Questions tagged [math]

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how to use ratio spread?

If I sell more options, then my gamma risk will be more difficult to control, but if I sell too few options, then when I judge the wrong direction, I will leave the market with a loss. I try to ...
BearSpread's user avatar
8 votes
5 answers
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 ...
Quant In Spe's user avatar
2 votes
0 answers
62 views

How to train mental math for trading? [duplicate]

I have a mental math test coming up for a quantitative trading firm. Anyone knows good websites to practice?
Quant In Spe's user avatar
1 vote
1 answer
315 views

Dice question - expected winnings of rolling dice $2$ times

Typical trading interviews consider gambling problems such as rolling a dice and winning its face value. The expected winnings are $\\\$3.5$, $\\\$4.25$, $\\\$\frac{14}{3}$ for one throw, two throws, ...
The One's user avatar
  • 113
0 votes
1 answer
248 views

Bachelier call option derivative w.r.t strike

I tried to take the partial derivative of the Bachelier call function w.r.t. strike price K (eqn 2.2 here), but my result is not lining up with what is shown on page 43 here.
Jay's user avatar
  • 11
1 vote
1 answer
66 views

Calculating coupon yield and continous compounding

I need to calculate the yield of a 2 year Coupon Bond. Price = 98, Coupon = 3.5, N = 100. Now when I try to solve this, I arrive at the equation: $$ 98 = 3,5*e^{-y}+103,5*e^{-2*y} $$ But I can't ...
mindandfields's user avatar
4 votes
1 answer
2k views

Pre-requisite math books, to the pre-requisite math needed to become a front desk quant

This question is about the pre-requisites to the pre-requisite math needed to become a front desk quant. I have done research online and I found that there are a lot of recommended books as a pre-...
TryingHardToBecomeAGoodPrSlvr's user avatar
1 vote
1 answer
96 views

Determine the error term of SKEW-calculation

I am trying to recreate the CBOE's SKEW Index in Python. I need to calculate the errors terms that are adjustment terms for the differences between the atm strike ...
HJA24's user avatar
  • 73
0 votes
1 answer
575 views

Generate Monte Carlo simulation of multivariate lognormal or weibull distributions in R

I intend to perform a Monte Carlo simulation of asset returns in R. I am currently using the rmvnorm function in the mvtnorm R ...
sjedi's user avatar
  • 13
1 vote
2 answers
504 views

How much shall we bet on head/tail with $1m bankroll?

I was asked this question in a trading interview: how much would you bet in a game where you win 300 on tail and loses your 100 on heads? how much will you bet if you can play game once or multiple ...
aallove's user avatar
  • 31
1 vote
0 answers
301 views

How to compute prediction interval if using simple moving average t o predict?

If I want to use simple moving average to make a prediction. For example given h=1 and m=13. $\hat{x}_{t+1}=\frac{\sum_{j=1}^{13}x_{t-j+1}}{13}$. What is the prediction interval going to be? How to ...
Ericcheng's user avatar
1 vote
0 answers
40 views

Residual Income Valuation with Term Structure

I'm implementing a residual income model (RIM) to value stocks as described by Ohlson. https://pdfs.semanticscholar.org/c0a5/4ef41311951fe406d15cd7d7ce19502cdc7c.pdf The key to this model is ...
Mild_Thornberry's user avatar
1 vote
1 answer
62 views

partial derivatives of multivariable function

Looking to verify whether the following formulation is correct. Suppose we have the following function, relationships: $$y=f(x)$$ $$x=g(a,b)$$ $$y=f[g(a,b)]$$ Is the below correct (including ...
bob sacamano's user avatar
2 votes
0 answers
182 views

How do i calculate Monthly French Fama RMW and CMA?

I have tried to transform the values from daily $R^d_t$ to weekly $R_t^w$ by calculating the cumulative return: $$RMW_t^w = \left[\left(\frac{RMW_1}{100} + 1\right)\left(\frac{RMW_2}{100}+1\right)...\...
MR Flo's user avatar
  • 21
6 votes
4 answers
3k views

Interview Question - Card betting

I had to answer questions for a job interview today and I got these questions. I had no idea how to answer them. There is a deck of 12 cards numbered 1 to 12. One card is pulled from the deck at ...
Trent Conway's user avatar
1 vote
1 answer
58 views

Why the variance of a process is $\left( \frac{dS_T^2}{dt}\right)^2$?

