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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140 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 ...
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1answer
135 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 ...
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1answer
947 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 ...
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1answer
73 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
30 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
35 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 ...
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1answer
75 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 ...
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1answer
52 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 ...
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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} = ...
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0answers
277 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 ...
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1answer
125 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 ...
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1answer
155 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 ...
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1answer
58 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 ...
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1answer
577 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
180 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 ...
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2answers
699 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, ...
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1answer
41 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
53 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?
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1answer
77 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 ...
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1answer
395 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 ...
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2answers
91 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 ...
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1answer
115 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). ...
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0answers
45 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 ...
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1answer
816 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 ...
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1answer
36 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 ...
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1answer
94 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 ...
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1answer
35 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 ...
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1answer
104 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 ...
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1answer
56 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 ...
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1answer
762 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
101 views
0
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1answer
78 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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1answer
69 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
1k views

Proof of Continuous compounding formula

Following is the formula to calculate continuous compounding ...
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2answers
463 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
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1answer
906 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
131 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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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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1answer
328 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
76 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 ...
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1answer
605 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 ...
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0answers
55 views

Financial mathematics 2

I've been given the following information: MR bob borrows 50000 now and promises to repay it in monthly installments over the next eight years. Interest is compounded monthly at 18% per year. ...
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1answer
210 views

Financial mathematics

I was given the following information: A young couple decide that they want to buy a house for 220000. They have saved a deposit of 80000 and are confident that they can pay 2500 per month, ...
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1answer
43k views

Finding Revenue Function and Max Revenue

Studying for a midterm. The demand function for a manufacture's product is $p=1000-\frac1{80} q$ Where $p$ is the price (in dollars) per unit when $q$ units are demanded (per week) by consumers. ...
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1answer
43 views

Loan: monthly payments plus additional amount paid at end of year

The interest rate on a 30 year mortgage is 12% compounded monthly. the mortgage is paid by monthly payments of 700. Suppose an additional 1000 is paid at the end of each year to payoff loan early, ...
0
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1answer
56 views

successive reduction percentage

I would like to aplly successively to reudction percentage to a price and I want to find the "global" reduction. Apply a reduction of 19.6% and a 20% is different to apply a reduction of 39.6%. So, ...
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2answers
40 views

How to calculate total profit in a set amount of days with a 2% daily gain?

I want to know if there is a formula that would give me the total amount at the end of a 365 day period with a 2% daily gain. Adding 365 days up would take for ever.
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2answers
68 views

How to find the rate of interest?

Q. The simple interest in 3 yrs and the compound interest in 2 yrs on the same principal and at the same rate are 1200 and 832 respectively. Calculate the rate. What I've done: SI in 3 years = ...
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1answer
44 views

How does perfect correlation between Brownian motions imply equivalence?

Assume that both $ B_t $ and $ Z_t $ are standard Brownian motions and that $ Corr(B,Z)=1 $. How do those properties imply that $ B_t = Z_t $ a.s. ? $Cov(B,Z) = t $ is as far as I can get, and I ...
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2answers
51 views

Working out the difference in earnings

I'm mathematically impaired/ignorant and trying to figure out the difference in earnings between my partner and I to work out a fair split of the bills. So; I earn £2060 per month and partner earns ...