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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Valuate the European option that pays the absolute difference between the share price $S_{T}$ at maturity and spot price $S_{0}$.

In previous exams there was this question: In the framework of the Black-Scholes model, valuate the European option that pays the absolute difference between the share price $S_{T}$ at maturity and spot price $S_{0}$. Assume that the stock does not…
Melina
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How to determine the current price of derivative

For a non-dividend paying share of a company whose price at time t is denoted by St, the current price of the share is S0=£100. In any year the price of the share can either increase by 20% or decrease by 20%. The continuously compounded constant…
F Erikssen
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How to determine price of a derivative (mathematics of financial derivatives)

For a non-dividend paying share of a company whose price at time t is denoted by St, the current price of the share is ${S0 = £100}$. In any year the volatility is $20\%$ (price of the share can either increase by $20\%$ or decrease by $20\%$). The…
F Erikssen
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Why does my mortgage repayment stay the same?

According to the general repayment formula, the mortgage repayment for month j is calculated by \begin{equation} Rj = \frac{L_{j-1}x_j}{1-(1+x_j)^{-(N-(j-1))}}. \end{equation} where $L_{j-1}$ is the loan amount outstanding from last month, $x_j$…
Julie
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Compound Interest on cash payment

A man buys a scooter on making a cash down payment of 16,224 and promises to pay two more yearly equal instalments of equivalent amount in next two years. If the rate of Interest is 4% p.a compounded yearly, then, the caash value of the scooter…
Shubham Raj
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Future Value and profit question

Delta stock (DAL) is trading at 11.70 dollars today. Consider an American put option on $1$ share of DAL with $K$ = 12 and expiration in $T$ = .25 years. The put is selling today for $1.46. Assume the risk-free rate is 1%. You hold the option…
user_123945839432
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Discounting annuity

Suppose that the present value of an annuity will provide 16 payments of $3100 once a year. If the first payment will come 15 years from now, and the annual rate of interest is 11.6%, what is the present value of the annuity? Wording in this…
Alex Vincent
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Calculate APR from loan, monthly payments, and amount of months

For some reason calculating APR is very difficult. A lot of people ask, but not a lot of great answers. I'm working on a project, where I need to calculate APR. I have already calculated what the loan is, how much the user has to pay each month, and…
MortenMoulder
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Saving up for retirement question, how much can he withdraw each year?

Ralph wants to quit his job and move to Hawaii on December 25, 2015. Once there, he anticipates that he will need to make annual withdrawals of $14500 (starting on December 25, 2016) from his savings account to supplement his income and he wants the…
Alex Vincent
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Calculating payments and APR for simple interest loans - different interest accrual methods.

I work for a small financial institution as an auditor. We do various small loans that are always simple interest. Currently, we calculate payments on loans using the =PMT() method in Excel. There are a few problems: We state on our contracts the…
Stigz
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Finding effective rate

Suppose a mortgage has an interest rate of 6.5% per annum with monthly compounding. Find the per annum interest rate with quarterly compounding that would lead to the same effective annual rate. I solved this one by: $$r_eff =…
user_123945839432
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Can interest and inflation rates be combined?

In problems calculating the future value of money with both an interest rate and an inflation rate, how can the two rates be combined? $$FV = PV \cdot (1 + r)^N$$ where $FV$ is the future value $PV$ is the present value $r$ is the interest rate…
Ralph
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annuities and interest

The loan of 30.000 euros is depriciated after 10 years, with equal annuities and interest of 11% of annual capitalization. how can the annuity be determined? -this one seems to be the toughest of them all for me.
Milingona Ana
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Compound interest using practical (approximation) method

Kyle wants to buy a car for $9200 in 2 years and 7 months time. How much does he have to invest today at j4 = 3.5% using the Practical method. I feel like I'm doing it right but the answer is not correct. 9200 = P(1+0.035/4)10(1+0.035(1/12)) 8407.90…
Alex Vincent
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Face value of bearing note required

Suzie wants to buy a car for $\$7500$. If she pays cash she receives a $5$% cash discount. To get the cash she signs a $120$-day non-interest bearing note. If the bank discounts notes at an interest rate of $5.5$% what face value is needed on the…
Alex Vincent
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