# 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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### What is the Accumulation/Distribution formula doing geometrically?

My understanding of the essence of the Accumulation/Distribution Index is that it tracks the closing price of a security during each period relative to its price range for that period, something like ...
104 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 $S$ ...
61 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 ...
26 views

### fulfilling the condition for backtesting scalping technique

I am backtesting scalping technique with the 3 sma, in aligator indicator. One of the conditions for scalping long, would be to see alll the three ema's are radiating out from one another as in the ...
1 vote
58 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/...
201 views

### Reflection principle of the Brownian motion

really appreciate some guidance on how to get the following equality:
1 vote
58 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) \...
38 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 $\widehat{p}$ ...
136 views

### How to handle negative income tax when calculating EBIT

I am using the formula (Net income + interest expense + tax expense) to get my calculation What happens if the Income tax expense is negative for that year do you still add that negative number or do ...
60 views

### How to calculate NOPAT if the effective tax rate is 0 or negative

I am trying to calculate NOPAT for L S STARRETT CO. The effive tax rate I calculated for 2020 was -0.09% Operating Income was -5.3 mill. Using the NOPAT formula Operating Profit * (1 - tax rate) I got ...
604 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 ...
52 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 ...
120 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 ...
72 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 ...
388 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
89 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 ...
34 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 ...