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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3
votes
1answer
125 views

Approximating the compond interest for a loan

A young boy (13 years old), son of friends of mine, is already very dedicated to mathemetics. He told me that, in the classical formula $$A=P\frac{i \,(i+1)^n}{(i+1)^n-1}$$ using his calculator he was ...
2
votes
1answer
76 views

Actuarial : “ Amortization - mortage”

What is the monthly payment for a $800,000 mortgage for the first 119 payments that is due in 10 years, has a 25 year amortization, at 5% interest? What is the amount of the 120th payment? I use ...
3
votes
2answers
3k 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 ...
1
vote
1answer
83 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 ...
3
votes
1answer
226 views

What is the Most Efficient Way to Calculate the Internal Rate of Return?

I have built a program that prices financial assets and it does this in part by calculating the IRR. The problem is that it does not run as quickly as I would like it to. I currently use the Newton-...
2
votes
2answers
692 views

Baseball betting and probablity

Here is a question that came up during class discussions on Friday: Your favorite baseball team is playing against your uncle's favorite team in the World Series. At the beginning of each game, you ...
2
votes
1answer
176 views

Is the following a martingale?

Let $X_{n}$ be a martingale with respect to a filtration $\mathbb{P}_{n}$. Define: $Y_{n}$ := $X_{n}^{3}$ Is $Y_{n}$ a martingale? Supermartingale?
1
vote
2answers
157 views

How to solve for $i$ and $n$ in compound interest formula?

Given that $$F = A{ (1+i)^n - 1 \over i}$$ How can you solve for $i$ or $n$?
1
vote
1answer
166 views

american put option

For a perpetual american put option $v(s)$, satisfies the following problem: $$\frac12\sigma^2S^2\frac{\mathrm d^2V}{\mathrm dS^2}+(r-D)S\frac{\mathrm dV}{\mathrm dS} - rV = 0\quad\text{for }S^*<S&...
6
votes
1answer
7k views

Price of a European Call option is a convex function of strike price K

I'm trying to show that the price of a European call option (payoff function is $(S_1-K)^+$) in a no-arbitrage market is a decreasing and convex function of K. That it shall be decreasing makes sense; ...
5
votes
0answers
420 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": $(dt)^2=0$ ...
4
votes
2answers
319 views

Book request: Mathematical Finance, Stochastic PDEs

I'm a math student, starting a PhD in the near future. My field of research will be mostly in the field of applied mathematics / numerics. Topics will deal with Kinetic Theory, Moment Equations, ...
4
votes
2answers
9k views

What's the math formula that is used to calculate the monthly payment in this mortgage calculator?

What's the math formula that is used to calculate the monthly payment in this mortgage calculator? I would like to know this math formula so that I can plug in the following values ...
1
vote
2answers
644 views

What is an alternative book to oksendal's stochastic differential equation: An introduction?

What is an alternative book to oksendal's stochastic differential equation: An introduction? But also An alternative that is over 300 pages and at the same level? Some professor refer that book as a ...
0
votes
2answers
274 views

Future Values of Annuities

Michelle has decided to invest $3000 at the end of each year for the next five years in a saving account that pays 8% annually, compounded semi-annually. How much is the annuity worth after 5 years? (...
4
votes
1answer
1k views

What is the definition of a “predictable process”?

I am reading a book on financial mathematics, and frequently encounter the phrase "predictable process", which I haven't seen definition of, and cannot find the definition online. At first I thought ...
3
votes
2answers
75 views

Does the term “selling price” mean the “cost price” or the “sale price” of a product/commodity?

I have been told that the idiom "selling price" is the same as the cost price of an item, that is the amount which a seller pays to, e.g. a wholesale merchant. The seller later sells the commodity at ...
1
vote
0answers
367 views

Calculating the interest rate for an annuity (Exam FM)

I have been searching for a way to solve for the interest rate given the monthly payments of a loan. I would like to set up a problem as the following. $X$=monthly payment , $i$=effective ...
0
votes
1answer
926 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 ...
0
votes
2answers
274 views

Resolving a paradox concerning an expected value

We have a coin that has a probability $p>1/2$ of coming up heads (and probability $1-p$ of coming up tails). We now play the following game: We start with a fortune of one dollar. We toss the ...
5
votes
1answer
339 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 of ...
4
votes
1answer
230 views

Maximizing gambling performance over the long run

Background. We can play a game in which we can put one dollar and get out $X$ dollars, where $X$ is 2 dollars with probability $p>1/2$, or zero dollars with probability $1-p$. We also assume that ...
4
votes
1answer
93k 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. ...
3
votes
6answers
26k views

Most efficient method for converting flat rate interest to APR.

