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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Zero-Coupon Bond Continuous Compounding

You are given B(0,1)=.92 for a one year zero-coupon bond with a face value of $1, assuming continuous compounding. What is the value of the zero-coupon bond at the end of each quarter? At what time will you realize a 6% return?
user130272
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Calculate projected compound interest based on many short term loans

I have a dataset of many short term bitcoin loans (duration <= 2 days) all with different interest rates, a fee to the broker and an amount. How can I calculate the overall interest rate achieved so far? Also how can I project these loans forward to…
nfvindaloo
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How long will it take to pay off a mortgage?

If a mortgage principal is $200,000, interest rate is 3.50% and the payment is $900 a month. Is there an equation to find how many payments it would take to pay off the loan? Edit 1 I have tried to solve n and have not been able too. So I tried…
null_pointer
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Foreign exchange arbitrage opportunity

Assume your return on U.S. dollar bonds is $$$ = 5% and the current exchange rate is S(0) = $ 1.6 per £ . Assume your return on British sterling bonds is £ = 12%. The Forward price of stock is S(1) = $ 1.45 per £ with delivery date 1 year therefore…
user130272
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finding the up-factor u and down-factor d for trinomial lattice tree.

Consider the call option above. After each period, there is a 40% chance for the stock price to go up, 25% chance to stay the same, and 35% chance to go down. Assume μ is the same as the risk-free rate. Stock price is $62. Call option price is 5.83…
manny singh
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Varying interest rate question with different payout times

Just wondering if anyone could help me with the most efficient solution to working this problem out. The only way I can think of right now is to work backwards but I know this is a tedious and long winded answer. Any help to find the most efficient…
Jason Huang
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Two step binomial tree

A stock is currently priced at 25. In 4 months it will be either 22 or 29. The risk-free rate is 6% per annum with continuous compounding. Let $S_\frac{4}{12}$ be the price of the stock in 4 months. Compute the price of a derivative that pays you…
user_123945839432
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How to annualize a weekly geometric mean?

I've calculated the geometric mean of 3 years of weekly returns (i.e. 156 returns) to be 0.001954. How do I annualize that return? Is it ((1 + 0.001954)^52 - 1) = 0.106823? Or some other method? Thanks in advance.
giantsrock28
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Cumulative rental payments over a period of time

What's the formula to figure out how much money you make on total rental payments over a period. Say each month I rent out 2 cars, and get $50 for each. The length of the rental period is indefinite. Jan, 2 cars = $100, $100 total Feb, 2 cars =…
gelat
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Mc Caulay Duration of a bond

Calculate the MacCaulay Duration for a $1$ year fixed rate coupon bond paying $6$ % semiannually. You know that the yield of the bond is $6.72$ %. $D_{mac}= \frac{\frac{(0.5)(1.5)}{1.0336}+\frac{(1)(1.5)}{1.0336^2}+\frac{(100}{1.0336^2}}{1.5…
Tosh
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How to work out the rate a tenant is paying interest on late payments

A tenant pays rent of £1400 on the 21st of each month. They have been paying it late now for 8 months, on the 10th of the following month with an additional £20 on top. I just wanted to confirm the method to work out what loan rate this would be…
Amy Rose
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Reverse Mortgage

You want to get a reverse mortgage that will give you monthly income for the next 20 years. The house is worth $400,0000. The term is 20 years. The rate is 6%. What are the monthly payments? I understand that with a reverrse mortgage, you are…
Marley Chatthews
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Overpaying your bill

(Please tell me exactly how you found the answer and what you did because I'm a Year 7 and this is a Year 9 question.) Mr. Rich decides to pay a bill using internet banking. The bill is a two-digit whole number $ab$. He accidentally inserts an extra…
bio
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Monthly payment sinking fund

Wanda takes out a 28-year mortgage for $178000 at an interest rate of j_1 = 8.1% (i = 0.081). After the 10th monthly mortgage payment, she decides to make some changes. To repay the loan, she will make 94 more mortgage payments (additional to the 10…
Alex Vincent
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Finance math comparison of puts

I am looking for some expert advice in answering this finance question. I am having trouble figuring out how to compare these put and strikes. Is there a formula to approach this type of problem? Let $p_K$ be the current price of a European put…
user_123945839432
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