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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.

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27 views

Finance engineering and risk management [on hold]

Compute the price of a zero-coupon bond (ZCB) that matures at time t = 10 t=10 and that has face value 100. at r o,o = 5% q = 1/2 i solved this question and got answer 61.34 but it is wrong.HOW CAN ...
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39 views

Financial Mathematics question, I know linear algebra stuff, but not this application question

A market has two stocks S1 and S2. Both S1 and S2 are valued at 1 per unit today and can be worth either 2 or 0.5 per unit after one year. Assume that money M valued at 1 per unit today does not ...
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1answer
36 views

How do I calculate fixed amount of monthly payments to pay off a debt with interest?

If my balance owed is 10,000 and my APR is 27%, if I wanted to pay the debt in full in 4 months, what would be my payments per month? here is the website where it takes inputs: https://www....
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1answer
18 views

Question about answer in 13th edition FM manual for example of a continuous annuity with varying force of interest

Am I just not seeing what happened to the negative sign? $e$ between the first and second steps on the last line"> Any clarification would be much appreciated!
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1answer
10 views

Find the net rate of interest

A building that costs USD 7,500, rents for USD 62.50 a month. If insurance and repairs amount to $1 \%$ each year, what is the net rate of interest earned on the investment? Method One: I assumed ...
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0answers
13 views

How is standard deviation calculated on a matrix of dependent variables?

This a follow up to a question I had here. So I have a Matrix $C$ that is the covariance between a set of stocks: I do as well have a vector $\vec{w}$ of weights: $\begin{bmatrix} 0.4 \\ 0.2 \\ 0.1 ...
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1answer
23 views

Using fission method with a series like v^5 + v^12 + v^19+…

I am studying for exam FM and I know we can use the "fission" method to represent a summation like $v^5 + v^{10} + ... + v^{100}$ as $\frac{ \require{enclose}a_{\enclose{actuarial}{100}}}{\require{...
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0answers
21 views

Simple Interest vs Amortization schedule

I'm writing a little piece of software to service auto loans using simple interest. When computing using simple interest calculators the numbers are different when compared to the amortization ...
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1answer
32 views

Finding return from Newton's Formula

I have Newton's formula ...
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0answers
18 views

How can I calculate the conditional expectations for the asset prices given partitions?

I have the following underlying asset, with the interest rate being zero: $$ \begin{array}{c|lcr} & \text{S(0, $\omega_i$)} & S(1, \omega_i) & \text{S(2, $\omega_i$)} \\ \hline \omega_1 &...
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1answer
16 views

Stretching the covariance of a daily change to the year

I'm diving into financial mathematics and have calculated a matrix that gives me the daily change of four given securities: The start of it looks like this: My Tutorial is now calculating the ...
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1answer
29 views

Splitting costs of a costcenter

This is probably stupid-simple for you guys, but I'm not mathy and I'm having difficulty figuring this out. In a fictional company C there are two costcenters and three employees. Costcenters: ...
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0answers
22 views

Required amount to invest now in a trust fund (difficulty with discount rate)

The parents of three children aged 1, 3, and 6 wish to set up a trust fund that will pay 25k to each child upon attainment of age 18, and 100k to each child upon attainment of age of 21. Assume that ...
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1answer
8 views

Capital after interest per month and additional deposits per month

Person A has 1000€ on the bank with 5% interest per month. He also puts 50€ per month to his bank account before he receives the interest. How much does he have after 12 months? My calculation 1000*...
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0answers
26 views

Relation between Simple Return and Continuously Compounded Return [closed]

Suppose S is the simple return and X is the continuously compounded return of a stock which has normal distribution. May I know how to show 1 + S = exp(X)?
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1answer
58 views

Kelly bet question

I stumbled upon Kelly bet during studies and decided to try simulating it. I chose a simple example where $b = 1$ and $p = 0.6$, which gave me the Kelly bet equal to $0.2$ of the wealth. I took $25$ ...
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1answer
50 views

Peaks of a curve. [closed]

I'd like to find the peaks corresponding to a curve most likely by using slope of tangent to the curve. enter image description here The attached curve has multiple peaks. I'm looking for an algorithm ...
3
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1answer
41 views