Consider an Ito process $dS_t = f(t,S_t) dt + g(t,S_t)dW_t $ What is the reason that we can compute the variance as: $\sqrt{VaR(S_t)} = \frac{(dS_t)^2}{dt}$
econmajorr's user avatar
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
3 votes
1 answer
173 views

Finding optimal trading of option on a foward

Assume you have a option on a forward $F$ with a payoff: $\max(F_T - K, 0)$. Assume also, that you have a bullish view on the forward in such a way that $E_{0}[F_T] > F_0 = E_{0}^{*}[F_T]$ (where ...
Snorrlaxxx's user avatar
1 vote
1 answer
94 views

Finding the extrinsic value of an option with conditions

Background: Consider a spread option with the payoff $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant. Let's also assume, that the correlation ...
Wolfy's user avatar
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1 vote
0 answers
48 views

Evaluating contract $D$ where the stock follows the Black Scholes assumption

Ch.7 Mark Joshi Problem 14 A contract, $D$, pays $30\%$ of the increase (if any) of a stock's value in a year. If $S_t$ follows Black-Scholes assumptions, give a formula in terms of the Black-...
Wolfy's user avatar
  • 708
0 votes
1 answer
98 views

Properties of Brownian motion and filtration, Exercise 6.22, Joshi Concepts and applications to mathematical finance

Let $W_t$ be a Brownian motion, and let $F_t$ be its filtration then for $t > s$ we are asked to compute $$\mathbb{E}\left[W_t^2|F_s\right]$$ We have $$W_t = W_s + (W_t - W_s)$$ and $$W_t^{2} ...
Wolfy's user avatar
  • 708
3 votes
1 answer
242 views

Mark Joshi, The concepts and practice of mathematical finance chapter 6 exercise 20,21

Find the Black-Scholes price of an option paying $$(S_T^{\alpha} - K)_{+}$$ at time $T$. Solution - The forward price is given by $$F_T(t) = e^{r(T-t)}S_t$$ So, $$F_T(0) = e^{rT}S_0$$ and $...
Wolfy's user avatar
  • 708
0 votes
1 answer
308 views

Joshi, Exercise 2.7 Concepts of Mathematical Finance

Let $D(K)$ pay $(S - K)^2$ if $S > K$, zero otherwise. Show that if $D(K)$ is differentiable function of $K$ then the third derivative w.r.t $K$ is non-negative. From what the hint in the book, we ...
Wolfy's user avatar
  • 708
1 vote
0 answers
100 views

Moving average variance [closed]

I have generated a random series of returns drawn from a normal distribution and generated a random price series by compounding these returns (X) so $P_i = P_1(1+X)^i$. I want to show the analytic ...
markm's user avatar
  • 43
1 vote
0 answers
250 views

What jobs in Finance are most math intensive? [closed]

I'm a math major and I've always been really interested in Finance; however, I'm starting to enjoy math more and more and would like to know which jobs in Finance use the most/more advanced math. Also,...
Luís Ferreira's user avatar
1 vote
1 answer
4k views

Given two risky stocks calculate the rate of return, standard deviation, beta, and risk-free rate

Consider a world where there are only two risky stocks, $A$ and $B$, whose details are listed in the table below: Furthermore, the correlation between the returns of stocks $A$ and $B$ is $\rho_{A ...
Wolfy's user avatar
  • 708
0 votes
1 answer
477 views

Using CAPM to derive the following

Background Information: Say there are $s = 1,\ldots,S$ possible future outcomes (states) with known probabilities $\pi_s > 0$, $\sum_{s=1}^{S}\pi_s = 1$. Define the expected payoff as $\mathbb{E}_\...
user avatar
-1 votes
2 answers
173 views

Given three stocks what is the fraction of each stock's risk is diversified away

Consider an equally weighted portfolio of three stocks, each of which is independently distributed of the others but have the same risk. I.e., $cov(r_i, r_j) = 0$; $\forall i \neq j$, and $\...
Wolfy's user avatar
  • 708
-2 votes
1 answer
369 views

How to solve $dX_t = X_t(\sigma_t dW_t + \mu_t dt)$?

Solve the SDE $$dX_t = X_t(\sigma_t dW_t + \mu_t dt)$$ where $\sigma_t$,$\mu_t$ are deterministic. Attempted solution We have $$dX_t = X_t(\sigma_t dW_t + \mu_t dt)$$ Let $f(x) = \log X$, applying ...
Wolfy's user avatar
  • 708
0 votes
1 answer
45 views

Price of every asset in discrete market model strictly increasing

If the price of every asset in a discrete model is strictly increasing, with probability one, then does the market admit arbitrage? Thoughts: I believe this is true but I am not sure how to give an ...
Wolfy's user avatar
  • 708
1 vote
1 answer
81 views

Implied Expected Stock Return from European Option Prices

We can calculate the expected stock return (under the measure $Q$) from at-the-money ($K=S_t$) option prices as: $$E\left(\frac{S_T-S_t}{S_t}\right)=\frac{e^{rT}}{S_t}(C_t-P_t)$$ The result is ...
emcor's user avatar
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