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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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Divergent or negative discount factor formula?

I have a question, maybe it is simple, maybe it doesn't make sense, but I haven't seen this addressed anywhere - what happens when the negative interest rates result in a badly defined formula for discounting? The discount factor formula for period…
feli
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Reinvestment Problem

I'm really curious on how to find the answer to this question John invests 100 at the end of year one, 200 at the end of year two, etc until he invests 1,000 at the end of year ten. The investment goes into a bank account earning 4%. At the end…
llawliet_78
  • 323
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Proof on Greeks for a delta neutral portfolio

Suppose that $ \Delta S $ is the price change of an underlying asset during a small time interval $\Delta t$ and $ \Delta \pi$ is the corresponding price change in the portfolio. Show that $ \Delta \pi = \Theta \Delta t + \frac{1}{2} \Gamma \Delta…
Tosh
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Question on Value At Risk given delta

The daily change in the value of a portfolio is, to a good approximation, linearly dependent on two factors (uncorrelated factors). The delta of a portfolio with respect to the first factor is 6 and delta with respect to the second factor is 4. The…
Tosh
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Minimum variance portfolio problem given risk free rate,covariance matrix and mean vector

Consider 3 assets $r_1,r_2,r_3$ respectively. Covariance matrix and expected return is given by $C=$ \begin{bmatrix} 2 & 1 & 0 \\ 1 & 2 & 1 \\ 0 & 1 & 2 \\ \end{bmatrix} and $\mu=$ \begin{bmatrix} 0.4\\ 0.4 …
Tosh
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Helen Borrows Money

Helen borrows a sum of money from a bank at 12% convertible monthly and wishes to repay it by 24 monthly payments. In total, she will pay 584 of interest. Determine the size of the loan. I have started by doing this: The total amount paid back…
Tiny-E
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A scholarship fund is accumulating and perpetuity

A scholarship fund is accumulated by deposits of $400$ at the end of each year. The fund is to be used to pay out one annual scholarship of $2000$ in perpetuity, with the first scholarship being paid out one year after the last deposit. Assume…
kicos
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Yield to Maturity Uniquely Defined for Positive Duration?

I have been struggling with the following question: Consider the yield to maturity of a static portfolio of coupon bonds, each with a finite expiry date, in which shorted bonds are allowed (so the total of the coupon payments as well as the…
user234
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Growing Annuity

A loan of $\$39,999.85$ is to be repaid by payments at the end of each quarter for eight years. Each payment is $2\%$ higher than its predecessor. The loan is made at a nominal rate of discount of $4\%$ payable quarterly. Find the balance just…
Allan
  • 536
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Bold, superscript plus symbol

I am reading "Arbitrage Theory in Continuous Time" by Tomas Björk, and stumbled upon what seems to me an odd use of the superscript plus-symbol, so here it goes. One instance is found on page 11, given by: $$(1^{\textbf{+}} R)x^{\textbf{+}} suy =…
WilliamGram
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Force of interest and Present value

Express the present value of the sums $c_{t_{1}},c_{t_2},...,c_{t_n}$ due at times $t_1,t_2,...,t_n$ in terms of the force of interest at time $t$, denoted by $\delta (t)$. The answer given is…
Mathxx
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Mortgage question

Assume i take the mortgage out over 25 years: using the mortgage payment formula below: $Monthly\ payment\ = L\ [{\dfrac{x(1+x)^n}{(1+x)^n -1} }]$ where L is the loan value, x is the interest % in month and n is the number of months In my…
Peter A
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Time Value of Money (Future Value/Annuity)

So I found this popular solution online (in the image above, below the question) and I was wondering why they chose this process. I think I get the process for the solution above but does my attempt work as well? My Attempt: When I saw the problem…
mathguy
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Future Value of Annuity

Textbook: If you invest \$2000 a year (at 9%) from ages 31 to 65, these funds will grow to $470,249 by age 65. ***the textbook did not say how they got this number, I just assumed it used FVA because it is in the same section My…
mathguy
  • 927
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How would I found the compound for the following on each account with compound interest?

Determine how much is in each account on the basis of the indicated compounding after the specified years have passed; P is the initial principal, and r is the annual rate given as a percent. After one year where P = $4700 and r = 2.5% Find the…
Kevin Diez
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