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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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"Problems and Solutions in Mathematical Finance, Volume 3: Interest Rates and Inflation Indexed Derivatives" by Eric Chin

I've heard about the book "Problems and Solutions in Mathematical Finance, Volume 3: Interest Rates and Inflation Indexed Derivatives" by Eric Chin, Dian Nel, and Sverrir Olafsson. Does ...
Petra Di Mario's user avatar
-1 votes
1 answer
86 views

Mental math method for large integer multiplication

I am practicing for trading interview, especially the quick calculation of mental math. But I am wondering is there any quick method to calculate the general multiplication? like the one ...
Xu Shan's user avatar
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0 votes
0 answers
40 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 ...
Alex's user avatar
  • 101
0 votes
0 answers
35 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 ...
nxtronic's user avatar
0 votes
1 answer
43 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/...
jamacoe's user avatar
  • 129
2 votes
1 answer
141 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 ...
LattePrincess's user avatar
3 votes
1 answer
414 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 ...
Arun Lama's user avatar
1 vote
0 answers
91 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 ...
Haseo1997's user avatar
5 votes
1 answer
522 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 ...
Botnakov N.'s user avatar
8 votes
5 answers
6k 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 ...
Quant In Spe's user avatar
6 votes
0 answers
124 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 $S$ ...
UNOwen's user avatar
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2 votes
0 answers
159 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 ...
Daniel  Hong's user avatar
1 vote
0 answers
66 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/...
Valentin's user avatar
  • 135
2 votes
1 answer
249 views

Reflection principle of the Brownian motion

really appreciate some guidance on how to get the following equality:
ice_fox21's user avatar
1 vote
0 answers
83 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) \...
lays's user avatar
  • 446
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0 answers
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 $\widehat{p}$ ...
WHYisTHAT's user avatar
3 votes
2 answers
1k 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 ...
user54908's user avatar
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-2 votes
1 answer
72 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 ...
Aaron Mitropolous's user avatar
2 votes
0 answers
363 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 ...
Literally an Orange's user avatar
0 votes
1 answer
103 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 ...
Valentin Garreau's user avatar
2 votes
1 answer
1k 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;...
bob's user avatar
  • 29
1 vote
0 answers
124 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 ...
develarist's user avatar
  • 3,000
0 votes
0 answers
54 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 ...
Pedro Pablo Severin Honorato's user avatar
0 votes
1 answer
759 views

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 $\...
develarist's user avatar
  • 3,000
1 vote
0 answers
107 views

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. ...
develarist's user avatar
  • 3,000
0 votes
0 answers
63 views

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, ...
develarist's user avatar
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0 votes
0 answers
43 views

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 ...
Revious's user avatar
  • 103
1 vote
1 answer
131 views

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 ...
develarist's user avatar
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2 votes
1 answer
93 views

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,...
Stéphane's user avatar
  • 2,476
1 vote
1 answer
86 views

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....
S_Star's user avatar
  • 23
2 votes
1 answer
132 views

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 ...
Randor's user avatar
  • 786
2 votes
0 answers
597 views

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 ...
lalalal's user avatar
  • 23
1 vote
0 answers
146 views

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 ...
Peter's user avatar
  • 11
-1 votes
2 answers
115 views

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 ...
pinchas fogel's user avatar
0 votes
0 answers
114 views

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 ...
Nick's user avatar
  • 1
0 votes
0 answers
262 views

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 ...
Hunger Learn's user avatar
1 vote
1 answer
123 views

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 ...
xyzt's user avatar
  • 341
0 votes
1 answer
57 views

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 ...
Claudio Moneo's user avatar
2 votes
1 answer
410 views

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 ...
sb1's user avatar
  • 23
7 votes
1 answer
3k views

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?
SlavicDoomer's user avatar
2 votes
1 answer
4k views

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.
Gracie williams's user avatar
2 votes
1 answer
169 views

How can I express this sum in a easier way?

For instance, I know that the sum of the first $101$ natural numbers can be expressed in the following easy computation: $\sum_{i=1}^{101}i = \frac{101*102}{2}$ One of the questions is: and what ...
Nobody's user avatar
  • 175
4 votes
1 answer
1k views

What the expectation of S^2 is from GBM? [closed]

I was at an interview and was asked to write down the SDE for GBM. $$ dS = S\mu dt + S\sigma dX $$ Then I was asked how I would compute the expectation of S^2. I didn't know where to start. Any ...
Daniel's user avatar
  • 51
1 vote
3 answers
3k views

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 $...
Idonknow's user avatar
  • 840
2 votes
2 answers
5k views

How to derive Black-Scholes equation with dividend?

Question: The Black-Scholes equation without dividend is given by $$\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2} + rS \frac{\partial V}{\partial S} -rV = ...
Idonknow's user avatar
  • 840
2 votes
0 answers
54 views

Estimator for Conditional value at risk (average value at risk)

I am following a book: Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization by Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi I'm learning about average value at risk. ...
Ceeerson's user avatar
  • 205
0 votes
1 answer
655 views

Do quants need to know bloomberg terminal and VBA? [closed]

I am a Pure Maths PhD student who will graduate in 2 years time. My aim is to land a quant job after gradauation. When collecting more information so that I can have some edges over others, I heard ...
Idonknow's user avatar
  • 840
1 vote
1 answer
58 views

How is hypothesis testing work in population sampiling? [closed]

I am learning the basics of quant trading from quantconnect's tutorial Confidence Interval and Hypothesis Testing. I understood the first part of the article but I dont understand "Hypothesis Testing"...
Eka's user avatar
  • 647
2 votes
1 answer
332 views

Forward Start Spread Options

Question: We have a spread option with payoff: $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant. At time zero only contract $G$ is available for ...
Wolfy's user avatar
  • 728
5 votes
4 answers
2k views

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 ...
Juho's user avatar
  • 153