Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

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Is this a self-financing portfolio?

I have $S_t = 10 + B_t$, $\beta_t = 1$, $a_t = 2B_t$, $b_t = -t - B_t^2 - 20B_t$ Then the value, $V = a_t S_t + b_t \beta_t$ Is this a self financing portfolio? Note, $B_t$ is brownian motion I am ...
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1answer
31 views

Compounded Interest with Exponentially Increasing Periodic Payments

Given the formula $$v_a = p\left(\frac{\left(1+\frac{r}{n}\right) ^{nt}-1}{\frac{r}{n}}\right)$$ for the value $v_a$ of an account growing at a periodic rate $r$ with a regular deposit $p$ compounded ...
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Single factor model question, related to the benefits of diversifying one's portfolio.

The question: Suppose in a single period investment problem we may divide our wealth between n assets and that the return on the ith security is given by $r_i = \alpha + \beta_i\theta + \epsilon_i,$ ...
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23 views

Design a swap (financial maths) [on hold]

This is an exam question on designing a swap related to interest rates and currencies Companies $A$ and $B$ are offered the following fixed interest rates on a five year loan. Company $A$; Euro $3\%$ ...
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1answer
25 views

Annuities problem- Part 2 [on hold]

Second problem is A factory can be purchased for 1 million. The factory historically has produced 2,000 units per month of a certain item. The entire production of that item is expected to be sold. ...
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7 views

Request for recommendation: Transition textbook for graduate course in mathematical finance or classical math reference book

I am looking for a well-written, theoretically rigorous textbook that contains all the mathematics necessary to transition smoothly to a graduate course in mathematical finance. I am graduating with ...
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1answer
38 views

Prove $\sum \frac{t}{(1+y)^t }= \frac{y+1}{y^2}$

I see on Wolfram Alpha that $\sum \frac{t}{(1+y)^t} = \frac{y+1}{y^2}$ when t goes to infinity. I cannot, however, proove it myself. What theory is used and how do I start the proof?
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1answer
47 views

Regarding “Two Singular Diffusion Problems” by William Feller

I'm currently reading the research paper, Two Singular Diffusion Problems, by William Feller (1950). However, I don't understand how Feller derived the solution $(3.5)$ given equation $(3.4)$ in his ...
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17 views

How to use the BA II Plus financial calculator to solve for IRR and NPV?

I've calculated the answers manually but would like to learn how to do so on the financial calculator to save time on the test and minimize errors. How to do this? Problem: You have been offered a ...
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15 views

How do I Find the unearned finance charge and the amount to pay off a loan? [closed]

Finance charge- \$9.90 number of payments- 12 frequency-monthly amount-\$15 number of payments left-3 what is the unearned finance charge? what is the amount needed to pay off the loan?
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22 views

Using var[ r ] = E[ r^2 ] − E[ r ]^2, obtain the formula σ^2 = w1^2σ1^2 + w2^2σ2^2 + 2w1w1σ12 [closed]

Able to solve it using var(x)= E[(x-E(x))^2] but cannot get anywhere with this one
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2answers
36 views

To mark up in retail by $20$%, do I add $0.20$ times the original cost, or divide by $0.80$?

Why is it that when I take a cost of say $\$15.60$ and want to mark the item up at retail 20% that I'm being told two different ways with two different answers? The first way (my way) would be to ...
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25 views

Bad and doubtful debts [closed]

A company keeps a provision for doubtful debts of $\$1000$. At the end of the year, the required provision is $\$500$. During the year, debts of $\$1500$ are written of and $\$100$ is received in ...
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1answer
46 views

Recurrence relation for a mortgage

Find a recurrence relation for the amount of money outstanding on a \$40,000 mortgage after n years. The interest rate on the mortgage is 10% and the yearly payment is \$2,000( the yearly payment is ...
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17 views

Isolate n in Compound Interest Formula

How would one isolate n in this comound interest formula? Another forum says that it is impossible and can only be estimated with a series but I'm wondering if anyone can confirm that or knows how. ...
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1answer
13 views

Equivalent Interest Rates

Suppose that the APR on a certain product $x$ whose dollar value is $x_1$ is 5%. Now suppose we subtract some amount $x_2$ from $x_1$ where $x_2 < x_1$. Call this new amount $y$. How does one ...
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23 views

Find the highest price which an investor can pay and still be certain of a yield of:

I'm having trouble understanding this example in Kellison's Theory of interest: Consider a 100 par value 4% bond with semiannual coupons callable at 109 on any coupon date starting 5 years after the ...
2
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1answer
40 views

Is there any interpretation to the imaginary component obtained when computing the geometric mean of a series of negative returns?

