Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

learn more… | top users | synonyms

1
vote
0answers
93 views

Compactness of the set of densities of equivalent martingale measures

Consider an incomplete market $(\Omega,\mathcal F,\mathbb P)$ driven by a semimartingale $S=(S_t)_{t\in[0,T]}$. Under the no free lunch under vanishing risk (NFLVR) assumption, the set $\mathcal ...
0
votes
1answer
306 views

How to handle the following percentage scenarios?

I have the following scenarios, but I am unclear on how to handle them correctly. I start off with a value like 200 and the following scenarios are: Remove 10% from 200, and then remove a compound ...
1
vote
1answer
457 views

Formula for APR with Odd Days

I need to programmatically calculate APR based on the following inputs: Principal Amount Number of payments (for example, 3 months loan is 3 if paying monthly, or 6 bi-weekly payments) Payment each ...
1
vote
0answers
83 views

Good reference on sample autocorrelation?

I'm not a statistician but I'm writing my thesis on mathematical finance and I think it would be neat to have a short section about independence of stock returns. I need to get better understanding ...
1
vote
1answer
124 views

Book or resources to learn about algorithms for detecting arbitrage opportunities in slow markets (not HFT)

All of the trading algorithms I see online relate to high-frequency trading in fast-moving high-volume markets. Can someone point me to some resources about automated trading (detecting arbitrage ...
3
votes
1answer
239 views

Futures pricing and futures price process under the real world measure

This is something that keeps bothering me about the Benchmark approach of Platen, which (very) shortly is as follows: Compare the development of an economic value with a growth optimal portfolio. ...
1
vote
1answer
227 views

One step in the derivation of Black-Scholes

One step in the derivation of Black-Scholes Assumptions:(1) ${\displaystyle \frac{\partial F}{\partial t}(t,x)+\frac{1}{2}\sigma^{2}x^{2}\frac{\partial^{2}F}{\partial ...
0
votes
2answers
1k views

How to calculate CAGR for shares bought at different times?

I have bought shares at following times: ...
0
votes
4answers
253 views

What is the difference between the 2 ways to remove percentages?

Given the value $690$, I want to remove $10$% from that and then remove another $20$% from the resulting value, so as an example, I am doing: $690 \over {(1 + 0.1 + 0.2})$ = $690 \over {1.3}$ = ...
0
votes
1answer
292 views

Figuring a loan payoff amount

I have a loan for a principal amount of \$117,000.00 at 9.75% interest and a total amount due (including the interest for 84 months) of \$191,805.60. I had 84 months to pay it off, or I could pay it ...
1
vote
1answer
710 views

brownian motion-proof of Martingale

Can anyone help me with the following problem? Let $W(t), t\geq 0$ be a Brownian motion with filtration:$F(t)$. Let $0\leq s\leq t$. 1- Show that $E\left [ W^{3}(t)\mid F(s) \right ...
0
votes
1answer
109 views

Determine Present value if you have a payment, interest rate, term

If I have a payment amount, interest rate, and term can I determine the Present Value? for example: ...
0
votes
2answers
3k views

Is it possible to calculate weights of a portfolio with negative values?

Sorry in advance if this question is either too basic or really dumb, but I've been researching this and am a bit confused. I'm trying to help my niece with a question she has and the gist of it is ...
1
vote
0answers
27 views

Standard practice for identifying outlying spend amounts

Hope this is mathematical enough to qualify as a question - I'm no mathematician! I have a set of individuals travel & entertainment credit card spend, and I'd like to highlight any outliers that ...
1
vote
0answers
78 views

Portfolio optimization - problem with a proof

I'm trying to proof Proposition 1 in this Paper about Markowitz Portfolio Opitimization on page 6/7 but I can't figure out how to do this. The author wrote "The proof of Proposition 1 can be found ...
2
votes
1answer
2k views

Continually Compounded Interest + Addition to Principal

This is essentially the continually compounded version of this question. I want to know how much money I will have after continually compounding interest, plus continually adding a fixed amount to ...
2
votes
1answer
3k views

Effective Annual Rate Calculation: Tricky periods and payout frequencies

For calculating the Effective Annual Rate (EAR) from various stated interest rates, I'm using the formula: $$EAR= \left(1+\frac{r}{p}\right)^{pt}-1$$ where, $p$ = no. of payouts in a period, $t$ = ...
2
votes
2answers
240 views

Black Scholes model

I am looking to program the Black Scholes model, but I don't understand how to write this equation as basic math. Equation => http://en.wikipedia.org/wiki/Black%E2%80%93Scholes Known inputs => ...
1
vote
0answers
396 views

Reading advice: Mathematical finance for a student of pure mathematics

Which books/lecture notes should a student with a background in pure mathematics (in my case it was geared towards algebraic geometry) read in order to do financial math? I have done one basic course ...
1
vote
1answer
418 views

today's price of a European put option with payoff $(K-S_1)^+$

I'm trying to calculate the today's price of a European put option, which strikes at price $K$, so that the payoff is $(K-S_1)^+$, in an arbitrage-free, one-period market. As of now, I can only think ...
4
votes
1answer
3k 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; ...
0
votes
1answer
629 views

Matlab multivariate normal distribution parameters (mvnrnd)

I need to use the mvnrnd function in matlab to generate random monthly returns for a set of assets. However, I am a bit confused about how to use this function to do it since it asks me MU and SIGMA ...
0
votes
1answer
474 views

Are quadprog and portopt equivalent in Matlab?

