Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

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3
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1answer
194 views

Text on Probability Theory applied to Actuarial Science

I am a senior undergraduate who has passed the first three actuarial exams on probability (P), financial mathematics (FM), and models for financial economics (MFE). I am working on passing the life ...
1
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1answer
298 views

Calculating the value of Annuities

Q: Instead of investing $3000$ at the end of $5$ years, and $\$4000$ at the end of $10$ years, Steve wishes to make regular monthly payments that will amount to the same total after $10$ years. ...
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1answer
17 views

Finding the compounding period

The future value of a 200 deposit in an account that earns 6.25% annual interest is $272.71 after 5 years. Determine the compounding period for this investment. This is what I have done: $272.71= ...
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2answers
176 views

Future Values of Annuities

Michelle has decided to invest $3000 at the end of each year for the next five years in a saving account that pays 8% annually, compounded semi-annually. How much is the annuity worth after 5 years? ...
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2answers
157 views

Compound interest problem

Find the present value and accumulated value after 10 years for an income stream with the rate of money flow $f(t) = 200 + 150t$ dollars per year and the rate of interest 12% compounded continously. ...
1
vote
1answer
50 views

Price of Product

Suppose an item costs $ \$10$. The expected demand for 4 years are: $$ \text{1st year}: 5$$ $$ \text{2nd year}:10 $$ $$ \text{3rd year}:1 $$ $$ \text{4th year}:2 $$ The actual demand is: $$ ...
0
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2answers
105 views

Financial Maths question - Calculate number of years over which loan will be repaid

A loan has to be repaid over 3n years, through annual repayment installments of 5000 each at an annual interest rate of 10%. Sum of the Interests paid in the (n+1) and that in the 2n+1 year is 5000. ...
0
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2answers
279 views

Growth Rate. A precise definition.

Recently I came across a problem (see statement below) growth rate . During my attempts to solve the exercise I concluded that I do not know the meaning of need backup growth rate when this rate is ...
0
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1answer
67 views

A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints

In Evans and Jovanovic (1989) you will find a model for entrepreneurs with credit constraints. The part that is important for my question follows. Here it is the production function and the income ...
0
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1answer
124 views

[solved]Compound interest problem

I must admit this is my homework, but I have tried to solve it from many different angles but I can't solve it. The problem is as follows: A person has a 500 dollar debt to be paid in 3 years at an ...
0
votes
1answer
110 views

solving apr using binary chop

I need to calculate apr in the uk using this formula http://en.m.wikipedia.org/wiki/Annual_percentage_rate#European_Union Ive been advised to try the binary chop method but I have no idea how to do ...
0
votes
1answer
750 views

How to calculate APR using Newton Raphson

I'm have a computer program to calculate apr using Newton Rhapson. I imagine most mathletes can code so i dont imagine the coding being an issue. The solution is based on this initial formula ...
0
votes
1answer
66 views

Find a function that highlights Gamma for short dated fx options and Vega for long dated fx options

I'm new to this and would like to try it out on the above question. A more detailed description is shown below: My professor has asked me to come up with a formula that will highlight, say the 100 ...
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0answers
28 views

How to sum correlation, or, calculate correlation of disjointed variables

I'm trying to calculate the correlation of 2 array of variables, but the array is disjointed in the middle - but I'm trying to obtain one correlation coefficient See the excel file I uploaded: ...
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0answers
28 views

Average Interest Payment For Specific Period of Ammortization Schedule

I would like to derive an equation that calculates the average interest payment x for an amortized mortgage loan in the first m ...
0
votes
1answer
72 views

Using Ito Formula to compute $E[cos(B_t)]$

During the semester my prof (for a basic Mathematical Finance course) gave us some more challenging type questions to think about if we plan to take future courses on the topic. One of the questions ...
0
votes
1answer
48 views

variance unchanged under subtracting mean - application in portfolio theory

I’m working through the following passage: We will be interested in the variance of the portfolio returns given the variances of individual asset’s returns. If we have assets with returns ...
0
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2answers
52 views

Algebra — Am I doing it right?

