...18 of 20 attractions
Resort B: $99/night...85/100 in favorable reviews...12 of 20 attractions
Resort C: $120/night...91/100 in favorable reviews...16 of 20 attractions
Resort B looks the most appealing in price, but is 3rd in the other 2 categories. Wherein, I can choose resort C for only $21 more a night and get more attractions and better reviews. Price is still important to me, but Resort A has outstanding reviews and a ton of attractions: Is $51 more worth the splurge?
I want to be able to populate a list that will order a lit from "best to worst" (I quote bc it is subjective to the consumer). How would I go about maximizing the value for each resort?
Should I put a weight for each factor (ie: 55% price, 30% reviews, 15% amenities) and come to the result of a set number and order them that way?
Do I need a mode, median and range for all the hotels and determine the average price, and have the hotels around the average price hold the most weight?
If it is a little confusing then check out www.hipmunk.com. They have an airplane sort they call Agony (and a hotel sort which is similar to my question) that they use as their own. I used resorts as an example to make my question hopefully make a little more sense. How does one put math to a problem like this?
I was about to ask the same question about multiple-factor weighted sorting, because my research only came up with answers (e.g. formulas with explanations) for two-factor sorting.
Even though we're both asking about 3 factors, I'll list the possibilities I've found in case they're helpful.
Possibilities:
Note: S is the "sorting score", which is what you'd sort by (asc or desc).
"Linearly weighted" - use a function like: S = (w1 * F1) + (w2 * F2) + (w3 * F3), where wx are arbitrarily assigned weights, and Fx are the values of the factors. You'd also want to normalize F (i.e. Fx_n = Fx / Fmax).
"Base-N weighted" - more like grouping than weighting, it's just a linear weighting where weights are increasing multiples of base-10 (a similar principle to CSS selector specificity), so that more important factors are significantly higher: S = 1000 * F1 + 100 * F2 ....
Estimated True Value (ETV) - this is apparently what Google Analytics introduced in their reporting, where the value of one factor influences (weights) another factor - the consequence being to sort on more "statistically significant" values. The link explains it pretty well, so here's just the equation: S = (F2 / F2_max * F1) + ((1 - (F2 / F2_max)) * F1_avg), where F1 is the "more important" factor ("bounce rate" in the article), and F2 is the "significance modifying" factor ("visits" in the article).
Bayesian Estimate - looks really similar to ETV, this is how IMDb calculates their rating. See this StackOverflow post for explanation; equation: S = (F2 / (F2+F2_lim)) * F1 + (F2_lim / (F2+F2_lim)) × F1_avg, where Fx are the same as #3, and F2_lim is the minimum threshold limit for the "significance" factor (i.e. any value less than X shouldn't be considered).
Options #3 and #4 look really promising, since you don't really have to choose an arbitrary weighting scheme like you do in #1 and #2, but then the problem is how do you do this for more than two factors?
In your case, assigning the weights in #1 would probably be fine. You'll need to fine-tune the algorithm depending on what your users consider more important - you could expose the weights wx as a filter (like 1-10 dropdown) so your users can adjust their search on the fly. Or if you wanted to get clever you could poll your users before they're searching ("Which is more important to you?") and then assign a weighting set based on the response, and after tracking enough polls you could autosuggest the weighting scheme based on most responses.
Hope that gets you on the right track.
What about having variable weights, and letting the user adjust it through some input like levers, so that the sort order will be dynamically updated?