Questions tagged [mathematics]
Used for question on application of mathematics in finance - from interest calculation to mathematical description of random processes.
197
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Exponential smoothing - alpha choice with given half-life
I have daily data for a year and I would like to perform exponential smoothing on this data:
I want a half-life of 3 months out of 12.
What is the formula to find the alpha then?
Thanks for your ...
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29
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How to tell when a vector (9-tuple) changes structure over time?
I have a 9-element vector I compute at any time T that is derived from the state of the order book. I plot the elements over time and get something like this:
I'm interested to see when the nature of ...
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5
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Does anyone know where to practice mental math for trader interviews in MC format? [duplicate]
I am currently using zetamac (has customizable number ranges but doesn't allow for decimals), tradermath (seems to be made to resemble the actual test for flow but costs money unfortunately), and ...
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1
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Swap contract comparative advantage
Corporation $A$ has an excellent credit rating and can borrow at a fixed rate of $5\%$ or a floating rate of LIBOR + $1\%$. Corporation $B$ has a somewhat less excellent credit rating and can borrow ...
5
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1
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How to find interesting open math problems in quantitative finance that I could publish articles about?
Which books on financial mathematics would you recommend for people with good background in probability, statistics and stochastic processes but without any background in financial mathematics?
The ...
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1
answer
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Calculate Federal Reserve Dollar Indexes
I'm attempting to validate the formula used to calculate the Federal Reserve Dollar Indexes, as published on January 15, 2019, in this document: https://www.federalreserve.gov/econres/notes/feds-notes/...
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1
answer
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Is the Gittins index useful in determining when to change an investment/trading strategy?
I've been reading about multi-armed bandits and the explore/exploit trade-off that can be solved with dynamic allocation indices such as the Gittins Index Theorem. Could this be applied to when to ...
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How can I go about applying machine learning algorithms to stock markets?
I am not very sure, if this question fits in here.
I have recently begun, reading and learning about machine learning. Can someone throw some light onto how to go about it or rather can anyone share ...
3
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1
answer
254
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Proper way to backtest strategy using bootstrap method
Should I back-test in a single (original) price series and bootstrap the strategy returns to get statistics of interest?
Or should I create bootstrapped price series using bootstrapped returns from ...
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4
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Implications of the Riemann hypothesis in finance?
I was recently at a seminar by a top hedge fund manager at a top university for finance students, when one of the finance professors asked him what do you think are important areas of research for my ...
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Hurst Exponent and Smoothed Hurst Exponent values are the same and incorrect plotting
I'm working on a script to calculate and plot the Hurst Exponent and Smoothed Hurst Exponent for a stock's historical price data using Python. When I run the script, I face two major issues:
The ...
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How to analyse the resilience of banks during financial crises using linear regression and other statistical methods?
I am a student in finance and have to work on a project for the semester.
I have to study the difference of resilience during financial crises between the 5 biggest US banks and the 5 biggest Canadian ...
- 8,438
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0
answers
329
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What is the relationship between Vanna and Gamma?
I'm trying to build a crude model for the effects of delta hedging on major indices like the S&P 500. My background is more in pure mathematics so a lot of this stuff is new to me. That said I ...
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How random are financial data series?
Pseudorandom number generators are often tested using e.g. a test suite like Diehard tests or Dieharder. If one would run these tests e.g. on stock market time series or other financial data, would ...
CommunityBot
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What are the requirements for no arbitrage to exist in a chaotic/dynamical system?
Consider the continuous dynamical system
$$\alpha\ddot{S}+\dot{S}=\mathcal{F}(S,t),$$
such that $\alpha\in\mathbb{R}$ and $\mathcal{F}$ is real and analytic. We assume that if a solution for $S$ ...
- 128
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135
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Zero coupon price using Vasiceks model under the Real-world P measure model
I'm wondering if there is a way to work out the formula for the price of the zero-coupon bond using the Vasicek's model (P measure). I have tried to find reference on it but could not, I don't know if ...
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Sharpe ratio and uniformly distributed random portfolio
I am currently working on this paper which derives the Sharpe ratio distribution of uniformly random porfolios:
https://www.researchgate.net/publication/...