Is this correct? $ \frac{1 + 0.05}{1 + x} = \frac{1 + 0.02}{1 + 0.06} $ $\frac{1.05}{1 + x} = \frac{1.02}{1.06} $ $\frac{1.05}{1 + x} = 0.9623 $ $1.05 = 0.9623(1 + x) $ $ \frac{1.05}{0.9623} = ...
2
votes
0answers
212 views

What does it mean to “pass to the limit” in mathematics?

I've been reading a finance paper and stumbled upon this phrase. What does passing to the limit mean in this context (or overall in mathematics)? Here is an excerpt from the paper: It is ...
0
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1answer
92 views

Questions on share prices of a Company.

Company Z is currently financed solely by common stock and has 1000 outstanding shares with a (time 0) market price of 10 dollars per share. The company’s expected earnings is 1000 dollarseach year ...
0
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1answer
127 views

Discounting Perpetuity Question

"A project pays a dividend of $0.75 next year and then grows at 12% for 3 more years, and then grows at 8% indefinitely thereafter, find PV" Okay so first step is to find the initial value of ...
2
votes
1answer
57 views

Help me optimize my work

I am a physician. I am required to work 14 shifts per month. I may work extra shifts for 1400 dollars per shift. In addition, I earn productivity based on a system called RVUs. For every RVU I produce ...
0
votes
1answer
459 views

compound interest with geometric series

Were studying geometric sequences in maths and this came up as one of the questions: A mortgage is taken out for 150000 and is repaid annually with 20000 installments. Interest is charged on the ...
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2answers
150 views

How to calculate profit share for this example [closed]

How can we calculate a profit share for Rs. 100,000 that remained in an account for 5 days only. See this question illustration below I was confused about which tags were more appropriate for ...
0
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2answers
469 views

Calculating monthly instalment after down payment

An item is available for $34000\$$ cash or $20000\$$ cash down payment together with $5$ equal monthly instalments. If the rate of interest charged under the instalment plan is $30\%$ per annum, ...
0
votes
1answer
40 views

Question on Black-Sholes Equation

Consider a call option having a strike price $K$ and exercise time $t$; let $r$ be the nominal rate, $\sigma$ volatility and $S_0$ the underlying asset at $t = 0$. How to show that $C(t, ...
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1answer
50 views

How to calculate the ⌉ operator?

In a book about finance, the following formula appears: $$\large a_{10 \,⌉\, 0.04}$$ What is this ⌉ operator and how to read / calculate it?
2
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1answer
73 views

Optimal Investment Strategy

I am not sure to solve the following investment problem: I have an investor which receives an income $I_n\ge 0$ at the start of year $n$. The investor chooses a proportion $p_n\in[0,1]$ of this in ...
9
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1answer
374 views

Modelling risk when market making

I'm interested in learning about algorithmic trading, particularly in bitcoin. Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest ...
3
votes
2answers
88 views

Calculating annuity payment

I have a time payment question I'm having trouble with: "Bill would like to save 60000 dollars for a deposit on his first home. He decides to invest his net monthly salary of 3000 dollars in a bank ...
0
votes
1answer
101 views

financial maths - payoff options

Consider the payoff of a call option $C=\max\{0,S(1)-K\}$, where $S(1)=S(0)(1+\mu+\sigma_X)$, X has standard normal distribution. Take $S(0)=80$, $\mu=0.3$, $\sigma=0.4$, $K=100$ (strike price). ...
2
votes
0answers
44 views

Reinvesting the interest (generalized version)

If I deposit \$1 at $t=0$ into an account which credits interest at the end of each year at a force of interest $\delta_t$ (assume it's integrable.) Then, if I reinvest the interest at an annual ...
0
votes
1answer
533 views

How to calculate negative profit margin?

