# 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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175 views

### Reflection principle of the Brownian motion

really appreciate some guidance on how to get the following equality:
51 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) \...
36 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 $\widehat{p}$ ...
39 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 ...
36 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 ...
425 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 ...
45 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 ...
89 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 ...
64 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 ...
205 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;...
77 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 ...
30 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 ...
170 views

Question: The Black-Scholes equation without dividend is given by $$\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2} + rS \frac{\partial V}{\partial S} -rV = ... 0answers 40 views ### Estimator for Conditional value at risk (average value at risk) I am following a book: Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization by Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi I'm learning about average value at risk. ... 1answer 401 views ### Do quants need to know bloomberg terminal and VBA? [closed] I am a Pure Maths PhD student who will graduate in 2 years time. My aim is to land a quant job after gradauation. When collecting more information so that I can have some edges over others, I heard ... 1answer 48 views ### How is hypothesis testing work in population sampiling? [closed] I am learning the basics of quant trading from quantconnect's tutorial Confidence Interval and Hypothesis Testing. I understood the first part of the article but I dont understand "Hypothesis Testing"... 1answer 233 views ### Forward Start Spread Options Question: We have a spread option with payoff: \max (P_{T} - HR\times G_T, 0), where P, G are underlying prices and HR is a constant. At time zero only contract G is available for ... 4answers 1k views ### Examples of discrete math and graph theory within quantitative finance The Wikipedia article on quants mentions discrete mathematics as a possible piece of their mathematical background. Are there good examples of problems within quantitative finance that are heavily ... 0answers 48 views ### Stochastic integral representation of F(T-s,X_s)-type equations For T\in R given and fixed consider:$$ {\rm d}F(T-t,X_t)=g(T-t,X_t)\,{\rm d}W_t. $$where g(t,x) is a given functions and X_t is a given process driven by a brownian motion (dX_t=(...)dt+(...)... 0answers 48 views ### Transformation of random variables and second-order stochastic dominance Suppose X and Y are two random variables where X SOSD* Y. Let g(\bullet) be a monotonic function and X'=g(X) and Y'=g(Y). Under what conditions of g is X' SOSD Y'? I know if g ... 1answer 72 views ### Why do most interest rate formulas, and indeed finance in general, add 1 to a rate and then subtract afterwards? [closed] For example, in the formula that shows the relationship between the nominal and effective interest rate shown below, 1 is first added to in/m and then 1 is subtracted from the result. What is the ... 1answer 216 views ### Approximation of Forward Rates in discrete time The forward rate from time t to T (f_{t,T}) can be approximated by:$$ f_{t,T}= \left[ \frac{(1+r_T)^T}{(1+r_t)^t} \right]^{\frac{1}{{T-t}}}-1 \sim \frac{(1+r_T)^T-(1+r_t)^t}{T-t} $$Why is ... 1answer 84 views ### standard brownian vs brownian motion We say Xt with paramters (µ,σ) is brownian process if (Xt-s - X t) ~N (µs,σ2 s) AMONG other conditons . Here we don't speak about any particular distribution for X t. We only say it is a brownian ... 1answer 148 views ### Finding the process of X/Y This comes from Mark Joshi's concepts of mathematical finance exercise 4 chapter 11. If$$dX_t = \alpha X_t dt + \beta X_t dW_tdY_t = \alpha Y_t dt + \gamma Y_t d\tilde{W}_t$$with W ... 3answers 376 views ### Is there an intuitive explanation for why Kelly gambling ignores odds? I have just learned about Kelly gambling from Chapter 6 of Cover & Thomas' Introduction to Information Theory. The mathematical setup is that we have a horse race, with horse i winning with ... 1answer 92 views ### 4-point Trapezium rule for numerical integration Background: This is in reference to Mark Joshi's concepts of mathematical finance ch.7 problem 11. Question: We have in the Black-Scholes model: S_0 = 1, T = 1, \sigma = 0.1, r = 0. A ... 1answer 170 views ### Anti-thetic sampling and second moment matching Background: This is in reference to ch 7 problem 10 of Mark Joshi's concepts of mathematical finance. Question: A normal random generator produces the following draws:$$0.68, -0.31, -0.49, -0....
Suppose a stock allows a geometric Brownian motion in a Black-Scholes world. Develop an expression for the price of an option that pays $S^2 - K$ if $S^2 > K$ and zero otherwise. What PDE will this ...