When computing returns in finance geometric means are used because the return time series of a financial asset is a geometric series: $\mu_r = \sqrt[T]{\prod_{t=1}^T r_t}$ where the return is computed ...
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1answer
28 views

Properties of brownian motion

I was doing some revision and had an admittedly elementary question. My lecture notes say, the following are properties of Brownian Motion {$B_t$} (Normal or Gaussian increments) For all $s < t, ...
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1answer
20 views

Savings account interest rate

Just a brief question regarding bank interest rates, my apologies if this is a duplicate, I did a quick search but came up with no results relating to my question, surprisingly. Also, please excuse ...
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22 views

prove why expected utility better than expected value in terms of unlimited value of expected

Why expected utility is better than expected value? i was asked by my supervisor to prove that expected utility is needed in mixed strategy and i need to prove it's better than expected value. i have ...
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1answer
32 views

Method for finding a arbitrage opportunity when market price of call is incorrect

The solution of the Black-scholes equation is the price of a European call. And the option price assumes the underlying stock is a geometric Brownian motion with volatility $\sigma_{1}>0$. ...
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1answer
37 views

Continuous Annuity Question

I need to calculate the present value of a level continuous annuity which pays $1000/mo. for 10 years. The force of interest is 5/(3+2t). I tried taking the integral of e^(integral of force of ...
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2answers
40 views

How to find the actual doubling time with the rule of 72.

I have a programming assignment in C# from my professor that involves the Rule of 72. He clearly says that in order to find the amount of time in years it will take for an amount to double, you have ...
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3answers
28 views

Finding the probability of loss from standard deviation in normal distribution

I am unsure how to approach the following question. The returns from a project are normally distributed with a mean of \$220,000 and a standard deviation of \$160,000. If the project loses more than ...
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1answer
35 views

How to calculate inverse of Variance Gamma call price formula using Newton-Raphson search

The Variance Gamma call price formula is given by: $$C(0)= \int\gamma(R) e^{-rT} \int f\left(S(0) e^{\theta R+\omega T+\frac12 \sigma^2 R} e^{rT-\frac12 \sigma^2 R+\sqrt{T}\sqrt{R/T} \sigma ...
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1answer
35 views

Factorals with exponents. Is their a way?

I know of multiplication factorials with the 4! = 4*3*2*1 and I know of the addition with the nth triangle. I am busy deriving my own equation for something, and i am getting stuck on how to furthur ...
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29 views

Optimization of stochastic differential equations

Is there a way to optimize or maximize a set of differential equations. such that each equation is represented by a time series S_((t+1),μ) = μ*(S_(t+1)-S_t) + S_t and μ = 2/(i+1), i=1,...,n. Then I ...
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0answers
27 views

Gaussian distribution finite population with unknown cardinality

I have taken a sample population of a population with unknown size. The sample size is 54 trades. The sample mean is 2.1% (1.021) return per trade. The sample standard deviation is 0.01. 100% of ...
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1answer
38 views

Market Making Card Bet Game

In an interview I received the follow question: We have 3 cards face down, and we give each card in a deck of 52 a numeric score ( A = 1, 2=2, .... , J=11, Q=12, K = 13). The interviewer asked me to ...
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3answers
57 views

Rule of 72 doubling time

I need some help understanding this. So as far as I can tell. The rule of 72 is used to determine when prices will double in years. This is done by 72 divided by the rate, or interest. So it would ...
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60 views

Price of derivative contract with payoff at time $2$ or $S_2/S_1?$

What is the price of a derivative contract with payoff $X_2=S_2/S_1?$ The question requires price $V_t$ for when $0 < t < 1$ and $1<t<2$? Really can't get my head around this, any help ...
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0answers
52 views

Estimating the value of a stock

I need a way to know the value of my stock. Let $(x_1, \dots, x_n)$ be the quantity of the products $1$ to $n$ I have in stock, such that, for example, if I have $8$ units of the product $2$, $x_2 = ...
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2answers
43 views

Loan and annuity (prospective methods)

The question is a loan of $10,000 is to be repaid over 10 years by level annual repayment of capital and interest. The interest rate to be charged on the capital outstanding will be 6% per annum for ...
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22 views

Spectral Analysis: How to interpret a periodogram.