A while ago, a rather sneaky car salesman tried to sell me a car financing deal, advertising an 'incredibly low' annual interest rate of 1.5%. What he later revealed that this was the 'flat rate' (...
3
votes
0answers
171 views

Algorithm/Formula to compute adding and/or removing compound and/or non-compound percentages from a value?

I will first start with a scenario, I have to apply some adjustments to a particular value. These adjustments are either compound or non-compounded and they can either be added or subtracted to the ...
2
votes
2answers
53 views

Compound interest: how to use the textbook formula?

To derive a general compound interest formula we can say: $$A_1=A_0 + rA_0=A_0(1 + r)$$ $$A_2=A_0 + rA_0 + r(A_0 + rA_0)=A_0 + 2rA_0 + r^2A_0=A_0(1 + r)^2$$ and so on. In general: $$A_t=A_0(1 + r)^t$$ ...
2
votes
1answer
451 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 ...
1
vote
2answers
59 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 ...
1
vote
1answer
50 views

Inequality of an expectation (here: perpetual put of an american option)

for a given function $u(x):=\sup_{\tau \in T_{0,\infty}}E[(Ke^{-r\tau}-xe^{\sigma B_{\tau}-(\sigma^{2}\tau)/2})_{+}1_{\tau <\infty}]$ and $x \in [0,\infty)$, K a positive real number, $(B_{t})$ a ...
1
vote
1answer
836 views

Determining tax percentage

I'm working a problem, attempting to find a income tax rate that will change depending on the gross paycheck amount. Some data points: $800 gross = 11% taxed $1500 gross = 16% taxed $2000 gross = ...
1
vote
5answers
41 views

How to calculate the price of a product without the sales tax, if we know the price including the tax and the rate of the tax?

The question is The price of a mobile phone is $8800 inclusive of a 10% GST (General Sales Tax). What is the original price of the mobile phone? This is how I approached it: The Sale Price <...
0
votes
1answer
159 views

Interest Rate Tree in Matlab

I would like to calibrate a interest rate tree using the optimization tool in matlab. Need some guidance on doing it. The interest rate tree looks like this: How it works: 3.73% = 2.5%*exp(2*0.2) ...
0
votes
1answer
90 views

Interest with Inspection Fee in Promissory Note

A man borrowed from a bank a promissory note that he signed in the amount of 25000 for a period of one year. He received only the amount 21915 after the bank collected the advance interest and an ...
0
votes
1answer
1k 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 ...
0
votes
1answer
80 views

Covariance in normal lognormal (NLN) mixture

Let $u = \epsilon e^{\frac{1}{2} \eta}$ where \begin{equation*} \left( \begin{array}{c} \epsilon \\ \eta \\ \end{array} \right) \sim N\left( \left( \begin{array}{c} 0 \\ 0 \\ \...
0
votes
1answer
164 views

Recurrence relation for a mortgage

Find a recurrence relation for the amount of money outstanding on a \$40,000 mortgage after n years. The interest rate on the mortgage is 10% and the yearly payment is \$2,000( the yearly payment is ...
0
votes
0answers
24 views

Cumulative Return between two dates

I have a table that carries data with cumulative return of some instrument. Data is described with start date, end date and cumulative return for date range (start-end): ...
0
votes
1answer
2k views

Money-Weighted and Time-Weighted Rate of Return

I have a question on Time-Weighted Rate of Return (TWRR) and then a question on the links between MWRR and TWRR, An investor invested £100 in a fund on Jan 1st 1998 and another £100 on Jan 1st 1999. ...
-2
votes
1answer
30 views

What is the difference between these two formulas that price a stock? [closed]

What is the difference between these two formulas? They are both related to the price of a stock in the black-scholes model. The fact that the second one uses $t$ as a subscript which means it's not a ...