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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552 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
54 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
179 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
40k 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
42 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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1answer
52 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
66 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
49 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
64 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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147 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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1answer
434 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
42 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
102 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
77 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
601 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 ...
2
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1answer
162 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
51 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
84 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
45 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
129 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
266 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
1k 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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1answer
266 views

Determining Total Assets, Total Liabilities From a Financial Statement with Missing Values [closed]

I at a loss trying to figure out the total assets and liabilities from what is given. K-Os Corporation Beginning of year Total ...
2
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2answers
58 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
134 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
218 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} + ⋯ + ...
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1answer
312 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
94 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
153 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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2answers
101 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
254 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
26 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
88 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 ...
2
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1answer
391 views

Compound interest -like calculation, but with increasing rate

Let's say an organization has 100 employees in the beginning of 2013 and grows to 110 employees by the beginning of 2014. This implies a growth rate of 10% for 2013. Now, let's say a hiring manager ...
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0answers
360 views

Calculate sell(sales) price from margin and cost price

Slight finance question, trying to program the calculation of sell price when we have %margin and cost price. ((CostPrice / ((1 - %Margin) / 100)) * 100) / 100 ...
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2answers
97 views

Why can moving averages of the prices indicate the trend of a stock?

In technical analysis of stock trading, we can use the moving averages of the historical prices of a stock to indicate whether it is currently in the uptrend or downtrend. Let me exemplify the idea ...
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2answers
194 views

interest rate not constant with constant installments

Do you know a formulae which would calculate a constant installment withe non constant interest rate. For example let's say that Mr A take a loan of 1000 and pays a monthly interest rate of 6% the ...
2
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2answers
98 views

How to split the rent if two roommates live there from the beginning and a third one joins in the middle of the month?

I've been thinking over it and I can't figure it out. Consider the rent of the house is $X$. Now there are two roommates from the beginning and a third one joins in the middle of the month. Now ...
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1answer
79 views

Interest Calculation

A university student receives his statement for his tuition and notices that he doesn't have enough money to pay it all off at once. The student inquires about interest rates at his university and is ...
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1answer
32 views

Mortgage calculating time for residual debt

I have a mortgage for C capital, with constant monthly payments, constant interest rate i (and constant duration in year D). I would like to know after how much time I reimburse $r$ dollars. For ...
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4answers
9k views

No-Arbitrage Principle

I hope you do not mind me asking a financial question in this section. I am having trouble understanding the concept of the no-arbitrage principle for a particular example in my notes: Suppose a ...
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0answers
95 views

How to get interest in the mathematics of tax

In a similar vein to my previous thread, I will also be teaching about the mathematics behind taxation - to a lot of people, this is very mundane - but that is not true of everyone. The practicality ...
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1answer
84 views

Portfolio which replicates given payoff

Consider the following payoff function: $$p(S_T) = \begin{cases} 0 & \text{if } S_{T} \leq 70 \\ S_{T}-70 & \text{if } S_{T} \in (70; 100] \\ -S_{T}+120 & \text{if } S_{T} \in (100; 120] ...
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2answers
81 views

Mathematical Finance Question

I am having trouble answering this question confidently. A walk through would be amazing.
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1answer
205 views

Calculate the yield rate on transaction

Problem:- 'A' is able to borrow $1000 from 'B' for one year at 8% effective and at the same time lend it to 'C' for one year at 10% effective. what is 'A's yield rate on this transaction? My ...
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2answers
182 views

Speculating on the stock exchange

Imagine you model each stock as a random walk (fractal) and also that you can buy and sell at any price. Suppose also that it 'walks' with the pace of 1. If you buy, for example, 1000 shares of ...
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1answer
184 views

Hedging a long position-one period

Consider a one period binomial stock model with $S_0=4$, $S_1(H)=8$ and $S_1(T)=2$. The interest rate is $25$%. Let's say I buy a call option for $1.20$ with strike price $K=5$ which expires at time ...
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1answer
1k views

Black-Scholes PDE to heat equation, nonconstant coefficients

Can someone provide me with details or a reference on how to transform the Black-Scholes PDE with nonconstant coefficients (i.e. $r=r\left(S,t\right)$, $\sigma=\sigma\left(S,t\right)$) to the heat ...
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3answers
173 views

$1500=P \times { (1 + 0.02) }^{ 24 }$, what is the value of $P$?

Hey guys could you please tell me what is the faster why to solve this equation. It's a compound interest equation and I'm stuck at the ${ (1 + 0.02) }^{ 24 }$ I really don't know how to proceed in ...