I'm reading a paper that has to do with financial volatility. The author uses a periodogram to estimate the power spectrum density of the volatility time-series. Evidently, the plot (below) is ...
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35 views

Calculate the Value at Risk

Let's have the following example: We have two independent investments. Each of them have: a 94% chance of a profit of 1 million a 3% chance of a loss of 1 million a 2% chance of a loss of 5 million ...
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25 views

Simple Interest Problem Ambiguity in Conventions

I am solving some simple interest problems. Following questions are creating ambiguity with conventions, hope someone will clarify what is going on. In what time does sum of money become 4 times ...
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1answer
58 views

Book Recommendation for mathematical finance

Does anyone know a book which covers topics on: Brownian Motion Martingales Stochastic Calculus Stochastic Differential Equations Options pricing. Black-Scholes model Fundamental Theorems. ...
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1answer
28 views

Having trouble solving this Exam FM problem with zero coupon bonds.

You have two 4-year annual-coupon bonds, each one of them has a face value of 8000 and a redemption value of 8000. The coupon rate of first bond is 7% and its price is 7908.57, while the second has ...
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1answer
41 views

Annuity present value formula explanation

Could somene please explain me how the formula evolves, ie. how does the fraction flip, etc? Thank you in advance!
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0answers
15 views

How to analytically find these rounding issues

Let's say we have a fixed yearly amount that we have to divide equally among an amount of days. For instance for $1,600 we may have: ...
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26 views

Negative option value

I have an exercise where I need to replicate the following graph: with my own parameters. To do this I use: $\begin{align*} \text{Call option value} =SN(d_1)-Ee^{-r(T-t)}N(d_2) \end{align*}$ ...
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0answers
12 views

Weighted Std Deviation of Securities

Corporate Finance problem - can't figure out if I'm right or not but here goes: Probability 15% 35% 20% 30% Security A 8% 5% -4% -6% I need to find mean and std deviation for security A. I got: ...
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1answer
31 views

Can't Get Present Value Answer?

I've done this problem at least 20 times a number of different ways, but I can't seem to get the correct answer. Please show all work and describe the EXACT formula you used: Find the present value ...
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Financial Mathematics Question - How to approach?

I know the answer, but I'm not sure how to 'approach' the question the right way. The question is "Katarina would like to buy a house in 4.5 years time and requires a deposit of $40000. What ...
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1answer
32 views

Simple vs compound interest rates and Taylor expansion

I am having trouble deciphering a portion from my finance text. Let $i = \text{interest rate}$, $n = \text{Some arbitrary time period}$ and $C = \text{Cash invested}$ And also $C(1+i)^n$ ...
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38 views

Reformulate this PDE in different notation

I would like to rewrite this general PDE \begin{equation} \alpha\partial_tu+\beta\partial_xu+\gamma\partial_{xx}u+\delta u=\varepsilon \end{equation} in this form $$c\left(x,t,u,\frac{\partial ...
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1answer
45 views

What to read after Shreve's “Stochastic calculus for finance 2”?

I am finishing the last pages of Shreve's Stochastic calculus for finance 2, and I was wondering what would be the best book to follow. I would like to go on with a book introducing more technical ...
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1answer
41 views

How long does it take an investment to quadruple in value if it earns 5% simple interest per year?

How long does it take an investment to quadruple in value if it earns 5% simple interest per year? I'm not sure about how to find it but the Awnser: 60 years
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1answer
20 views

How do you calculate a fee percentage to handle a fee being charged?

Problem is that we get charged a 3% fee. We add this 3% fee to the invoice. When we get the amount back they charge 3% on the invoice plus on the fee we added. What formula can I use to figure out ...