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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2
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1answer
200 views

Calculate interests

Simply wants to calculate interests of an initial amount $N$, with a monthly payback $m$, and a year interest rate of $R$ I guess the interests are not cumulated each month, but just at the end of ...
2
votes
1answer
149 views

Black scholes model type

I want to study the following market: $$S_1(t)=S_1(t)(\mu_1dt + \sigma_1dW_1(t))$$ $$S_2(t)=S_2(t)(\mu_2dt+\sigma_2dW_2(t))$$ for $t\in [0,T]$, constants $\mu_i,\sigma_i$, initial values ...
1
vote
1answer
287 views

Compound interest quarterly

I know the financial formula for calculating compound interest: Compound Interest Multiple = [1+(Annual Interest in decimals/365)]^(number of days). I have a initial and final date. I calculate the ...
2
votes
2answers
761 views

Daily rate loan APR

This example comes from used car software that is approved in Texas, a state which calculates interest using a true daily earnings method (definition below): The terms are: Amount financed: 5,000 ...
0
votes
1answer
29 views

Capping part of a sum

I have a financial constraint which states that: spend on x cannot exceed 15% of total spend, where ...
2
votes
0answers
452 views

Analogue of Leibniz Rule for Stochastic Integrals

Suppose $$f(t,u)=f(0,u)+\int_0^t{\mu (w,u)dw}+\int_0^t{\sigma(w,u)dB_w}$$, where $B_w$ is a standard Brownian motion. I would like to calculus the drift and diffusion of $Y_t=-\int_t^s{f(t,u)du}$ ...
1
vote
1answer
296 views

Net Present Worth Calculation (Economic Equivalence)

I'm currently doing some work involving net present worth analyses, and I'm really struggling with calculations that involve interest and inflation, such as the question below. I feel that if anyone ...
7
votes
2answers
386 views

Significant digits

We use currency conversion rates for financial calculations. Our currency conversion table stores conversion rates to and from each currency (about 150 world currencies) for each day, going back 20 ...
1
vote
1answer
105 views

PayDay loan APR

I'm not convinced I'm getting the correct figure when I calculate an APR rate. I have an amount I want to loan £100 I want to pay this back in 14 days. Interest for this loan is 15% The fee for this ...
0
votes
1answer
72 views

annuities and interest

The loan of 30.000 euros is depriciated after 10 years, with equal annuities and interest of 11% of annual capitalization. how can the annuity be determined? -this one seems to be the toughest of them ...
1
vote
2answers
39 views

Percentage of capitalization

After how many years the deposited sum of K-euros will triple itself if the interest percentage of capitalization is 12%, the capitalization is annual.
1
vote
2answers
134 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 $n$?
2
votes
1answer
714 views

Converting an Annuity due to Annuity immediate

I'm working on the following problem at the moment while preparing for an exam. Find the present value of payments of 200 every six months starting immediately and continuing through four years from ...
1
vote
4answers
2k views

Second Price Auction (Generalized Second Price)

I am trying to find out why we pay second price, but can not understand it. All that I found it is an explanation that it is a real market price, but why it is ? May be some example helps me. For ...
2
votes
1answer
256 views

How to compute ideal investment leverage ratio to maximize median return? [closed]

If I had an investment that with 50% likelihood quadruples your investment on a given day and you lose it all also with 50% likelihood, what percent of your money should you invest each day to ...
1
vote
0answers
96 views

Uniform convergence of series with utility function

Let $u(x)$ be a real function with the properties $u(x)$ is continuous and non-decreasing in $x$ $u'(x)$ is non-increasing in $x$ $u(0)=0$ $u'(0)=1$. In other words, $u(x)$ is a utility function. ...
0
votes
1answer
98 views

Showing an inequality with interest rates and compounding

Suppose that your grandmother is receiving Social Security at the start of next year and has to choose between two plans for how to receive her payments. Divide each year into $k$ payment periods ($k$ ...
3
votes
1answer
4k views

Confused about Effective Rate of Discount- Theory of Interest

I'm currently reading Kellison's book, The Theory of Interest. I've reached the chapter on Effective Rate of Discount and it's somewhat confusing. The book explains it as a loan where interest is paid ...
1
vote
1answer
620 views

Help understanding confusing present value question (Theory of Interest)

I'm currently enrolled in a theory of interest class that covers the same material that's on exam 2/FM. At the instructors recommendation, I'm working through all of the problems in the book on my own ...
2
votes
1answer
459 views

How to get Annualized volatility from monthly return?

Suppose the average monthly return is $\mu$, the monthly standard deviation is $\sigma$ and denote the autocorrelation of monthly returns by $corr(r_i,r_{i+h}) = \rho(h)$ Prove that, when $\sigma$ ...
1
vote
1answer
558 views

How to find Profit percent in this case?

A trader allows a discount of 20% on his goods and still makes a profit of 25%.Find the profit percent made, if he sells his goods at: (1) the Marker price (2) at 10% discount What i've tried: ...
1
vote
1answer
10k views

How do you calculate “excess returns”?

(Although this is perhaps a very simple question, math-wise, it still has me puzzled so it's okay to ask for help here I guess. I really need to understand this, so any help is appreciated) First, ...
1
vote
2answers
234 views

How to find the original population if it increases with a constant rate?

The population increases by 5% every year. What was the population in 1982, if in 1985 it was 1,85220? My working: ...
0
votes
2answers
3k views

How to find rate of depreciation in this problem?

The value of a machine is estimated to be 27,000 at the end of 1994 and 21,870 at the beginning of 1997. Supposing it depreciates at a constant rate per year of it's value at the beginning of the ...
-1
votes
3answers
40k views

What is the formula for the difference between CI and SI?

if principal, time and rate are given how do i find the difference between Compound interest and Simple Interest? P=12,000 n=1 and a 1/2 yrs. R=10% per year ...
1
vote
1answer
147 views

Calculate Compounding Interest Rate From Total Interest Rate?

I would like to be able to calculate the interest rate that is compounded for a given total interest rate, and number of compounding events. TotalInterestRate = ...
3
votes
1answer
85 views

How the banker limits his risk?

In a game like Deal or no Deal, what is the formula the banker uses to give an offer to the contestant? The banker offers the contestant an amount of money to quit the game, the offer based roughly on ...
1
vote
0answers
109 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
497 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
603 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
1answer
137 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
275 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
251 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 ...
1
vote
2answers
2k views

How to calculate CAGR for shares bought at different times?

I have bought shares at following times: ...
0
votes
4answers
361 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
327 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
932 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
121 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
4k 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 ...
2
votes
0answers
29 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
96 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
3k 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
5k 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
267 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
1answer
508 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 ...
5
votes
1answer
5k 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
900 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
560 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
3k 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
74 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. ...