Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [finance]

Questions related to the various aspects of financial mathematics. Topics include option pricing, arbitrage theory, market completeness and stochastic analysis.

Mathematical finance, also known as quantitative finance, deal with finance and financial markets in a mathematical manner.

Some examples of mathematical finance are the fundamental theorem of asset pricing which provides the conditions for a market to be arbitrage-free and complete, and the Black–Scholes equation, which uses partial differential equations to describe the price of an option over time.

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2637 questions
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"Real" total cost of zero-interest loan

Many solar panel manufacturers and banks are offering zero-interest loans to induce buyers to pull the trigger on a residential install. I have been doing some calculations and it seems that if I get a competitive quote then it should be rational…
user14717
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Financial Mathematics: Annuity relating to loan

You took a loan of 500,000 which required to pay 25 equal annual payments at 10% interest. The payments are due at the end of each year. The bank sold your loan to an investor immediately after receiving your 6th payment. With yield to the investor…
Liow Wei Sheng
  • 65
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Net Present Value

You run a construction firm. You have just won a contract to construct a government building. It will take one year to construct it, requiring an investment of $9.78$ million today and $5$ million in one year. The government will pay you $22.5$…
C. Matthews
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Money Interest Problem

Jake has loaned 20000 pesos from the bank with an interest of 10% every year. If Jake completes the payment within 3 years, what amount should be paid to the bank? Could someone explain to me the entire solution?
Mczaqyah
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Trinomial tree option model

I need help with this exercise: Consider the market model with two assets risky represented by: $S_0=220, S_u=230, S_m=210, S_d=190, D_0=105, D_u=115, D_m=105, D_d=100$ The market interest rate is 1%. Show that the model has opportunities of…
Mathuser
  • 59
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4 answers

Negative time value of put option

I am analyzing valuation of European put options in non-Gaussian environment. I realized, that put option can easily get negative time value, when it is deep in the money (spot price close to zero). Ultimate proof, that such negative time value…
Jyrki
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Rate of return on t-bill

An investor bought a $63$-day Treasury bill with a face value of $\$105000$ to yield $3.55$%. The investor sold the T-bill $23$ days later to another investor who yields $2.8$%. What rate of return did the original investor realize? So right off…
Alex Vincent
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Force of interest

Suppose the force of interest over the time interval $[1,3]$ is given by $\delta (t) =\alpha +\beta t^{-1}$. If $100$ invested at $t=1$ grows to $120.74$ at $t=2$ and $100$ invested at $t=2$accumulates to $114.00$ at $t=3$. Find $\alpha$ and…
Tosh
  • 1,614
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1 answer

Finding effective annual rate of interest

The present value of $2x$ paid at the end of $k$ years and the present value of $x$ paid at the end of $2k$ years sum up to $2x$. Show that the annual rate of interest is $(\frac{\sqrt{3}+1}{2})-1$ I tried summing the present values of each…
Tosh
  • 1,614
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2 answers

Finding the monthly payment for fixed-rate mortgage, but with first month interest free.

I'm trying to calculate the monthly payment of a fixed-rate (annuity) loan, but with the twist that the first month is interest free. I.e., I have a principal $P_0$ - the total sum that I've loaned - and I want to pay it off completely in $N$…
skagedal
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Math Finance Question NPV?!

A foundation announces that it will be offering one MIT scholarship every year for an indefinite number of years. The first scholarship is to be offered exactly one year from now (today is year $0$, one year from now is year $1$). When the…
Jackie Vazquez
  • 65
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1 answer

Financial mathematics annuities problem

I'm having trouble understanding the solution of this problem. Find the present value of a ten-year annuity which pays $400$ at the beginning of each quarter for the first 5 years, increasing to $600$ per quarter thereafter. The annual effective…
user270494
  • 687
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Financial Mathematics problem.

Consider a property developer who buys a property at time $0$ for $\$90,000$. He also spends $\$10,000$ at time $0$ to buy some materials he will use to develop the property. Ignoring Inflation , the investor thinks that the property will be worth…
User9523
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Financial Mathematics problem

$i^{(p)}$ is the nominal interest converted p-thly i.e the total interest per unit of time paid on a loan of amount 1 at time 0 where interest paid in p equal installments at the end of each p-th sub-interval. I can't understand the statement given…
User9523
  • 2,094
2
votes
1 answer

Calculate payoff time for PV system

I want to calculate the payoff time for a photovoltaic system. Some constants: Current electricity price per kWh: 0,122 EUR Electricity production per yearh: 4427 kWh Annual electricity price increase: 5% Feed rate into the power grid: 68% Costs:…
testing
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