Questions tagged [math]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
0answers
30 views

How do i calculate Monthly French Fama RMW and CMA?

i have tried to calaucte the values from daily -> weekly. I have cumulated all. First, i have dived all by 100, than (RMW1+1)*(rmw2+1).......)-1 but the results are not the same as in the values given ...
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

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"...
1
vote
1answer
39 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: $\sqrt{VaR(S_t)} = \frac{(dS_t)^2}{dt}$
3
votes
1answer
143 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
54 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-...
3
votes
1answer
108 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
73 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} ...
0
votes
1answer
155 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
71 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
169 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
651 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
155 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
96 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 $\...
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 ...
-2
votes
1answer
223 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 ...
1
vote
1answer
62 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 ...