Simplifying the Derivative of a European Call Option

I know the title suggests finance, but I'm stuck on the mathematics of this. I need to take the following derivative: $$ -\frac{\delta C(X)}{\delta X}=-\frac{\delta}{\delta X} \Big[Se^{-dT}N(d_1)-Xe^...
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1answer
49 views

Compare two different prices in stock market

I am trying to develop some algorithm in stock market, I want to compare two different sets of prices, please see below image to understand clearly, If you see above image I have plotted two ...
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0answers
22 views

Derive all the Present values and Future values formulas assuming continuous compounding (for multiple cash flows)

$\lim_{n\rightarrow \infty } A(1+\frac{r}{m})^{mn}=Ae^{rn}$ Derive all the Present values and Future values formulas assuming continuous compounding (for multiple cash flows). Can anyone help out? ...
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1answer
23 views

Finding n for amortization

I have this formula for amortization PMT = PV * (i / (1 - (1+ i)^(-n) ) ) I'm having issues isolating n in cases where I'm given the present value, the payment value, and the interest rate, but not ...
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0answers
31 views

Geometric Brownian Motion Price Processes in high Dimensions

This is my first post so I am open for an suggestions in formating improvement. For some reason I can not find suitable literature for the following problem What I want to do is calculate the option ...
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2answers
46 views

Convert flat interest rate to effective interest rate

My bank currently has promotion on personal loan on flat interest rate which is 3.80%. And there are some minor remarks Terms and Conditions apply. Effective rates vary from 7.07% p.a. to 7.15% ...
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2answers
63 views

Markov Chain: Optimal stopping to determine the price at which stock is traded

The stock price starts at 100\$. At any given time, there is 50% probability that stock price increases further by 1 and 50% probability that stock price goes back to 100\$. You are paying 1\$ to ...
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0answers
17 views

Discounted Value of Ordinary Annuity

Hello I tried to do the problem below, and I'm not sure where my calculations went wrong or my method was incorrect. I would like some assistance. An annuity pays 1000.00 weekly for 4 years and ...
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1answer
39 views

Finding a future value given force of interest

One of my actuarial exam problems asks to find $\ddot{s}_{\bar{2}|}$, given $\delta_t=\frac{2t}{10+t^2}$ $(t\geq 0)$. Here's what I've done: From the definition of $\delta_t=\frac{A'(t)}{A(t)}$, $A(t)...
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0answers
24 views

Solving for Annual Deposit annually

Irene plans to retire on January 1, 2020. She has been preparing to retire by making annual deposits, starting on January 1, 1980, of 2050 dollars into an account that pays 9.8% compounded annually. ...
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1answer
36 views

Find the value of 10X

At a compound interest rate of $5 \%$ per annum, the accumulated value 3000 has the same accumulated value as deposits of 5X and 3X made at time t=0 and t=3, respectively. Find the value of 10X. ...
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1answer
18 views

Straight line depreciation confusion

My problem: A computer bought for $3892$ is to be claimed as a tax deduction using straight-line depreciation of 15% of its original value each year until the total value has been claimed. Calculate ...
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0answers
99 views

Digital Option risk neutral probability

In the $T$-period binomial model, if the asset price is $S$ at any time, the next period's price will be either $SU$ or $SD$. The interest rate per period is $r>0$ and $D^* < 1 < U^*$, ...
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1answer
35 views

What could the formula of the present value for such a saving plan?

Trying to make the problem as simple as possible. I decide to start on January $1^{\text{st}}$ a saving plan for which the bank will give me a constant interest rate $r$ (the interests being paid on ...
2
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1answer
116 views

Determine fair price of a digital option

A digital option pays one dollar at time $t = T$ if the asset price is above a fixed level (strike) $K$ and is worthless otherwise. Consider the following model, with $r = 0$: \begin{...
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1answer
14 views

I have yearly sales forecast and constant seasonality (% of yearly sales). How can I come up with a seasonality that smooths the monthly growth?

Let's say I have a yearly sales forecast (in $), such as {100,300,400,500} I also have a monthly seasonality percentage (as % of total yearly sales), such as ...
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1answer
28 views

Financial Math - Appreciation of a House. Help?

