# Questions tagged [mathematics]

Used for question on application of mathematics in finance - from interest calculation to mathematical description of random processes.

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33 views

### 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 ...
29 views

### 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 ...
40 views

### 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/...
121 views

### 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 ...
254 views

### 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 ...
53 views

### 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 ...
1 vote
88 views

### 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 ...
413 views

### 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 ...
4k views

### 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 ...
122 views

### 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 $S$ ...
135 views

### 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 ...
1 vote
65 views

### 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/...
242 views

### Reflection principle of the Brownian motion

really appreciate some guidance on how to get the following equality:
1 vote
79 views

### 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) \...
42 views

### 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 $\widehat{p}$ ...
977 views

### 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 ...
69 views

### 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 ...
329 views

### 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 ...
97 views

### 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 ...
959 views

### 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;...
1 vote
114 views

### 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 ...
43 views

### 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 ...