Questions tagged [finance]
Questions having to do with financial mathematics. This is not a tag about financing, which is not within the scope of mathematics defined by the help center: http://math.stackexchange.com/help/on-topic Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.
0
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0answers
24 views
Dividend paying option
An American call option with exercise price $K = 90$ written on an asset where the asset prices in dollars are given below, the interest rate per period is zero, and a dividend of $5$ is paid between ...
0
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0answers
34 views
VaR and ES of Bonds
An investment is composed by 2 defaultable bonds. Each bond has a 3% probability of default. The default probabilities are independent. When a bond defaults the investor loses $50.
a) Find the value-...
2
votes
0answers
34 views
Writing out a differential equation
Someone deposits money in a bank account at a continuous rate of $5000$ per year, and the account earns interest at a continuous rate of $7\%$ per year. Is the differential equation for the balance $B$...
-1
votes
2answers
19 views
Tax rate question
How do you solve this question?
A company has taxable income $758,000. The federal tax is 35% of that portion
left after the state tax has been paid. The state tax is 15% of that portion after
...
0
votes
0answers
15 views
Calculate annual loan rate having loan amount, total payment and loan period
The problem is:
I want to borrow an amount of money loanAmount for a period of period and I have to calculate the ...
1
vote
0answers
22 views
Annuities, lottery and interest rate
I am having trouble doing this question.
Mary Jones won $\$4,000,000$ in a state lottery.
She will receive a cheque for $\$200,000$ now and a similar one for each year for 19 years. To provide ...
0
votes
0answers
15 views
Convert formula to look for rate [on hold]
This is the formula used in excel
$ PV*((1+Rate)^nper) + pmt(1+rate*type) * (((1+rate)^Nper) -1 )/ rate)+ FV = 0 $
What is the equivalent formula when you are specifically looking for "rate"?
Thanks!...
0
votes
0answers
14 views
Why is the bond market arbitrage-free?
In the book "Martingale methods in Financial modelling" it says that the family of bond-prices are arbitrage free if there exists an equivelent martingale measure such that
$B(t,T)=E_{P^*}[e^{-\...
-1
votes
0answers
8 views
cumulative dividend in risk neutral pricing [on hold]
In this question, we consider a derivative whose payoff at time T is the cumulative dividends of the risky asset over the time period 0 to T.Derive an explicit expression for the price of this ...
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0answers
11 views
Put-Call Parity for a stock with dividends in Black-Scholes
I want to find a put-call parity relation for European options in the Black-Scholes model where the underlying stock pays a continuous dividend.
I know that the relation will be $$S_0e^{-\delta T} - ...
0
votes
0answers
19 views
Given a trading strategy, find another that meets the definition of an arbitrage opportunity.
Suppose we have a self financing trading strategy $\varphi=(\varphi_{t})_{t=1}^{T}$ such that $V_{0}(\varphi)=0$ and there exists some $0 < t_{0} \leq T$ such that:
$$V_{t_{0}}(\varphi)\geq 0 \...
0
votes
0answers
61 views
Stochastic Integral with exponential
Good day,
I am working with Ito's formula for both time dependent and time independent $f$'s. $S(t)$ is, as usual, asset price and $W(t)$ is a Brownian Motion (or Weiner Process).
$$\int_0^T exp\...
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votes
1answer
33 views
Financial Math Problem
Q: John is to invest $100 at the end of every 3 months for the next 12 yrs. 20 years from now he will retire. Calculate the amount of accumulated money he will have when he retires if the money is ...
0
votes
0answers
6 views
The formula of CCI (Commodity Channel Index) indicator in stock market and the mathematical proof of it.
I am looking for the formula of CCI oscillator and the mathematical proof. If you can advise me some references, I am really thankful! Thank you so much!
0
votes
0answers
20 views
Brownian motion to model future asset values
https://quant.stackexchange.com/questions/45104/brownian-motion-for-modelling-future-asset-values
Assume that an asset price $S$ is given by a Brownian motion. Argue from the definition why it is ...
0
votes
1answer
21 views
Compounded Interest homework help problem!
How would I do the following problem:
Jimmy opens a savings account with a X deposit at the beginning of the month. The account earns P% annual interest compounded monthly. At the beginning of each ...
0
votes
1answer
18 views
How do I solve for n (number of periods) in a loan repayment formula?
Where
A = payment Amount per period
P = initial Principal (loan amount)
r = interest rate per period
n = total number of payments or periods
How can I rearrange the formula to solve for n?
