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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Calculating deposit based on interest and required withdrawal in future

I am really stuck with example 2-5 and 2-6. I don't really understand example 2-6 and example 2-5 I just can't figure out...I was able to do example 2-4 which was easy... For example 2-4 I did F=P(1+ interest)^n 6500=P(1+0.03)^4 I solved for P and…
Raynos
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the reverse of PV of a series of cashflows

I have calculated the PV of a set of cashflows over a period of 10 years. Here is the equation: YEAR/CASHFLOW 50,000 51,500 53,045 54,636 56,275 57,964 59,703 61,494 63,339 65,239 PV of the cashflows = $415,940 at a discount rate of 6% Here's…
Debbie French
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How to calculate monthly payment?

An annuity certain with payments of $500 each at the beginning of each quarter, for a certain number of years, is to be replaced by an annuity with the same present value and lasting for the same number of years, but with payments at the end of each…
Kai Feng Gan
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Annual percentage interest rate

An annual percentage interest rate of $30\%$ is equivalent to a monthly compound interest rate closest A) $2.02\%$ B) $2.21\%$ C) $2.50\%$ D) $2.66\%$ The answer is B Can anyone tell me how?
AYESHA
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Proving a corollary of CAPM formula

I have to prove that $\mu_\pi=r+\beta_\pi(\mu_M-r)$, (where $\mu_\pi$ is the expected return of a portfolio, $r$ is the interest rate, $\beta_\pi$ is the beta factor of the portfolio, and $\mu_M$ is the expected return of the market), using the CAPM…
Silvia Rossi
  • 800
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Geometric Coupon Payment

An investor owns a bond that is redeemable for 250 in 6 years from now. The investor has just received a coupon of $c$ and each subsequent semiannual coupon will be 2% larger than the preceding coupon. The present value of this bond immediately…
llawliet_78
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1 answer

Tripling Money at Nominal Interest Rate

Not sure what this questions means by "part of a year"? What assumptions should be made? Question: How long will it take to triple your money at a nominal interest rate j1 = 12% if simple interest is allowed for part of a year? Can anyone help?
Gregggg
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Annual Effective Rate Compounded Quarterly

Confused with this question especially with what to do with the "expense charge"? Can anyone help? A fund earns interest at the nominal rate of 8% compounded quarterly. At the end of each quarter, just after interest is credited, an expense…
Gregggg
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2 answers

Discounted Value at Simple Interest

Struggling with this question: Mr. A borrows 2000 now and 3000 in 4 months. He agrees to pay X in 6 months and 2X in 8 months (from now). Determine X using a focal date 8 months from now at simple interest rate r = 12%. Thanks in advance.
Gregggg
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1 answer

Convex combinaton of bonds with different maturity

I am given two bonds, Bond 1 with maturity 30 years and Bond 2 with maturity 2 years. How to find an $\alpha$ such that portfolio $(\alpha$, $1-\alpha)$ of bond a and bond 2 has a duration of 10 years. Here $\alpha$ lies in $(0,1)$. I am confused…
sachin garg
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Modified duration

A zero coupon bond matures in eight years. It is sold to yield 5% annually. Find the modified duration D(.05,1) This question comes from the Second Edition Mathematics Interest Theory textbook, section 9.2 #3. The answer provided is D(.05,1)=…
uytt
  • 75
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Finding forward rates implied by given prices

The current prices on one-year, two-year, and three-year $10,000$ zero-coupon bonds are $9765$, $9428$, and $8986.82$, respectively. Find forward rates $f[0,2]$ and $f[2,3]$ implied by these prices. This question is from Mathematical Interest…
uytt
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2 answers

Fair value of European Call

Assume that the ABC stock pays no dividend and is currently priced at $S0 = \$10$. Assume that, at the expiry time $T > 0$, the stock price goes up to $u*S0$ with probability $0 < p < 1$ and down to $d*S0$ with probability $1 − p$. We know that $d…
abharti
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PMT equation result

I want to calculate the PMT value. I have the following equation: $$P =\frac{P_vR}{1-(1+R)^{-n_p}}$$ where present value $P_v=8262$, interest rate $R=0.875$ and number of periods $n_p=60$. If I use the calculator, I get $-7229$. When I use the PMT…
farahm
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Monthly effective interest rate to 6-month effective interest rate

I am given that the monthly effective interest rate is $1\%$ and I would like to find the 6 month effective interest rate for a problem. I used the formula $r_e=(1+r)^\frac{m}{n}-1=(1+.01)^\frac{12}{2}-1=.0615=6.15\%$ Since I am going from effective…
Silvia Rossi
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