I need help figuring out where I went wrong. Question: Emily is purchasing a house for $185000 that appreciates at a rate of about 1.5% per year. She will finance this purchase with a 15-year ...
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1answer
23 views

Need clarification with a simple 'balance' sheet calculation

I really don't understand how they got the net air sales amount?Do you not need to take into account the contract savings, amount lost and all the other stuff below it? Can anyone clarify this, that ...
0
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1answer
31 views

Minimum Rate of Return

Question: A businessman wishes to earn 7% on his capital after payment of taxes. If the income from an available investment will be taxed at an average of 42%, what minimum rate of return, before the ...
2
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1answer
39 views

Volatility in an at-the-money call option

I understand that the vega of the Black-Scholes equation is a positive function, which means the value of the option is an INCREASING function of the volatility, since vega is the derivative of the ...
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0answers
25 views

GMM application

I have a sample iid ${({X_i})_{i=1}^{n}}$ from a distribution with mean $ \mu$, where $\mu\in R$. suppose you also know that the distribution is symmetric around the mean(skewness is $0$). If you need ...
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1answer
52 views

Current price of a European call option

I have the following situation: Consider a European call option on a non-dividend paying stock, with strike $K$, time to expiry $T$ and current stock price $S_0$. Assume that the risk free rate is ...
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1answer
15 views

Finance Questions : Credit Card interest

Working through some problems on personal finance and this is the only set of questions I seem to not get a grasp on. I feel kind of like an idiot though for not being able to understand what to do. ...
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0answers
31 views

Compound Interest - Changing interest rates

Problem Calculations Hello, my problem involves compound interest specifically with changing interests. I tried doing the problem above by doing it in (2) and even tried putting it in a solver to do ...
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0answers
96 views

Risk-neutral probability measures

Consider a market with $\Omega= (\omega_1, \omega_2, \omega_3)$, $r = 0$ and one asset $S$. Suppose that $S(0) = 2$ and $S$ has claim $\bar S = (1, 3, 3)$ at time 1. Find all the risk-...
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1answer
86 views

Sure Thing Arbitrage

Consider the following model with assets $S_1, S_2$ and three states, and suppose that $r = 10\%$ \begin{array}{|c|c|c|c|} \hline n&S_n(0)& S_n(1,\omega_1) & S_n(1,\omega_2) & S_n(1,\...
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2answers
30 views

Interest involving different years, but same or lower 2nd value?

When selling your property you receive the following offers : (a) € 100 000 on 1.1.18 and € 100 000 on 1.1.20 (b) € 150 000 on 1.1.18 and € 50 000 on 1.1.19 Assume interest is 3% Which offer is ...
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1answer
101 views

Is there arbitrage?

An economist writes a 1-period expectation model for valuing options. The model assumes that the stock starts at S and moves to $2S$ or $\frac{1}{2}S$ in 1 year's time with equal probability. ...
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1answer
24 views

What would the interest rate have to be to make the two shares to be equally valuable?

Marco dies and leaves behind a perpetuity paying $1000/month. His wife is entitled to the payments for the first 20 years, and then payments go to Marco's favourite charity. Interest rates are 6% ...
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0answers
18 views

Compound Interest with monthly deposits

If i have S starting cash, and I make X monthly deposits, at an Y monthly interest rate, how would I go about calculating the total after Z months?
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1answer
61 views

Applying Ito's formula to $D^x(t)=(\partial/\partial x)S(t)$

Let $\gamma:[0,T]\times (0,\infty)\to \mathbb{R}$ be continuous, bounded above, $(\partial/\partial s [\gamma(t,s)])$ is continuous in $(s,t)$. Consider the following process $$dS_{\gamma}^x(t)=S^x_{\...
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1answer
39 views

Additivity of Value at Risk

I'm struggling with the following exercise: Let $(\Omega,\mathcal{F},\mathbb{P})$ be a probability space and $X,Y$ be two real-valued random varaibles such that their corresponding cumulative ...
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1answer
116 views

Market quotes and arbitrage argument

DUPLICATE ON HOLD Use an arbitrage argument to construct a formula relating the price of the European to the price of an American. Good day, I wanted to ask for help with a question from one of my ...