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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2answers
351 views

Tricky Finance-related Question

Suppose I have acquired 103,304 customers for a transaction-based business at 12 months into the business and their number has increased at a monthly rate of 40% (from month 1, in which 2,551 ...
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1answer
193 views

Interest of interest calculations without logarithm

I have some problems understanding a question in a math class test for 10 year olds. The question is: Someone pays in 200€ to a bank. The interest rate is 3.75%. Some time later, he looks at the ...
0
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1answer
254 views

Stock/Futures put options

How do you find out how much a put contract would cost? Example: The premium for a 99.00 Eurodollar futures put option is 0.55 and the spot price is 98.51 So I have the intrinsic value which ...
0
votes
3answers
91 views

Annuity immediate

An annuity immediate has quarterly payments of $1000$ for $25$ years at a rate of $6 \%$ converted quarterly. Find its present value. The effective interest rate $i$ is $0.06/4$. So let $v = ...
0
votes
3answers
979 views

Loan Repayment and Annuities

A loan for $50,000$ has level payments to be made at the end of each year for 10 years at an annual rate of $9 \%$. (a) Find the balance at the end of $3$ years. (b) Find the interest paid in the ...
2
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1answer
133 views

Payments and Interest Rates

Suppose you have two options for making a payment: (A) Pay $90 \%$ of the purchase price two months after the date of the sale. (B) Deduct $X \%$ off the purchase price and pay cash on the date of ...
0
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1answer
626 views

proof that value at risk VaR is monotonic

I want to show that if $X$ and $Y$ are the two loss variables such that $X\leq Y$, then $\text{VaR}_\delta(X)\leq\text{VaR}_\delta(Y)$.
2
votes
1answer
340 views

Derivatives of Brownian motion or Box Options Greeks

Here's the probability (I think) that a particle in Brownian motion (w/ standard deviation $\sqrt{t}$) will exceed $m$ between times $t_1$ and $t_2$: $$\frac1{2\sqrt{2\pi}}\int_{-\infty }^m ...
3
votes
1answer
258 views

Black-Scholes equation

In Stein-Shakarchi's book Fourier Analysis (p. 170), the solution of the Black-Scholes equation $$\frac{\partial V}{\partial t}+rs\frac{\partial V}{\partial s}+\frac{\sigma^2s^2}{2}\frac{\partial^2 ...
0
votes
1answer
560 views

Instalment APR Calculation Formula

I have a problem that I cannot solve regarding interest payments, and payment holidays. The scenario is this If I purchase a product which is paid for over a 12 month period, I need to calculate the ...
6
votes
2answers
791 views

Black Scholes PDE and its many solutions

I know the general Black-Scholes formula for Option pricing theory (for calls and puts), however I want to know the other solutions to the Black-Scholes PDE and its various boundary conditions. Can ...
14
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2answers
1k views

Farkas’ lemma: purely algebraic intuition

Here is a statement of Farkas Lemma from the Wikipedia. Let $A$ be an $m \times n$ matrix and $b$ an $m$-dimensional vector. Then, exactly one of the following two statements is true: There exists ...
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2answers
189 views

Stochastic/finance monte carlo question

When pricing a european option by monte carlo over 30 days for instance, what's the difference between one big 30 day jump vs 30 one day steps?
5
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5answers
4k views

Understanding Black-Scholes

Assume I have only basic math knowledge, what specific areas of math would I need to learn in order to understand the following webpage: Black-Scholes Many thanks.
1
vote
2answers
217 views

Principal and Annuities

Suppose you want to accumulate $12,000$ in a $5 \%$ account by making a level deposit at the beginning of each of the next 9 years. Find the required level payment. So this seems to be an annuity due ...
2
votes
1answer
203 views

Annuities and Loans

A loan for $8,000$ must be repaid with 6 year end payments at an annual rate of $11 \%$. What is the annual payment? I know that the present value of an annuity with end payments is $\frac{1-v^n}{i}$ ...
3
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2answers
250 views

Measuring Financial Investment Performance

I'm trying to understand how the performance of financial investments are measuring when the asset has multiple points of investment. For example, say I invest ...
2
votes
2answers
2k views

Repayments of a loan with compound interest

Suppose I have a loan of M dollars. At the end of each year, I am charged interest at rate R and make a repayment of P. The loan is repaid after n years. How long (n) does it take to repay the loan ...
3
votes
1answer
283 views

How to determine annual payments on a partially repaid loan?

A 10-year loan of $500 is repaid with payments at the end of each year. The lender charges interest at an annual effective rate of 10%. Each of the first ten payments is 150% of the amount ...