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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How long would it take for the value of the per year interest quadruple?

A principal earns 5% per year simple interest. How long will it take for the future value to quadruple? (Round your answer to two decimal places.) What would the formula be to find the answer to this question? Would it be include $$(.05)\times…
Kevin Diez
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What is the link between 'discounted value', 'forwarded value' and 'present value'?

In my notes, I have an example: Question: Suppose that John is self-employed and wants to save for his retirement in 20 years. From the time of his retirement onwards he wants to withdraw £1,000 every month at the beginning of each month for 30…
YinWai Tse
  • 65
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Compound interest quarterly

I know the financial formula for calculating compound interest: Compound Interest Multiple = [1+(Annual Interest in decimals/365)]^(number of days). I have a initial and final date. I calculate the difference between these two dates in days. Then i…
user50179
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annuity interest payments

Someone takes a loan of $S_1$ as an annuity at an annual interest rate $i$, paid back in monthly installments of $M$. Now I wonder how I can get the annual interest payments for each year $t$. I can calculate the remaining debt after each year using…
bumblebee
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Diversifiable risk

The standard deviation of portfolio A is 8%, the covariance between A and the market portfolio is 0.008, and the standard deviation of the market portfolio is 6%. Find the diversifiable risk of P. I have tried using the single index model, but am…
John
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Optimal exercising time for an American put with S$_0$=4

In a one-period model with parameters S$_0$= 4, u= 2,d= 1/2, and r= 1/4, consider an American put option with strike priceK. Determine the values of K for which it is optimal to exercise the option at time 0.the problem (additionally I calculated p…
ctde
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Yearly discounting to equivalent monthly discounting

Say annual benefit is $120$. Taking an annual discount rate of 3.5%, the present discounted value of the benefit a year from now is $\frac{120}{1+0.035}=115.94$. Assume that benefit is accrued evenly throughout the year i.e. $10$ per month. How do…
Hamza
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Annuity : yearly to monthly

Kenton borrows $250,000 on January 1, 2012 to be repaid in 12 annual installments at an effective annual rate of interest of 12%. The first payment is due on January 1, 2013. Instead of annual payment he decides to make monthly payments equal to…
Liow Wei Sheng
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Calculating the fair price of an option knowing that selling the stock to the market carries a $2\%$ fee

Two scenarios are foreseen for a certain stock after one period, one in which the stock value is $110 E$ and another in which the value is $90E$. Its current value is $S_{0}= 100E$. Furthermore, each operation of selling the stock to the market…
Anabella Woud
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Calculating the fair value of an exchange rate

Let $u$ be the continuously-compound borrowing rate in the UK and $r$ that in continental Europe. An investor wants to fix a exchange rate $V_{T}$ in a forward contract in which $V_{T}$ euros are exchanged for one pound at a time $T$. I now want to…
Anabella Woud
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Calculating the amount we shorten the repayment time of a loan by readjusting installments

Assuming we can afford to pay 1000 E/month and we subscribe to a 20-year mortgage plan at 5% annual rate. I first want to know what the maximal mortgage can be. I have the following formula: $C=\cfrac{P}{\cfrac{1-(1+r/12)^{-n}}{r/12}}$, where $n$…
Anabella Woud
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PayDay loan APR

I'm not convinced I'm getting the correct figure when I calculate an APR rate. I have an amount I want to loan £100 I want to pay this back in 14 days. Interest for this loan is 15% The fee for this service is 0.20p per day. From this I calculate…
Jonah
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Find the continous compounding rate if the monthly rate is $12$%

I am clearly missing something here but in the solutions I have that: $e^r = (1 + \frac{0.12}{12})^{12}$ I am aware of the limit form of $e $ but I don't understand where the above equation came from.
Geoff
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Finding put/call price of EU option when k is very large/small

I am trying to approximate the price of a European put with strike K and expiration T. I have to assume that the spot price $S_0$ is a lot less than $K$ or a lot more than $ K$. I understand how this would work with digital options, where the…
user_123945839432
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interview question on estimating delta

While recently interviewing at a prestigious bank, I received a question that I stumbled on. Went something like this: If one knows a stock price, a strike price and the premium, estimate the delta of the option. Can I estimate other greeks given…
szd116
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