- 43
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1
answer
242
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Reflection principle of the Brownian motion
really appreciate some guidance on how to get the following equality:
- 5,008
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0
answers
79
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Bergomi's model normalisation
On his book https://www.amazon.fr/dp/B019FNKQS8/ref=dp_kinw_strp_1 Bergomi derives a multifactor mean reversible volatility of the volatility such that :
\begin{equation*}
d \xi_{t}^{T}=\omega(\tau) \...
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how can properties of transition matrix be applied in the transcation cost of option
I am currently reading the PP BOYLE's article ' Option Replication in Discrete Time with Transaction Costs' written in 1992. Here is one place i couldn't figure out:
Where does that $\widehat{p}$ ...
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2
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How do you derive this Carr-Madan-like equation?
How do you derive equation (3) below? The equation is tagged as equation (11) in this paper:
http://janroman.dhis.org/finance/IR/Heston%E2%80%93Hull%E2%80%93White%20Model%20Part%20I.pdf
There are ...
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1
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One-Period Binomial Model
So, I'm required to consider the one-period Binomial market model for a particular question. We're told that the savings account is \$1 at time 0 and \$β at time 1. The stock price is given by S0 = 1 ...
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1
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Anti-thetic sampling and second moment matching
Background:
This is in reference to ch 7 problem 10 of Mark Joshi's concepts of mathematical finance.
Question:
A normal random generator produces the following draws:
$$0.68, -0.31, -0.49, -0....
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1
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97
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Calculate resistance / support on 5 minutes timeframe
I'm starting to learn resistance / support.
I'm trying to calculate it, but i'm not sure to understand something.
Let say i have an array of 5 last trades done (i can have much more, it's just for the ...
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1
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959
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Optimal Strategy in 3 Dice Game
In a recent interview I received the following question (an optimisation/strategy game)...which left me a bit stumped.
The rules of play, you start with 0 points, then:
Roll three fair six-sided dice;...
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1
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128
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help with derivation of equation 8 in Derman and Kani's binomial tree for local vol
in this paper "The Volatility Smile and Its Implied Tree" - Derman and Kani 1994 i understand the derivation of all equations up to 7.
But eq 8 i cannot figure out how to derive! i have ...
CommunityBot
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Prove norm $\frac{1}{p}\sum_{i=1}^n |w_i|^p$ of min-variance portfolio $\leq$ max-Sharpe portfolio
The minimum-variance portfolio weight vector is
$$\boldsymbol{w}_{MV} = \frac{\boldsymbol{\Sigma}^{-1} \boldsymbol{1} }{\boldsymbol{1}' \boldsymbol{\Sigma}^{-1} \boldsymbol{1}}$$
whereas the maximum ...
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Calculating currency indexes weights?
I was looking at this formulas:
USD_INDEX= 50.14348112 × EURUSD^-0.576 × USDJPY^0.136 × GBPUSD^-0.119 × USDCAD^0.091 × USDSEK^0.042 × USDCHF^0.036
and
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1
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663
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Mathematical proof that the covariance between two portfolios is $w_A^\top\Sigma w_B$
How to prove in a line-by-line derivation that the covariance between two mean-variance efficient portfolios is equal to
$$w_A^\top\Sigma w_B$$
where $w_i$ is a unique portfolio weight vector, and $\...
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0
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97
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Mathematical proof of out-of-sample disappointment in portfolio performance being a function of a portfolio's variance
The minimum-variance portfolio is considered more optimal than the maximum Sharpe ratio (tangency) portfolio on the grounds that its in-sample performance is less likely to disappoint out-of-sample.
...
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0
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Entropy-implied volatility requires itself to be calculated?
\begin{align}
H &= \frac{1}{2} \ln (2\pi\sigma^2) + \frac{1}{2}\\
&= \frac{1}{2} \ln (2\pi e \sigma^2)
\end{align}
is the analytical solution for the entropy of a Gaussian random variable, ...
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4
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Examples of discrete math and graph theory within quantitative finance
The Wikipedia article on quants mentions discrete mathematics as a possible piece of their mathematical background.