1
vote
1answer
26 views
Formula for calculating total interest that will be paid over non-fixed loan
I am trying to calculate the lifetime interest paid on a credit account. I know that I can enter it into a spreadsheet and take the sum of the interest, but is there a formula to calculate such a ...
0
votes
0answers
17 views
How do I calculate a monthly payment from the *beginning* of the month?
I'm needing to calculate monthly payments -- but from the beginning of the month, as opposed to the end which appears to be standard. This is the standard monthly payment formula:
$$M = P\frac{i(1+i)^...
0
votes
0answers
10 views
Widow annuity- change of mortality
I have a task:
Take widow annuity for her (x), which pay 1000 per year from the death of him (y). Premium will be paying as continuous annuity until the time of first death with intensity $P$. We ...
0
votes
0answers
17 views
$\text{ES}_{X^2}(p)$ where $X\sim \mathcal{N}(0,1)$
I am studying for my final exam and solving practice problems. One of the problems I solved was to calculate $\text{VaR}_{X^2}(p)$ and I managed to get;
$$\text{Var}_{X^2}(p)=\left[\Phi^{-1}\left(1-\...
0
votes
0answers
24 views
Fair price of a coupon paying bond
Consider a coupon paying bond with a maturity of $3$ years, that pays coupon annually. Let $c$ be the coupon rate (percentage) and let $F$ be the face value. This means that the holder of the bond ...
0
votes
1answer
23 views
Does PCA always have to reduce dimensionality?
I came across this paper where the authors implement a regularized learning model to estimate the covariance matrix of a dataset. The authors say they "...propose a regularized form of Principal ...
0
votes
2answers
35 views
Construct portfolio given certain payoff function
My question is similar to https://quant.stackexchange.com/questions/37419/replicate-a-portfolio-with-given-payoff but I am not quite sure how to apply this to my problem.
A portfolio of European ...
0
votes
0answers
7 views
Interest Rates. Amortization. Finding the balance after n payments have been made.
$B=$ Balance after n payments
$L=$ Loan amount
$i=$ Interest rate per period
$P=$ Payment
The formula I found online at the website https://brownmath.com/bsci/loan.htm is:
$B=[L(i+1)^n]-\frac{p}{...
0
votes
0answers
12 views
Formula for CDF of investment returns with continuous addition to principal
Assuming returns are normally distributed, the probability of returns is given by:
$$
\text{Lognormal}((\mu-\sigma^2/2)T,\ \sigma\sqrt{T})
$$
Where $\mu$ is the expected return of the stock and $\...
0
votes
1answer
20 views
Formula for CDF of investment returns
How can I calculate a cumulative density function or probability density function for investment returns based on expected return of a stock and volatility of a stock?
My current solution is below, ...
1
vote
1answer
39 views
Calculating monthly payments of a savings plan
The question reads:
A savings plan requires you to make payments of £250 each at the end of every month for a year. The bank will then make six equal monthly payments to you, with its first payment ...
0
votes
1answer
38 views
Flat tax on an evolving value
I am going to deposit 261.33€ on an account each month.
Each month, 0.1% of the total value of the account is debited. So for the first month with the account starting at 0, it would be 261.33 * 0.1% ...
1
vote
2answers
32 views
How to Annualised 3months monthly returns?
Hungary's monthly CPI growth rate has been as follows for the past 3 months:
Dec 18 - $2.8\%$
Jan 19 - $3.2\%$
Feb 19 - $3.5\%$
I am wondering how you'd calculate the annualized growth rate $r$ ...
0
votes
0answers
26 views
Looking for a book about mathematical proof of technical analysis in trading stocks!
I am looking for a book which contents mathematical proof of technical analysis in trading stocks! I have read a lot about techniques in trading stocks, but never that they prove it. I am really ...
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votes
0answers
8 views
NPV of investment
Firms initial fund: 600
investment opportunity: $420
Investment return rate: 35%
market rate 15%
FV of investment = 420*1.35=$567
NPV = FV/(1+r)t - investment
NPV = 567/1+0.35 - 420
NPV = 73.04
...
0
votes
0answers
14 views
How long to repay a loan with quarterly payments
I am currently studying financial management and am at a loss of how to calculate this:
One of your friends takes a loan of 10,000 from a bank at 14% interest rate. If your friend plans to repay $1,...
2
votes
0answers
60 views
How to solve the following (heat?) equation?
Let $u(x,t)$ be defined on $\Bbb R\times [0, T]$ such that:
$$u_t + (a - bx) u_x + \frac12 c^2 u_{xx} = xu,\quad u(x,T)\equiv 1$$
in which $a,b,c>0$ are constants. How to solve this PDE? Is it ...
