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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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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82 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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45 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
264 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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63 views

Financial mathematic with Feynman-Kac

I have a really big task in financial mathematics and a small part of it (to set up the problem), I need to write a PIDE (the Feynman-kac) where we estimate options with jumps. It is derived from the ...
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48 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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56 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
166 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 ...
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1answer
286 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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1answer
832 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
144 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
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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
263 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
33 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
82 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
6k 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
34 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, ...
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28 views

Does MACD have exact or approximate upper bound and lower bound?

A MACD is a difference between two moving averages, typically, 12-day Exponential Moving Average and 26-day Exponential Moving Average. With some stock prices, I observed that the range of there MACD ...
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25 views

Evaluating sales accounts across salespeople

This isn't homework, it is real work- but I couldn't find a better tag, so I thought this would be a good place for this type of question. I'm just curious if there is a standard approach to ...
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1answer
31 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
43 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
33 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
45 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 ...
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2answers
41 views

Actuarial Science FM Question

$$a(t)=Zt^2+Bt+1$$ If \$100 at $t=0$ grows to \$152 at $t=4$ and \$200 at $t=0$ grows to \$240 at $t=2$, what are $Z$ and $B$? Please show work. Also, what would \$1600 invested at $t=6$ grow to at ...
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106 views

Geometric Brownian motion problem

Here's the question: Let $S(t)$, $t \geq 0$ be a Geometric Brownian motion process with drift parameter $\mu = 0.1$ and volatility parameter $\sigma = 0.2$. Find $P(S(3) < S(1) > S(0)).$ Is ...
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86 views

When does variance fail to meet its purpose in mathematical statistics? [closed]

It have shown in a lot of both math and statistics book, however, When the books define the variance, it doesn't give much attention to math based theoretical background, i wonder if some formula that ...
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1answer
253 views

Normal Distribution Quantiles and Value at Risk

I'm preparing an exam, Quantitative Methods for Financial Markets. My book is not really clear for what concerns the calculation of normal distribution quantiles that have to be used in VaR's formula. ...
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0answers
24 views

How to find sigma-algebra over omega3 generated by the log-return ln(S2/S1) and ln(S3/S2)?

I calculated {S2/S1} = {u, u*u/d, d, d*d/u}, and then get ln(S2/S1)= {ln(u),ln(u*u/d), ln(d),ln( d*d/u)}. I am not sure my way of doing this question is right, because i m confuse about how to get ...
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1answer
46 views

Computing monthly loan payments when interest is 0%

I'm writing a Javascript program to display a mortgage amortization from a user input form that asks for typical things such as loan amount, interest rate, etc... A lot of sites, such as this one, ...
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2answers
57 views

annuities - equations of value

Chuck needs to purchase an item in $10$ years. The item costs $ \$200$ today, but its price inflates at $4 \%$ per year. To finance the purchase, Chuck deposits $ \$20$ into an account at the ...
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2answers
317 views

Perpetuity Immediate Present Value Question

A perpetuity-immediate pays $X per year. Brian receives the first n payments, Colleen receives the next n payments, and Jeff receives the remaining payments. Brian's share of the present value of ...
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1answer
119 views

Variance Covariance Matrix, positive definiteness

Suppose we have a variance covariance matrix $\Sigma$. Under what conditions on the variance covariance matrix, $\Sigma$ is positive definite, that is $\forall w \neq 0, w^T \Sigma w>0$. In fact, ...
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1answer
33 views

financial calculus put option

Consider a 1-year European put (right to sell) with a strike price of 52 on a stock whose current price is 50. We suppose that there is only time step at which the stock moves either up by 20% or down ...
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1answer
66 views

financial calculus call option

A stock price is currently 50. It is known that at the end of 2 months it will be either 53 or 48. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a ...
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1answer
36 views

Lump Sum + Series of Payments Future Value = X Amount

say I have $X saved already and I will from now on save a constant amount each year (Amount Y). I also want to have amount Z saved in the future. The question is how long do I need to save? I want to ...
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1answer
76 views

simple interest rate to product of interest rates

Which simple interest rate over six years is closest to being equivalent to the following: an effective rate of discount of 3% for the first year, an effective rate of discount of 6% for the second ...
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1answer
96 views

Present Value Cash Flow Questions - Discounting

At an annual effective interest rate of i, i > 0 all the following are equal: i. the present value of 10,000 at the end of 6 years ii. the sum of the present values of 6000 at the end ...
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2answers
770 views

Financial Linear Programming Problem

I'm very new at linear programming and I'm trying to figure out a way to approach this problem below: ...
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0answers
63 views

Finding arbitrage-free price interval in a relatively simple market.

Heres my problem: Define in a two time model the market as having one risky asset on $\Omega = \{\omega_1,\omega_2, \omega_3\}$, $p_i = \mathbb{P}(\{\omega_i\})>0$, and $s_i = S(\omega_i) > 0$ ...
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2answers
56 views

quartely payment

A Loan of R65 000 with an interest rate of 16% per annum compounded quartely is to be amortised by equal quartely payments over 3 years Question : how do I calculate the size of the quartely payment? ...
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1answer
99 views

Outstanding part-way balance for loan compounded quarterly

A loan of $R65000$ with an interest of $16\%$ per annum, compounded quarterly, is to be amortized by equal quarterly payments over $3$ years. Question: What is the outstanding amount on the loan at ...
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2answers
137 views

Solving i for annuities equation without financial calculator

I would like to know if there was a way to approximate i here without a financial calculator, in the following equation: $\displaystyle -50000 + \frac{12992}{1+i} + \frac{12992}{(1+i)^2} + ⋯ + ...
2
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1answer
221 views

formula to calculate the monthly repayments of this contract

I know that the interest rate is constant through the whole period and the interest method is declining balance. By declining balance mean that the interest at period t is calculated on the balance of ...
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2answers
68 views

Accrued interest

I know how to calculate accrued interest over time on an initial amount. However, my assignment has me artificially adding additional sums intermittently. I'm curious if there is a formula to do that. ...
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1answer
127 views

Paying less interest rate in credit card

I think I've found a way to pay off my credit cards faster, and therefore paying less interest rate. There's a Google Spreadsheet with my work at http://goo.gl/NqliZM My question What payment ...
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80 views

Help with Effective Rate of Discount- Theory of interest

I am just beggining Financial Mathematics. One of my assignment questions are as follows: (Q) Find the amount of interest earned from the principal of $1000 during the fourth period If the ...
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1answer
136 views

Financial Math - Nominal and Effective Rates [closed]

I am currently studying for the actuarial exam FM with the mathematical interest theory textbook from MAA. I have been doing a bunch of problems and the one below is giving me a lot of trouble to ...
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1answer
23 views

Question About Notation of CRR

I am reading a book on financial theory and it has been a while since I took a notation heavy math course so could someone help me out here... Now with this equation how does the sum work? Do I do ...
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1answer
61 views

How does one calculate product pricing to cover processing fees from $\$5$ to $\$5,000$ while maintaining a profit?

Credit card processor charges, for each transaction, $2.9\% + \$0.30$. I need to find an amount that covers that cost, from $\$5$ to $\$5,000$, on a per item basis, all while maintaining a small ...