I sold a pair of shoes last week a \$150.00. The cost is \$100. My profit margin for last week is 33% (Revenue - Cost) / Revenue What if the customer returned the shoes? Is my profit margin $0$ or ...
0
votes
1answer
32 views

statistics and financial ratios

Currently i am trying to derive the volatility of a financial ratio. I have calculated the volatility (standard deviation) of both the denominator and numerator however I am running into trouble ...
0
votes
1answer
79 views

Question on duration matching and reddinggton's immunisation

An insurance company has liabilities of 6 million due in 8 years’ time and 11 million due in 15 years’ time. The assets consist of two zero-coupon bonds, one paying X in 5 years’ time and the other ...
0
votes
1answer
33 views

Annuity Future Value Factor

Question: How much money will you have at the end of four years if you deposit $1,000 a year (at the end of each year) into a bank account paying 10% interest? We could answer this by calculating ...
1
vote
1answer
97 views

Stochastic differential for general semimartingale

By using the canonical representation of a semimartingale in Eberlein, Glau and Papapantoleon: "$H = B + H^c + h(x) \ast (\mu − \nu) + (x − h(x)) \ast μ$ where $h = h(x)$ is a truncation ...
0
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1answer
54 views

financial mathematics question

An investor is interested in purchasing shares of ABC company. The company pays annual dividends, and a dividend payment of 1.2 per share has just been made. Future dividends are expected to grow at ...
0
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1answer
606 views

Comparing annualised volatility from monthly and annual data

I fear there is a very simple answer to this question and its killing me that I can't see it. I am interested in calculating historical volatility: I have monthly index values starting in Jan 2005 ...
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1answer
96 views
0
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1answer
75 views

Compute $d(\log(S_t))$ using Ito's Formula

We are given the following: d$S_t$ = $\sin(S_t)t^2dt + e^{\sqrt{S_t}-t}dB_t$ And are asked to compute several different things, one of which is $d \log(S_t).$ If I'm understanding Ito's formula ...
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vote
1answer
65 views

How to prove that the multi-period market satisfies Non-arbitrage given that the single-period market admits Non-arbitrage

Here is the question: Let $(Ω,\mathscr F,\mathbb P,\mathbb F= (\mathscr F_k)_{k=0,...,T})$ be a filtered probability space and $S=(S_k)_{k=0,...,T}$ a discounted price process. Show that the ...
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2answers
954 views

Proof of Continuous compounding formula

Following is the formula to calculate continuous compounding ...
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2answers
366 views

A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual…

A farmer buys a used tractor for Rs $12000$. He pays Rs $6000$ cash and agrees to pay the balance in annual installments of Rs $500$ plus $12 \%$ interest on the unpaid amount. How much will be the ...
2
votes
1answer
730 views

Financial mathematics question about mortgage loans

The following question is what I was working on. A bank gives a mortgage of 450,000 dollars for a 30 year loan with 6% annual interest which requires the person to pay monthly. They require ...
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0answers
125 views

Intensity Function of Stochastic process`

I'm fitting some financial data to a model based on a stochastic process and evaluating the fit of it by looking at the compensator. However, I cannot understand well what does it mean to take the ...
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vote
1answer
2k views

How are Annuity problems solved?

I'm unsure how to solve the following problem: Angie wants to plan a trip to Hawaii with her husband on their 10th wedding anniversary in two years. She anticipates that the all-inclusive trip will ...
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vote
1answer
276 views

Dividend paying stock's risk-neutral probability proof

Question: Consider the one-period binomial model with a stock that pays continuous dividend $\delta$. I want to show that the risk-neutral probability is given by $$p=\frac{\exp((r-\delta)\Delta ...
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4answers
73 views

Calculating future value and Present Value

I have been stuck on this one for hours ... not too great at math can someone help. Thanks. Isaac borrowed $\$4000$ at $11.5\%$ compounded quarterly $5.5$ years ago. One year ago he made a payment ...
0
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1answer
492 views

Why the $Vega$ of the Black Scholes Model is at its maximum for at-the-money options?

In my course script, it is said that the Vega of the Black Scholes Model is at its maximum for at-the-money options. In order to verify this, I did the following calculations: In the Black Scholes ...