What exactly is the difference between quadprog and portopt in Matlab? For example if I use quadprog (minimizing the variance) in a loop in which I continuously iterate through the expected returns of ...
1
vote
1answer
2k views

Matlab Trust-region-reflective algorithm warning

I am very new to matlab and trying to solve portfolio optimization problem (minimizing the variance) using quadprog: ...
0
votes
2answers
66 views

How is it possible to revise for a maths test of this type - Which is the best method to solve it

I need some help with this question, My answer to question E) is 1880 pounds per year, can anyone suggest a different answer, also does anyone know how would I revise for questions of this type. ...
0
votes
2answers
2k views

Using Matlab quadprog to solve markowitz model

I have the markowitz model shown below and I need to use the quadprog function to solve it (i.e get the values for w_i values). However I am a bit new to mat lab and not sure which definition of ...
1
vote
1answer
442 views

Markowitz portfolio optimization

Say that there are 5 assets with given mean values, standard deviations and correlations. Is it possible to find the expected return of a risk-seeking portfolio (maximum expected return) by using ...
0
votes
1answer
375 views

Price-Yield Curve with Matlab

Not sure if this is the right place to ask but I was wondering if anyone has an idea about how to draw a Price-Yield curve. Is there ready-to-use formulas for this purpose ? An example of curve and ...
8
votes
4answers
661 views

How do you solve equations of any degree?

I have stuck solving this problem of financial mathematics, in this equation: $$\frac{(1+x)^{8}-1}{x}=11$$ I'm stuck in this eight grade equation: ...
0
votes
2answers
251 views

Portfolio Optimization Problem Without Correlation Info

I received this interesting problem from a friend today: Assume that you are a portfolio manager with $10 million to allocate to hedge funds. The due diligence team has identified the following ...
3
votes
4answers
56k views

What is the formula for calculating Profit Percentage?

Let cost price of an item be $C$, selling price be $S$. Assume the seller gets benefited. Then, Profit, $P = S - C$. Now, What is formula for calculating Profit Percent? $P \% = \dfrac{P}{C} ...
0
votes
4answers
1k views

Find out monthly growth based on yearly growth

Let's say I have a number, 10, and over a period of a year that number has increased by 100% to ...
6
votes
1answer
6k views

Average percent increase not equal to total percent increase?

I tried searching around for this but it was difficult to boil down the search terms. Plus nothing seemed to be showing up anyway. What's an easy way to show that the average percentage increase of n ...
0
votes
2answers
92 views

What is the value of x with exponential growth but decreases as it reaches its maximum?

I am building a financial model. I am looking for the value of Y:number of subscribers over X:month. The model calls for the following. Competing of a market with 500,000 exclusive subscribers. ...
0
votes
1answer
424 views

Real-world example for utility theory

I'm stuck with Utility Theory. As I understand it, we have vector $\vec{x}$ representing evidence about the world $n$ possible states of the world $S = \{S_{1}, S_{2}, ..., S_{n}\}$ $m$ possible ...
0
votes
1answer
95 views

Reducing balance with overall percentage

Hi I have an item for £4000 which should have a reduction of 20% over the year. I want to calculate the value for each month. What equation would I use?
4
votes
1answer
191 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 ...
0
votes
2answers
218 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 ...
0
votes
1answer
51 views

Is there a way to find precision used based on margin of error in compound interest problem?

As the question states, is there a way to find precision used based on margin of error in compound interest problem? The question is based off the following scenario: A financial system that ...
0
votes
2answers
47 views

Calculating monthly reduction in value

If I can assume a value of $100,000 will reduce by a sum of say 25% each year, how do I calculate the amount it will reduce by each month over a period of 3 years.
1
vote
2answers
20k views

Calculate gross salary when knowing the net salary and tax brackets

Assume the annually gross salary is $100,000. Tax brackets: 0 - 50K - 10% = 5K in taxes 50K - 70K - 20% = 4K in taxes 70K - $90K - 30% = 6K in taxes 90K and up - 40% = 4K in taxes The income tax ...
4
votes
2answers
184 views

Calculating credit card charges based on provided APR, balance amount and monthly payment amount?

Please first see the below sums and then the info below it to get a better understanding of my question: My input: ...
1
vote
1answer
379 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 = ...
0
votes
1answer
195 views

I am not getting correct currency converstion

Please can someone kindly aid me with correct solution. The question ask: If EUR 100 were used to purchase British Pounds in Year 1, what would be their approximate value if they were kept for a ...
0
votes
1answer
73 views

Have I correctly used currency conversion

Please can you help me with this question? I think I have the right answer but I want to make sure. The question asks: JPY 1,000 in Year 1 is worth how many US dollars in Year 1? Assume Value ...
1
vote
2answers
150 views

how seconds per year does the average worker work?

Approximately how many seconds per year does the average 18 – 21 year women factory worker work? Choices are... A] 2,526 B] 80208 C] 5700 D] 3,443 E] 3958 assuming Accident per person per year is ...
1
vote
1answer
299 views

not getting the right proportion

I got this answer wrong. I thought it was 55% but it seems the answer is different. Please can you have a look at this and tell me where have I gone wrong and it should be. Thanks in advance. Q) ...
0
votes
0answers
367 views

best revenue to Costs ratio

Would you say for best revenue to costs ratio would be D as cost is 0.4. Thanks in advance for your help. A) 109 (Sales Revenue) : 141 (Cost) = 0.77 B) 533 (Sales Revenue) : 307.92 (Cost) = 1.73 ...
3
votes
2answers
669 views

Maximizing a function containing an integral

Problem. Let $\rho\colon[-1,\infty)\to\mathbb{R}$ be a function such that $$\int_{-1}^\infty\rho(x)\,dx=1.$$ Let $G\colon[0,1]\to\mathbb{R}$ be a function that is defined with $$G(f) := ...
0
votes
1answer
47 views

Do I need to calculate the payments of revenue earned as well, for present value?

A service bureau is considering renting a computer for $24$ months at $\$15,000$ per month. The first $11$ months will be required to test software for the particular application to be offered by ...