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 can we model the stock price as random error around a bond price?

Right now I am taking a course on financial math and we want to model the stock price. For continuous compound interest we have the formula $B(t) = b_0 e^{rt}$ where $r$ denotes the interest rate and $b_0$ the initial principal. Now we want to…
Josh.K
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Time value of money.

I need help with the following problem: Amres Corporation has the opportunity to receive 20,000 dollars right now, or, 3254.91 dollars per year for the next ten years. The first payment will be available after one year. For what rate of interest…
Nishant_1988
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Optimal exercise time in Binomial model

Let (B, S) a multi period binomial model that is arbitrage free. Prove that the unique time for an American call is the maturity T. I would like to prove that the unique optimal exercise time for an American call option is the maturity time T. My…
Jennifer
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Return on investment & Interest rate comparisons

For the question to make sense I need to provide some context on the products available, below is an example of how banks make money for just two products. We have infrastructure bonds at 12% per/year interest paid twice a year and principal at the…
sqwale
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How to get Effective Rate?

When googling for Effective rates, i'm getting a different result for the formula compared to what we are using in our current company. Google Result: Effective Annual Rate(EAR) = ((1+i/n)^n)-1 where i = annual interest rate n = Compounding…
MagsTester
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What's the math formula that is used to calculate maximum mortgage amount like in this calculator?

What's the math formula that is used to calculate maximum mortgage amount like in this calculator? Visual Reference: Take a look at these images to see which tool I'm specifically referring to: Purchase Budget with $0\%$ Interest Purchase Budget…
Luis Moraguez
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Given a sum, how to find a set of numbers that grow by a percent of the preceding number that total to the sum.

This is used for calculating monthly costs that increase by a certain percentage month-over-month when given a forecasted annual budget. An annual increase of 15% annually or 1.28% monthly (equalling 15% annually) is expected. Given that I know the…
Artem Yevtushenko
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Why is this not correct way of calculating real value ( stupid question)?

inflation $= 3\%$ per year, amount of time $= 5$ years, nominal value = $\$5070.6$, real value = ? real value* $1.03^5 = \$5070.6 $, real value = 4373.94, this is correct answer why not : $5070.6\times(1-0.3)^5 =$ real value, which gives…
Pls Help
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Risk free profit with a put option

From Terence Tao Blog the price of a put option at time $t_0$ cannot exceed the strike price P at time $t_1$. The reason is that otherwise there would be an arbitrage opportunity. Everyone in the market could build a put option Simply putting aside…
user1095117
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Calculating APY from N percent earned over X days

What equation could I use to calculate the APY where percent interest and number of days are variable? For instance, suppose I invested $100 and earned 10% interest in 5 days.
EcomEvo
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What is the total cost of 55k units?

Kaplan Ltd. is one of the premier industries that manufactures fan belts for automobiles. If a belt is not sold in the year of production, it becomes defective and has to be scrapped. The following estimates reveal all the costs of Kaplan Ltd. If…
Joypal
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how to calculate number of years in compound interest

I'm trying to calculate the number of years in compound interest, but I find that the online formula can't get the answer I want. I don't know why. Does anyone know what the specific formula is? I know the calculator can done that, but I need to use…
python learner
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How to calculate interest rate in compound interest

I'm trying to calculate the interest rate in compound interest, but I find that the online formula can't get the answer I want. I don't know why. Does anyone know what the specific formula is? I know the calculator can done that, but I need to use…
python learner
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How i can calculate the Macaulay Duration without knowing the price of the bond?

For an annual bond with coupons $c =40$ and 10 years maturity $n=10$ ,face value $P_p=1000$ and interest rate $y = 0.08$ calculate the Macaulay Duration defined as : $$ D= \frac{1}{P} \left( \frac{ 1\times c}{(1+y)} +\frac{ 2\times c}{(1+y)^2}…
Homer Jay Simpson
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What is the price difference between the two companies?

Fireside Shop offers chimney caps for 120 dollars less trade discounts of 25/10. The same chimney cap is being offered at Builder's Supply for $111 less than the trade discounts of 25/5. What is the price difference between the two…
Chayan
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