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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Average Interest Payment For Specific Period of Ammortization Schedule

I would like to derive an equation that calculates the average interest payment x for an amortized mortgage loan in the first m months of the loan. Call the interest rate i and the principal p and the number of months n. I understand the…
ChemDev
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XIRR and Interest Rate Calculation

I am having trouble reconciling the XIRR function in Excel with real world amortization schedules. I have narrowed down the issue to a really simple example. Interest Rate: 7.5% per annum compounding daily Principal: $100,000 Loan term: 1…
Phil Degenhardt
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How to calculate the ⌉ operator?

In a book about finance, the following formula appears: $$\large a_{10 \,⌉\, 0.04}$$ What is this ⌉ operator and how to read / calculate it?
Alexander Rechsteiner
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How are Annuity problems solved?

I'm unsure how to solve the following problem: Angie wants to plan a trip to Hawaii with her husband on their 10th wedding anniversary in two years. She anticipates that the all-inclusive trip will cost $9500 for both of them and wants to start…
jmasterx
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Calculating future value and Present Value

I have been stuck on this one for hours ... not too great at math can someone help. Thanks. Isaac borrowed $\$4000$ at $11.5\%$ compounded quarterly $5.5$ years ago. One year ago he made a payment of $\$1500$. What amount will extinguish the loan…
user100115
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Loan: monthly payments plus additional amount paid at end of year

The interest rate on a 30 year mortgage is 12% compounded monthly. the mortgage is paid by monthly payments of 700. Suppose an additional 1000 is paid at the end of each year to payoff loan early, compute for outstanding balance at the end of 10…
Yolo
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Price sensitivity under Uniswap

Question. Under the uniswap pricing rule, what determines how much the price of an asset increases when you buy that asset? Note. while this is a mathematical question, answering it requires an understanding of uniswap. For this reason, I apologise…
afreelunch
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Why is the inequality $c>S-Xe^{-rT}$ (relating European call option price to spot price and strike price) strict?

Define \begin{align} c & \text{ the price of a European call option at time } t = 0, \\ S & \text{ the spot price of a share at time } t=0, \\ X & \text{ the strike price for the option}, \\ T & \text{ the expiry time of the option}, \\ r & \text{…
mjc
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Question About Notation of CRR

I am reading a book on financial theory and it has been a while since I took a notation heavy math course so could someone help me out here... Now with this equation how does the sum work? Do I do the factorials first? Is it a sum for each value…
Jackie
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How is this solution for two different stock growths calculated?

There was a problem in my lecture and I'm having difficulty understanding the solution. It is this: A common stock was paid a dividend of $2. The dividend is expected to grow at 8% for three years, then it will grow at 4% in perpetuity. What is the…
Juniper
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How does one calculate product pricing to cover processing fees from $\$5$ to $\$5,000$ while maintaining a profit?

Credit card processor charges, for each transaction, $2.9\% + \$0.30$. I need to find an amount that covers that cost, from $\$5$ to $\$5,000$, on a per item basis, all while maintaining a small profit. For example, a customer may want to purchase 3…
jasonsfa98
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Conflicting results regarding a problem in Simple Interest

I am having trouble solving a certain question on a basic Simple Interest. Here's the question "Person A borrows a sum of 6300 dollars from Person B at the rate of 14% per annum for 3 years. Person A added some more money in it and lent it to Person…
Minto P
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Calculating the present value of a payment after n days (APY)

I am currently trying to fully understand the APY concept in finance (I know very basic). I would be very greatful, if you could help me with my problem. The following example is given: The current 1 month market rate is 5%. The term-structure is…
Alex
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why can we add accumulated values in example shown below?

Can you explain to me why we're able to add the accumulated amount of 1000 invested for 5 years to the additional accumulated value of 1000 they invested after 3 years?
John van Zalk
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Sufficient condition for no arbitrage in a discrete time market

Assume there is a multi period discrete market i.e. a finite Probability space, finite time periods $\lbrace 0,1\ldots, n\rbrace$, a stochastic process $(S(t))_{t\in\lbrace 0,1,\ldots,n\rbrace}\subseteq \mathbb{R}^d$ with $S_0(t)>0$ for all…
MackeyTopology
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