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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How is the daily/month compound interest calculated?

I am trying to work out how this website is calculates the daily and month compound interest. The website is taking the profit/loss from the broker for each trade and calculating the overall % gain. The it calculates the compound. I am not sure how…
Keith Power
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Solving for unknown number of payments in drop payment annuity

A fund of 2,000 is to be accumulated by n annual payments of 50 by the end of each year, followed by n annual payments of 100 by the end of each year, plus a smaller final payment made 1 year after the last regular payment. If the effective rate of…
MinYoung Kim
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Financial Mathematics : Annuity loan with a different first period?

Edit:Typo in $\LaTeX$ transcription. Edit 2: Please note that my assumption here is wrong. The correct equation is available in my separate answer. When trying to teach myself some finance math I've stumbled to get the exact same decimals for the…
Johan
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Assumptions in converting between nominal/effective interest/discount

$$ \left(1+\frac{i^{(m)}}{m}\right)^m = 1+i = \frac{1}{1-d} = \left(1-\frac{d^{(n)}}{n}\right)^{-n} $$ where $i=$effective interest rate, $d=$ effective discount rate, $i^{(m)}=$nominal interest rate , $d^{(m)}=$nominal discount rate First, the…
MinYoung Kim
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Discounting and Interest

The amount of interest earned on A for one year is 336, while the equivalent amount of discount is 300. Find A. Correct answer: $A=2800$ My work: From the interest, I get that $A(1+i)-A = 336 \iff Ai = 336$ However, I'm not sure how to interpret…
MinYoung Kim
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Two investments and accumulation function

Suppose that $a(t) = 0.1t^2 + 1$. At time 0, 1000 is invested. An additional investment of X is made at time 6. If the total accumulated value of these two investments at time t=8 is 18800, what is X? My work: From original investment, at time t=6,…
MinYoung Kim
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Why is the annual interest rate given if the principal isn’t compounded annualy?

Back in middle school, We learned that if the interest rate given, r, is annual, it must be divided By the number of times compounded per year, n, to get interest rare per period. I was reviewing compound interest for a standardised test and it got…
Vulgar Mechanick
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Given a varying force of interest where $\delta=kt$, where an unknown amount of money will double itself, find an expression for K

The book says the answer is $\frac{ln(2)}{50}$ but I do not see how unless this a typo or I am missing something very fundamental It is known that an amount of money will double itself in 10 years at a varying force of interest of $\delta=kt$. Find…
K. Gibson
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Converge to a Dirac Delta Function

I was reading something when the author said that "x converges to a dirac delta function". Was wondering if someone could explain what it means. I work in IB and am unsure what this means. The exact comment was "The longer the maturity, the more and…
Winnie
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Financial Mathematics Effective rate of interest

If you invest \$1000 , and you get paid \$500 in 5 years, \$1000 in 10 years, and \$1500 in 15 years and then get a final payment of \$2000 in twenty years, what is the effective annual rate of interest you got? Assume that your bank account pays 1%…
Kartik Ohri
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Conflicting Loan Amortization Formulae

When running a financial loan payoff simulation, I realized that my calculated monthly payment differed from the calculator offered by popular loan service Sallie Mae. I found two formulas for loan amortization when constraining number of payments.…
Ra31513
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Bond pricing and arbitrage

I'm struggling to come up with an arbitrage argumento to prove the following statement: Let $B(t,T)$ denote the cost at time $t$ of a risk-free $1$ euro bond, at time $T$. Assume that the interest rate is a deterministic function. Show that the…
Diogo Fonseca
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Calculate effective interest including fees, mortgages and nominal interest

In order to compare credit cards I would like to calculate the effective interest of each with the following variables: nominal interest = e.g. 10% startfee = e.g. 300 monthly_fee = e.g. 25 period = e.g. 36 (months, e.g. 3 years) credit_sum =…
Christoffer
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Black-Scholes Pricing for Fixed Payout Derivative

I have a question about how to derive a Black-Scholes-esque pricing model, given a fixed payout rather than one that varies with stock price. More specifically, if given a derivative which pays out a fixed \$x if the share price $S(T)$ is greater…
Math
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Isolate Variable in Fraction

I can approximate u with a calculator by guessing or using excel but I want to isolate it. $100 = \dfrac{1 + \dfrac{1}{(1+u)^6}}{u}$ Can not seem to do it by hand myself. Is it possible using only simple algebra?
Haydow
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