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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Constructing equivalent martingale measure (lognormal distribution)

Please, help me with next problem. It's from Follmer's and Schied's Stochastic Finance. An introduction in discrete time. First, I'm looking for conditions for $X_t$ to be a martingale: $$ E[X_t|\mathcal{F}_{t-1}] = E[X_0 \prod_{i=1}^{t}…
Dima R.
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Studying the anomalies mathematically

The efficient market theory which says that there’s nothing in the data, let’s say price data, which will indicate anything about the future, because the price is sort of always right, the price is always right in some sense. But that’s just not…
J.Doe
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What is the name of this symbol ( ┐) and what does it mean

Sorry bout the dumb question, it's just that I'm taking a mathematical finances class and the teacher started using this symbol today but I've never seem it before, was trying to google it but don't know its name and searching for the symbol itself…
Alan Broderick
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How to calculate CAGR for shares bought at different times?

I have bought shares at following times: Buy - 5th March 2006 - Price > $ 70 - Quantity - 10 Buy - 2nd May 2007 - Price > $ 33.5 - Quantity - 100 Buy - 1st Oct 2008 - Price > $ 57.7 - Quantity - 17 Buy - 5th Jan 2012 - Price…
meetpd
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Altering a Lease Calculation to take into account an upfront payment

I am trying to find the interest rate of a lease if we know the monthly payment amount but have an advance payment. I have found a site with part of the calculation we need (Scenario 2 on the link…
Varedis
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Repayments of a loan with compound interest

Suppose I have a loan of M dollars. At the end of each year, I am charged interest at rate R and make a repayment of P. The loan is repaid after n years. How long (n) does it take to repay the loan if I am given the other variables? How much are…
Casebash
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Measuring Financial Investment Performance

I'm trying to understand how the performance of financial investments are measuring when the asset has multiple points of investment. For example, say I invest $1000 in a stock. After 6 months, it's worth $1200. At this point, I invest an additional…
Cerin
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Financial mathematics question about mortgage loans

The following question is what I was working on. A bank gives a mortgage of $\$450,000$ dollars for a $30$ year loan with $6$% annual interest which requires the person to pay monthly. They require the person to pay $\$2700$ dollars each month.…
hyg17
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how to find delta when the force of interest is unknown

An investment of 1000 accumulates to 1360.86 at the end of five years. If the force of interest is δ during the first year and 1.5δ in each subsequent year. How to find δ?
fae
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Maximizing compound interest with fee per compound

Given the following: initial principle $P$, interest rate $r$, flat fee whenever interest is applied $x$, period between applying interest $p$, total time period $t$ How do I calculate the final amount $A$? the objective is to maximize $A$ by tuning…
iluvAS
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Find Swap Rate given Spot Interest Rate Curve

Question: Spot interest rate curve: $$\begin{array}{c|c} t & r_t \\ \hline 0.25 & 1.50\% \\ \hline 0.5 & 1.65\% \\ \hline 0.75 & 1.79\% \\ \hline 1 & 1.92\% \end{array}$$ I have a one year loan for $1,000,000$ with principal paid at the end of…
jeremy909
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Why do we divide by the number of compounding periods when calculating compound interest?

I know this is a very, very basic, but I am attempting to fully understand the implications of the equation that calculates compound interest and can't find anywhere that explains why the equation is the way it is - most sites and textbooks simply…
robbmanes
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Forward Price with Dividends

Consider a stock whose stock price is 100 on January 1st. This stock pays a dividend of 4 at the end of every quarter. You are Holding a Forward contract with delivery date of one year. Assume the interest rate is 6% compounded continuously. a) What…
user130272
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How to understand "force of interest" in simple interest?

I am struggling to understand "force of interest" in simple interest. I understand that "force of interest" can be interpreted as compound interest with infinitely small time interval. That is, the new interest generated any infinitely short moment…
Valia
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Calculate the amount of withdrawal

Question Person A deposits $5000 to his account. He is going to make a withdrawal twice, first one after 6 months and the second one at the end of the year (after 12 months). After these two withdrawals his account will be empty and the amount of…
imas145
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