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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A binomial model, draw a domain on the $(x,y)$ plane representing the set of all portfolios $(x,y)$ that lead to a self financing one-step strategy?

Consider a binomial model with $r_B = 10\%, r_S^{-}= -10\% , r_S^{+}= 20\%, S_0 = 100, B_0 = 10$. On the $(x,y)$ plane draw a domain representing the set of all portfolios $(x,y)$ that lead to a ...
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59 views

Problem involving nnual dollar-weighted yield-rate on stocks…

Full problem: Arthur buys $\mathbb{$}2000$ worth of stock. Six months later, the value of the stock has risen to $\mathbb{$}2200$ and Arthur buys another $\mathbb{$}1000$ worth of stock. After ...
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1answer
65 views

Guess-and-check for annual effective interest rate and annual yield rate

Here is the full problem: Kurt loans Randy $\mathbb{$}14000$. Randy repays the loan by paying Kurt $\mathbb{$}4000$ at the end of one year and $\mathbb{$}6000$ at the end of two years and as well ...
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14 views

Does interest apply for the last month of an amortization?

I'm working out the loan repayments using the amortization formula $$\frac{\text{principal} \cdot \text{paymentPercentageInDecimal}}{1 - (1 + \text{paymentPercentageInDecimal})^{-\text{payments}}}$$ ...
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44 views

Amortize the debt problem

Monthly payments are made on 130000 dollars at 5% for 25 days. Determine the payment needed to amortize the debt.
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22 views

compounding interest annuity

In the following ordinary annuity, interest is compounded with each payment, and the interest is made at the compounding period. An IRA earns tax deferred interest. Tim and Karen both make deposits ...
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28 views

Solving Black scholes PDE using Laplace transform

I'm trying to obtain the Laplace transform of Call option price with repect to time to maturity under the CEV process. The well known Black scholes PDE is given by $$ ...
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1answer
31 views

Prove $\sigma_V=x\sigma_S$. (Financial Mathematics)

Prove that the standard deviation of the value $V(T)$ at time of any portfolio $(x,y)$ at time $T$ in a one-step binomial is given by $\sigma_V=x\sigma_S$, where $\sigma_S$ is the standard deviation ...
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1answer
24 views

Compound interest question

Mrs. Hart, at age 65, can expect to live for 25 years. If she can invest at 11% per annum compounded monthly, how much does she need now to guarantee herself $500 every month for the next 25 years?
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1answer
28 views

Is there a way to do this? Fixed deduction for x rounds where total = fixed amount

I am trying to calculate the reduction amount / step per round for the given: rounds = 1000 points = 80 starting at reward = 1 point So from round 1 which has a reward of 1 point deduct a fixed ...
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1answer
39 views

Markov property question

In every book I can find, the Markov property for ito diffusions, $E[f(X_{t+h})\mid F_s] = E^{X_t}f(X_h)$ is stated for $\textbf{bounded}$ Borel functions. However, I have the following statement ...
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158 views

numerical method (implicit , backward difference or forward difference) for nonlinear pde

$\newcommand{\lbar}{\underline{\lambda}}$ In this linear PDE: \begin{cases} B_t+b^Q(r,t)B_r+\frac{1}{2}d^2(r,t)B_{rr}+(\mu(\lambda,t)+\alpha \sigma (t))(\lambda -\lbar)B_{\lambda} \\ ...
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1answer
19 views

Compound interest problem with increasing deposits

An Investor starts with an initial investment : $A$ He earns a steady profit of 10 percent per year. But every year he adds additional amount which increases by 15 percent every year. At the end of ...
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30 views

Reverse Engineer Math(financial) Answer.