Are there good examples of problems within quantitative finance that are heavily ...
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Estimating the XIRR of a very non uniform cash flows
It's my second post, so please bear my lack of experience in this field.
I've a very irregular cash flow (here you can see the set of date - cumulative cash flow)
The XIRR, calculated with Excel, is ...
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2
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3k
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Preparation for interview: influx of power of the moon
I am preparing myself for an interview for a quantitative analyst position and one of the sample questions asked in previous examinations was:
"Suppose the moon were to disintegrate, and fall to ...
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1
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Does Value-at-Risk have any mathematical equivalence to copulas?
Portfolio Value-at-Risk estimated using the copula approach often just means generating artificial data sampled from a parametric copula('s joint multivariate distribution) as a model fit over the ...
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1
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Question on the use of a limit in a proof
I ran into a step in an argument that I can't quite figure out. It's basically how they use a limit that I don't seem to understand. The context is local-to-unity asymptotics in vector autoregressions,...
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1
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Contingent Claim Bounds
In my course on discrete-time finance we derived the following equality for a lower bound for the value of a not necessarily replicable contingent claim $D$. Here we are looking at a single period ...
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1
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Option proofing: Analytical solution for option math
How do I prove the following equation:
P(X=100)≤(P(X=110)-P(X=90))/2
I am not sure how to start and whether it involves using the Black-Sholes formula or not (something like this: https://www.youtube....
- 2,996
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0
answers
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Why does the Hurst exponent pseudo code not match the Python implementation?
I am working on understanding the Hurst exponent calculation by Ernest Chan; however, the description of the algorithm does not match the Python implementation.
Chan [Algorithmic Trading: Winning ...
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2
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Is there a way to formulate a Martingale series that will never explode?
Martingale's betting method can be seen here:https://www.investopedia.com/articles/forex/06/martingale.asp My question is if there is a way to put a non-exploding martingale,
[There is one attempt to ...
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The distribution of mean reversion time from the OU process
I was reading the paper Statistical Arbitrage in the US Equity Market and I couldn't understand the figure that plots the histogram of the empirical distribution of characteristic time to mean ...
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111
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What is the differential Value-at-Risk?
I am currently working on a Machine Learning Project, implementing portfolio optimization algorithms according to different risk measures. I have found sufficient information on Sharpe Ratio ...
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0
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226
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Dynamic programming and Bellman equation to obtain the maximum
This is the problem of Marhsall (1992) "Inflation and Asset Returns in a Monetary Economy" and Balvers and Huang (2009) "Money and the C-CAPM"
Suppose an endowment economy where the representative ...
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1
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Is the variance calculation correct in the book?
I'm reading the book "Financial Markets Under the Microscope" for my market microstructure studies. In the book, the variance of the market maker's gain is calculated as follows:
Assume that with ...
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1
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CDS protection/contingent leg pricing, taking expectation of interest and hazard rates
The Pricing and Risk Management of Credit Default Swaps, with a Focus on the ISDA Model
Screenshot: Pricing protection leg of a CDS, by OpenGamma
In the screenshot above, I am having trouble ...
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1
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321
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How can I convert rolling annual returns back to quarterly returns?
I have a series of rolling annual returns and would like to convert these back to quarterly returns, which have not been provided. Is this possible formulaically, or is something like Excel's solver ...
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Abstract algebra in economics and finance
Are there any applications of abstract algebra (group theory, rings, fields etc.) in any branch of either economics or finance?
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2
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Hurst Exponent Calculation
I am trying to calculate the Hurst Exponent using Excel. I am facing a problem where the exponent value sometime goes beyond 1. Can someone share a link / material so that it will help me to calculate ...
2
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1
answer
3k
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What is the formula to calculate Implied Volatility Percentile [closed]
I googled and I am unable to find any formular . Can some one give me the formula to calculate IVP , based on sets of IV's given.
Thanks.
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3
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How to calculate standard deviation of continuously compounded four-year stock returns?
Currently I am preparing for quant interview and I encounter the following question in Heard on the street.
Question: If the standard deviation of continuously compounded annual stock returns is $...
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