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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Utility function and risk aversion

Let $U(\cdot)$ be a twice differentiable (increasing) utility function and $x$ the agent's initial wealth. For $\varepsilon\in[0, x]$ define a bet that pays either $+\varepsilon$, or $-\varepsilon$. Define $p(x, \varepsilon)$ by $$U(x) =…
Sergio
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Is there a formula to determine equivalent units after an exchange rate?

The easiest example is money. Let's say I have $100 USD, and I want to convert part of this money to CAD, at an exchange rate of 1.3. I want to have the same quantity of USD as CAD at the end of the process. If you do rough napkin math for the $100…
Mike Trpcic
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What rate of simple interest is earned?

atempt If we call $P$ our debt, and if $a(t) = 1+it $ is the accumulate amount and i is the interest rate, then $Pa(90/360)$ is the total amount to pay after 90 days and we have $$ P a(90/360) - Pa(30/360) = P 0.02 $$ which implies that (90-30) i/…
James
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What is the accumulated value at the end of two years?

Suppose we make a $\$100$ deposit at $t=0$ . A year later, you make a withdrawal of $\$50$. If we have an annual simple interest rate of $10\%$, what is the accumulated value at $t=2$? Well, obviously, at the end of a year we have…
James
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Finance Compound interest

Tom plans to go to college in 5 yrs but is in need of car right now. He plans to invest into a 4% annum compound interest w periods of monthly compound. His school will cost him $8000$ dollars and he has $6000$ dollars right now. How much can he…
Aurora
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Puzzling price of a bond

I was asked to solve this question: given a bond which grants the following cash flow (year $t$, return): (0, not reported) (1, 10) (2, 10) (3, 20) (4, 20) (5, 100) What is the bond price in $t=3$ with flat rate of 3% per year for the entire…
Clyde A. Jansen
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Solving financial mathematics using a graphing calculator

Merlin spends six weeks at his cabin every summer. He loves to go fishing and he has decided that he wants his oenter preformatted text herewn boat this summer instead of going fishing with his neighbour all the time. He could purchase a used boat…
Savannah
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How to derivate the implied volatility?

I want to calculate $\frac {\partial w}{\partial y}$ and $\frac {\partial ^2 w}{\partial y^2}$, with $w = \hat{\sigma}^2*T$ and $y = ln(K/S)$ in order to compute the local volatility. To get $\hat{\sigma}$ I use the inverse function of it : $d_1 =…
memela
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Find Interest RATE of Mortgage When Got Loan & Payment

I can seem to find an answer to this question. It sounds like it should be simple but i can't find antying online and only found one answer on stack that seem overly complicated. I have a loan amount, term and total payment and i need to simply…
user982853
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Prove that the duration of a bond without a coupon is equal to its maturity.

I am supposed to prove that the duration of a bond without a coupon is equal to its maturity. I know it will have something to do with weighted average maturity periods, but I don't know how to formulate it. Can anyone help me?
Shelley
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Modelling changes in stock prices

I am reading a book by Donald Saari on mathematical finance. I am trying to understand the intuition behind modelling the rate of change of the stock price $S$ (excluding randomness for the moment) as $\Delta S = \mu S \Delta t$ (eq.1) ($\mu$ is a…
Andy
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One periodic binomial model

I need to look into a one-period Binomial model $(B_t, S_t)$ with interest rate $r = 0.1$ , $S_0 = 100$ and $$ S_t= 120 \, \text{with probability}\, 0.5 $$ $$ S_t= 60\, \text{with probability}\, 0.5 $$ a) I need to show this market has no…
KingDingeling
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Regular annual pension

I am supposed to solve the problem: A 24-year-old man decides to invest 200,000 euros at a 7% annual interest rate to bring him a regular annual pension from 31 to 50 years inclusive. What will be the pension? What I did was that I used the formula…
Shelley
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Value of different portfolios

Suppose in the following portfolios all options are based on the same stock, have expiry date $T$ and strike price $K$ (unless otherwise stated). In each case find the portfolio value at time $T$ in terms of $S_T , K$: one call option and one put…
KingDingeling
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Spotting arbitrage from spot and forward FX rates

Dealer $A$ in Chicago will buy pounds a year from now at a rate of $\$1.58$ to a pound. Dealer $B$ in London will sell pounds immediately at a rate of $\$1.60$ a pound. Furthermore, dollars can be borrowed at an annual rate of $4\%$ while pounds…
KingDingeling
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