I'm starting to question the Payment amount generated by the software my lender is using, but it could be my calculations that are wrong. I would like confirmation before I proceed. Is my approach ...
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27 views

Locate proof of Second Fundamental Theorem of Asset Pricing

Where can I find a $\textbf{rigorous}$ proof of the Second Fundamental Theorem of Asset Pricing. That is, A market is complete if and only if it has a unique risk neutral measure. Please do not ...
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1answer
39 views

On estimating monthly credit card payment amounts (some pragmatic constraints inside)

Right off the bat, I do hope this question doesn't attract a bunch of derisive comments about my personal affairs. I give the lengthy personal anecdote because I don't have the mathematical training ...
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31 views

How to find out when the profit of a transaction will hit $500,000

The question I have been trying to wrap my head around is a little complicated. Supposing you buy ten contracts worth 62,500 each and you double the total number of contracts each time you make a ...
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2answers
21 views

Question about a summation problem from finance

I'm studying a journal article about finance and I have trouble understanding how the author reach a result. The equation he begins with is: $$VTS_0=TD_0+T\Sigma_1^\infty PV_0[ΔD_t] \tag 1$$ Then ...
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2answers
138 views

Find prize per unit that will maximize profit at a given $x$-value

Struggling while reviewing my old math books. The problem has a prize-function and wants to know how the prize-per-unit should be chosen to maximize the profit at $\mathbf{x=160}$. First I look ...
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1answer
33 views

Effective interest rate given two loan payment options…

Here's the full problem: You have two options to repay a loan. You can repay $\mathbb{$}6000$ now and $\mathbb{$}5940$ in one year, or you can repay $\mathbb{$}12000$ in $6$ months. Find the ...
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31 views

Intuition behind American option pricing

The price of an American option is given by $V_n = \max\{G_n, \frac{1}{1 + r}(pV_{n +1}(H) + qV_{n + 1}(T)\}$, where $p$, $q$ are the risk neutral probabilities. I have two questions. How can ...
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1answer
33 views

Understanding APR - can it be calculated as a dollar amount

If the APR (as used in the US Truth in Lending Act) is considered "the cost of your credit as a yearly rate," can an APR be converted to a dollar amount? For example 10% simple interest per year on a ...
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37 views

Mortgage bond monthly repayment

I was given the following question: A mortgage bond of 280000 is taken out on a house at a rate of 19.25% p.a., compounded monthly over 25 years. Question: Calculate the monthly payment ...
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1answer
47 views

My doubt about a problem of financial mathematics.

I state that I am italian, so, if there are some mistake in my questions say it to me, and I correct as soon as possible. I've known this forum in an italian forum about molecular biology, where I was ...
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1answer
57 views

ROI Forumla for this scenario

I couldn't come up with a proper formula for the scenario below. I'm not so good at Maths. With, $X$ - monthly gains in percentage $C$ - Initial capital $N$ - number of years $M$ - Amount ...
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2answers
49 views

Pay back loan with an annual withdraw

I was given question 7b as homework: I am guessing that there are numerous ways of approaching this. The one method I have tried was to calculate the effective interest year for the year. Then ...
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1answer
39 views

How do i solve this to find PMT?

I know this may seem like a stupid question but i've been up late working on this math assignment and this question just isn't working when i transpose it. So this is the formula to find Present ...
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27 views

Finding interest rate in simple annuities, without interpolation

How do you solve for i from this equation? 4.37={[(1+i)^4] - 1}/i
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2answers
35 views

Bactracking to find compound interest

I'm trying to find what percentage 5000 dollars compounding monthly over 120 months will be if the final sum will be 7000 dollars. So: 7000=5000(1+r/12)^120 When working backwards to find r I ...
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2answers
50 views

Proof of the Black - Scholes pricing formula for European Call Option

I want to prove the following The price of a European call option with strike price $K$ and time of maturity $T$ is given by the formula $\Pi(t) = F(t,S(t))$, where $$F(t,s) = ...
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10 views

EBIT and EPS indifference

how do i find the EBIT indifference level associated with the following to financial proposals and the individual EBIT and EPS of each plan... Plan A- $\$5,000,000$ raised by selling 160,000 shares ...
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48 views

Vanilla swap payoff

The payoff of a plain vanilla swap with respect to measure $Q$ is : $$V_{\mathrm{swap}}(t) = \beta(t) \sum_{n=0}^{N-1} \tau_n E_t^Q \left( \dfrac{1}{\beta(T_{n+1})} ( L(T_n, T_n, T_{n+1}) - k) ...
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1answer
81 views

Derivation of Black-Scholes equation by riskless portfolio

The following is a summary of the derivation of the Black-Scholes equation as given on wikipedia (http://en.wikipedia.org/wiki/Black-Scholes_equation#Derivation) - I have a question regarding the ...
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1answer
15 views

Formula for fitting step-wise increasing loan payments into a given term

My company is developing a product that helps people project out what-if scenarios for paying down their student loan debt. One of the government options for paying off debt is called the "graduated" ...
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2answers
66 views

How much more than will you pay on a 30 year mortgage than if you paid it all up front?

