Questions tagged [math]
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19
questions
1
vote
1answer
49 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
52 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:
$$RMW_t^w = \left[\left(\frac{RMW_1}{100} + 1\right)\left(\frac{RMW_2}{100}+1\right)...\...
6
votes
4answers
1k views
Interview Question - Card betting
I had to answer questions for a job interview today and I got these questions. I had no idea how to answer them.
There is a deck of 12 cards numbered 1 to 12.
One card is pulled from the deck at ...
1
vote
1answer
42 views
Why the variance of a process is $\left( \frac{dS_T^2}{dt}\right)^2$?
Consider an Ito process $dS_t = f(t,S_t) dt + g(t,S_t)dW_t $
What is the reason that we can compute the variance as:
$\sqrt{VaR(S_t)} = \frac{(dS_t)^2}{dt}$
1
vote
1answer
43 views
How is hypothesis testing work in population sampiling? [closed]
I am learning the basics of quant trading from quantconnect's tutorial Confidence Interval and Hypothesis Testing. I understood the first part of the article but I dont understand "Hypothesis Testing"...
3
votes
1answer
150 views
Finding optimal trading of option on a foward
Assume you have a option on a forward $F$ with a payoff: $\max(F_T - K, 0)$.
Assume also, that you have a bullish view on the forward in such a way that $E_{0}[F_T] > F_0 = E_{0}^{*}[F_T]$ (where ...
1
vote
1answer
56 views
Finding the extrinsic value of an option with conditions
Background:
Consider a spread option with the payoff $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant.
Let's also assume, that the correlation ...
1
vote
0answers
39 views
Evaluating contract $D$ where the stock follows the Black Scholes assumption
Ch.7 Mark Joshi Problem 14
A contract, $D$, pays $30\%$ of the increase (if any) of a stock's value in a year. If $S_t$ follows Black-Scholes assumptions, give a formula in terms of the Black-...
0
votes
1answer
79 views
Properties of Brownian motion and filtration, Exercise 6.22, Joshi Concepts and applications to mathematical finance
Let $W_t$ be a Brownian motion, and let $F_t$ be its filtration then for $t > s$ we are asked to compute
$$\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
121 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
173 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
73 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
187 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
738 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
179 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
97 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
239 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
36 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
64 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 ...
