Questions tagged [math]
The math tag has no usage guidance.
28
questions
1
vote
1answer
120 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, ...
0
votes
1answer
60 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.
1
vote
1answer
48 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 ...
5
votes
1answer
804 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-...
1
vote
1answer
60 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 ...
0
votes
1answer
338 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 ...
1
vote
2answers
189 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 ...
1
vote
0answers
152 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 ...
1
vote
0answers
37 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 ...
1
vote
1answer
58 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 ...
2
votes
0answers
88 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:
$$RMW_t^w = \left[\left(\frac{RMW_1}{100} + 1\right)\left(\frac{RMW_2}{100}+1\right)...\...
6
votes
4answers
2k views
Interview Question - Card betting
I had to answer questions for a job interview today and I got these questions. I had no idea how to answer them.
There is a deck of 12 cards numbered 1 to 12.
One card is pulled from the deck at ...
1
vote
1answer
49 views
Why the variance of a process is $\left( \frac{dS_T^2}{dt}\right)^2$?
Consider an Ito process $dS_t = f(t,S_t) dt + g(t,S_t)dW_t $
What is the reason that we can compute the variance as:
$\sqrt{VaR(S_t)} = \frac{(dS_t)^2}{dt}$
1
vote
1answer
48 views
How is hypothesis testing work in population sampiling? [closed]
I am learning the basics of quant trading from quantconnect's tutorial Confidence Interval and Hypothesis Testing. I understood the first part of the article but I dont understand "Hypothesis Testing"...
3
votes
1answer
159 views
Finding optimal trading of option on a foward
Assume you have a option on a forward $F$ with a payoff: $\max(F_T - K, 0)$.
Assume also, that you have a bullish view on the forward in such a way that $E_{0}[F_T] > F_0 = E_{0}^{*}[F_T]$ (where ...
1
vote
1answer
72 views
Finding the extrinsic value of an option with conditions
Background:
Consider a spread option with the payoff $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant.
Let's also assume, that the correlation ...
1
vote
0answers
44 views
Evaluating contract $D$ where the stock follows the Black Scholes assumption
Ch.7 Mark Joshi Problem 14
A contract, $D$, pays $30\%$ of the increase (if any) of a stock's value in a year. If $S_t$ follows Black-Scholes assumptions, give a formula in terms of the Black-...
0
votes
1answer
90 views
Properties of Brownian motion and filtration, Exercise 6.22, Joshi Concepts and applications to mathematical finance
Let $W_t$ be a Brownian motion, and let $F_t$ be its filtration then for $t > s$ we are asked to compute
$$\mathbb{E}\left[W_t^2|F_s\right]$$
We have $$W_t = W_s + (W_t - W_s)$$
and
$$W_t^{2} ...
3
votes
1answer
173 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
$...
0
votes
1answer
238 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 ...
1
vote
0answers
87 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 ...
1
vote
0answers
223 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,...
1
vote
1answer
3k 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 ...
0
votes
1answer
355 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}_\...
-1
votes
2answers
135 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 $\...
-2
votes
1answer
305 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 ...
0
votes
1answer
38 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 ...
1
vote
1answer
72 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 ...
