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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Why are call options necessary?

My question is actually less ambitious and more specific then the title may have lead you to believe. Suppose the interest rate is $25\%$ you have a stock at time zero price of $S_0=50$ and at time 1 its price will either be $S_1=25$ or $S_1=100$. …
Set
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Valuing Bonds With Continuous Coupon Yields

How do I find the value of bonds with continuous coupon yields and interest rates that are both a function of time?
Podski
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Clean Price calculation

Very struggling with the following problem: Let's suppose you buy a T- note. The trade day is Oct $2, 2020$. The note matures on Nov $15th 2021$ with a $5%$ coupon and yield to maturity $1.6%$. What is the clean price of the note, given face value…
Effective Learning
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What's the meaning behind annuity coefficient?

There is a formula for mortgage month payment calculation: $$ A=P\cdot {\frac {r(1+r)^{n}}{(1+r)^{n}-1}} $$ where: ${\displaystyle A}$ is the periodic amortization payment; ${\displaystyle P}$ is the principal amount borrowed; ${\displaystyle r}$…
gavrilikhin.d
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PV of compounded Perpetuity

I need to find the present value of the growing continuously compounded perpetuity. The question is: Suppose you receive a payment of 4,000 one year from now, but in year 2 the payment will have grown by 1.8% to 4,000 times (1 + 1.8/100), and in…
Effective Learning
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Financial Itô question

Let $(W_t)$ a Brownian motion. Express $W_t^8$ as a sum of Itô and Riemann integral. Use part 1) to deduce $\mathbb E(Z^8)$ where Z has an $\mathcal N(0,1)$ distribution. This is a financial mathematics question, I've reviewed the lecture and…
Ryan
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Forward and Futures Contracts and Arbitrage Profit

Is it possible to make an arbitrage profit by taking a long position in the futures contract and a short position in the forward contract when Forward Contract F(0,0) > Futures Contract G(0,0)? That is, the forward contract and futures contract at…
UnevenMango
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How would I calculate the Present value of a perpetuity growing at a fixed dollar amount - not a fixed rate?

Calculating the present value of a growing perpetuity is relatively straight forward. However how would i go about calculating the present value of a perpetuity growing at a fixed dollar amount. That is, the perpetuity pays 1 at the end of the…
chrischris
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Find formula for average compound interest rate given 2 discrete interest rates

For an example, have p=.4 for an interest rate of .1 and $p = .6$ for an interest rate of $-.05$, It seems to me that the average interest rate should be $.1(.6) -.05(.6) = .01$, but when I plug the numbers into excel with $100$ data points I get an…
Greengo
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Suppose $40,000 was invested on January 1, 1980 at an annual effective interest rate of 7%

Suppose 40,000 was invested on January 1, 1980 at an annual effective interest rate of 7% in order to provide an annual (calendar-year) scholarship of $5,000 each year forever, the scholarships paid out each January 1. (a) In what year can the first…
Jen
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Amortization of increasing payment annuity

A loan is repaid with $20$ increasing annual installments of $1,2,3,· · · ,20$. The payments begin one year after the loan is made. Find the principal contained in the $10$th payment, if the annual interest rate is 4%. Correct Answer: $4.88$ My…
MinYoung Kim
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What is the compound interest if the money put in the bank, with the required compound interest in $a$ years increases by $b%$

The task is to write a program which for given $a$ and $b$ returns what is the compound interest if the money put in the bank with the required compound interest in $a$ years increases by $b\%$. I do not see how can I find the compound interest if I…
untitled
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Do these compound interest units make sense?

"Imagine a graph in which the x-axis depicts number of interest compounds per year and the y-axis depicts dollars owed. Does this function have a limit?" Do the units on this graph make sense $ x compounds / year ? Does the derivation of this graph…
ubuntuquestions
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Discounting and comparing present values

A business permits its customers to pay with a credit card or to receive a percentage discount of r for paying cash. For credit card purchases, the business receives 97% of the purchase price one-half month later. At an annual effective rate of…
MinYoung Kim
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Comparing effective interest rate

You have 1000 that you want to deposit in a savings account. Bank A computes the amount value of your investment using the amount function $A_1(t) = 1+0.049t$ whereas Bank B uses the amount function $A_2(t) = > (1.4)^{12t}$. Where should you put…
MinYoung Kim
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