0
votes
0answers
23 views
Prove that this set of expected values is convex
I am facing the problem of proving that the following set $K$ is convex, it's part of a proof for the First Fundamental Theorem of Asset Pricing:
$$K := \{d \cdot E_\mathbb{Q}(\boldsymbol{X}): \...
1
vote
0answers
26 views
What is the Feynman Kac Formula for the Merton model
I know that for the diffusion process
$$
X_t = \mu(t, X_t) dt + \sigma(t, X_t) dB_t,
$$
the function
$$
u(t, x) = \mathbb{E}_{x, t}[e^{\int_t^T r(s, X_s) ds} g(X_T)]
$$
with the boundary condition $u(...
1
vote
0answers
15 views
Black Scholes Framework
Assume the Black-Scholes framework. You are given:
•A stock S pays no dividend
•The continuously compounded risk-free interest rate is 8.5%
•A contingent claim Y pays $\frac{S(4)}{S(2)...
0
votes
0answers
26 views
Weekly Compounding Amortizing Loan
I'm trying to understand the example stated on the Fundbox 'How It Works' site and calc the compounded annual rate.
The site is here.
The data they provide is:
$1000 loan
12 week term
4.66% rate
...
0
votes
0answers
14 views
Universal Portfolios: Re-creating the simple example.
I have just become aware of a very interesting theory for portfolio management which is grounded in mathematics, called Universal Portfolios. I am focused on the paper of the same name, here's a link. ...
0
votes
1answer
32 views
Proposed 'exact' solution for the Asian Option
https://www.researchgate.net/profile/Moawia_Alghalith/publication/331075967_Exact_Pricing_of_the_Arithmetic_Asian_Options_A_Simple_Formula/links/5c704a07a6fdcc47159419a0/Exact-Pricing-of-the-...
0
votes
0answers
16 views
Can row/column penalty be zero in Vogel's Approximation Method?
If I have row with the following digits 10, 5, 12, 16, 5, 7
Will the row penalty be
5-5=0
or
7-5=2
In most books they ...
1
vote
1answer
34 views
Best Buy marked a computer down from $\$4,500.00$ to $\$3,300.00$. What was the total percent markdown based on its original price?
I've tried doing this problem several ways and I can't seem to achieve the given answer of $41.3\%$.
0
votes
1answer
24 views
Join of random variables - relation to max
On Wikipedia in the article Snell envelope author uses 'join' operation on random variables. Following line is relevant:
$$ U_n = X_n \lor \mathbb{E}^\mathbb{Q}[U_{n+1} | \mathcal F_n] \quad \text{...
0
votes
0answers
16 views
Cds and cva charge
ow can CDS contracts be used in order to hedge (neutralize) CVA charge movements with respect to changes in the underlying rates for a counterparty?
In here CVA is a proportion that’s subtracted from ...
1
vote
0answers
22 views
How do I determine significant “moments of change” in a forecast?
I have a function returning a trendline and a forecast for that line. I need to identify "significant" moments of change (ie, in slope) in the forecast region. Each timestep in the series is 15 ...
1
vote
1answer
38 views
Continuously Compound Interest
You invest 100 dollars with continuously compounding interest. The interest rate is compounded annually with interest rate $R$ that has a pdf of $f(r)= 1.5r - 0.75r^2$ 0<=r<=2. Lets say the ...
0
votes
0answers
23 views
Finding the unique solution of an SDE
For a given Weiner process W consider the 1-d interest rate model
\begin{align*}
dr_t&=4(4-r_t)dt+\sqrt{|r_t-6||r_t-2|}dW_t, t\in[0,T] \\
r_0&=4.
\end{align*}
Show that this equation has a ...
0
votes
1answer
26 views
Computing the present value, compounded monthly
This is a problem from Ross's Elementary Mathematical Finance book:
A five-year $\$10,000$ bond with a $10\%$ coupon rate costs $\$10,000$
and pays its holder $\$500$ every six months for five ...
0
votes
2answers
38 views
General Annuity practice question
I'm taking an introductory course in finance but I don't understand how to do this question:
A used car may be purchased for 7600 cash or 600 down and 20 monthly payments of 400 each,the first ...
0
votes
1answer
19 views
Find the present value of 300 pounds paid every 3 years
Using an interest rate of 7% per annum, find the present value of fifteen payments of
amount £300 each payable every three years, with the first payment made at the end of
the second year
I thought this ...