There are hundreds of loan calculators online but none of them tell me this, Say I take out a 30 year mortgage on a 80,000 dollar house for 4% interest. How much more than $80k will I spend at the ...
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1answer
27 views

Question on interest

I have a question about interest on a loan from a family member, and it is difficult figuring out. I borrowed \$35,000 @ 3.5% in June, 2013, and here's the break down of the payments I've made: ...
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1answer
56 views

What is the purpose of a trailing minus sign?

I cashier at a grocery store and the POS system we use (SurePOS by IBM/Toshiba) uses trailing minus signs for all of its representations of negative numbers. Examples: Coupon being rung up: ...
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92 views

In stochastic calculus, why do we have $(dt)^2=0$ and other results?

I'm doing actuarial problems of Exam MFE and it covers some of the stochastic calculus (like Ito's Lemma). One of the frequently used results are the so-called "multiplication rules": $(dt)^2=0$ ...
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1answer
27 views

Break Even Point

Suppose that x thousand units of a product will be sold when the price is p(x) = 50 - 1.25x dollars per unit and the cost of producing x thousand units is C(x) = 20x + 100 thousand dollars. a) What ...
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21 views

Multi year installment loan. Know monthly compouning rate, wish to find simple equivalent rate

First of all, thank you very much for your time. Since I have no math background whatsoever, please pardon me for my ignorance (which is not bliss here). I am not looking for the formula to get a ...
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1answer
16 views

Deffered annuity with perpetuity

An annuity immediate has $40$ initial quarterly payments of $20$ followed by perpetuity of quarterly payments of $25$ starting in the eleventh year. Find the present value at $4\% $ convertible ...
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11 views

Time homogeneous asset dynamics model

I'm studying asset process. As i know, Black scholes model and CEV model is time homogeneous diffusion model. Are there time homogeneous model ???
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38 views

Basic question mathematical finance, law of one price in single period markets.

I am reading Pliskas Introduction to mathematical finance. And I am at single period models. It is the law of one price I am having a hard time of understanding. I have some questions about this: ...
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1answer
31 views

Dynamics of short rate in HJM

According to a simplified HJM framework, we have: Forward Rate: $f(t,T)=\sigma W_t +f(0,T) +\int_0^t{\alpha(s,T)}ds$, where $W_t$ is brownian motion. Dynamics of forward rate: ...
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57 views

Altering a Lease Calculation to take into account an upfront payment

I am trying to find the interest rate of a lease if we know the monthly payment amount but have an advance payment. I have found a site with part of the calculation we need (Scenario 2 on the link ...
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1answer
19 views

Method to calculate the best way to repay two different loans given a set amount of money per month?

Given two (or more) loans of different balances and interest rates and a single amount of funds available per payment period, is there a way to calculate the best way to split the available funds to ...
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26 views

the intuitive difference between expected utility and utility of expected profit in a gambling game

What is the intuitive difference between expected utility and utility of expected profit in a gambling game ? Which one is the "usefulness of the game" to a player ?
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2answers
73 views

Compound interest with a compounding interest rate

I have an investment which pays 3% interest (r) annually but it also increases the interest rate every year by 5% (g). I re-invest all interest payments at the start of each year. How many years (t) ...
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1answer
50 views

Shape of utility function

I have read in a paper (http://www.public.asu.edu/~kirkwood/DAStuff/refs/risk.pdf) that the shape of the utility function depends on the attitude towards risk. My question is does not it also depend ...
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1answer
45 views

Discrete Fourier Transform Interpretation

Using Mathematica I took the Discrete Fourier Transform (DFT) of a vector whose entries are volumes of a particular stock. The power spectrum is plotted below: There are two questions that I have ...