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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2
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2answers
39 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 ...
2
votes
1answer
47 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 ...
2
votes
1answer
66 views

Annuity problem, calculating the accumulated value.

the following is the problem I am trying to work on. Kathryn deposits 100 into an account at the beggining of each 4 year period for 40 years. The account credits interest at an effective annual ...
2
votes
1answer
69 views

Intuitive understanging of re-investment.

There was an interesting problem that I would like to have some input from people who knows a bit of finance. The following is the situation. Smith loans $\$10,000$ for $i=5\%$ for $10$ years. ...
2
votes
1answer
56 views

On estimating monthly credit card payment amounts (some pragmatic constraints inside)

Right off the bat, I do hope this question doesn't attract a bunch of derisive comments about my personal affairs. I give the lengthy personal anecdote because I don't have the mathematical training ...
2
votes
2answers
29 views

Question about a summation problem from finance

I'm studying a journal article about finance and I have trouble understanding how the author reach a result. The equation he begins with is: $$VTS_0=TD_0+T\Sigma_1^\infty PV_0[ΔD_t] \tag 1$$ Then ...
2
votes
1answer
40 views

Arbitrage opportunity for call price set on avarage

I have the following problem. Let C(K) be the market price of a Option Call with respect to the strike K. Let $C(100) = \frac{C(110)+C(90)}{2}$, then show that there exists an arbitrage opportunity. ...
2
votes
1answer
58 views

Help me optimize my work

I am a physician. I am required to work 14 shifts per month. I may work extra shifts for 1400 dollars per shift. In addition, I earn productivity based on a system called RVUs. For every RVU I produce ...
2
votes
1answer
77 views

Optimal Investment Strategy

I am not sure to solve the following investment problem: I have an investor which receives an income $I_n\ge 0$ at the start of year $n$. The investor chooses a proportion $p_n\in[0,1]$ of this in ...
2
votes
1answer
869 views

Financial mathematics question about mortgage loans

The following question is what I was working on. A bank gives a mortgage of 450,000 dollars for a 30 year loan with 6% annual interest which requires the person to pay monthly. They require ...
2
votes
2answers
50 views

Working out the difference in earnings

I'm mathematically impaired/ignorant and trying to figure out the difference in earnings between my partner and I to work out a fair split of the bills. So; I earn £2060 per month and partner earns ...
2
votes
2answers
607 views

Perpetuity Immediate Present Value Question

A perpetuity-immediate pays $X per year. Brian receives the first n payments, Colleen receives the next n payments, and Jeff receives the remaining payments. Brian's share of the present value of ...
2
votes
1answer
323 views

formula to calculate the monthly repayments of this contract

I know that the interest rate is constant through the whole period and the interest method is declining balance. By declining balance mean that the interest at period t is calculated on the balance of ...
2
votes
1answer
47 views

Calculating percentage reduction from results only.

I've been looking over some loan repayment statements, and I'm trying to work out: What the precentage interest is per month. How long it will be until the final amount reaches 0. Whether there is ...
2
votes
1answer
4k views

How to convert interest rate to discount factor

I'm studying on Kellison's Theory of Interest and I'm stuck on the exercise 20/a of the 1st chapter. If the $i=0.1$ then $d = 0.0901$ $d_5=\frac{A_5-A_4}{A_5}$ when I insert $d$ into this ...
2
votes
2answers
74 views

Cost for hedges under a Wiener process

I'm trying to estimate the hedging costs relating to a financial derivative which moves like a Wiener process, and I'm struggling to find the correct setup to solve the problem. Suppose I have a ...
2
votes
1answer
444 views

How to get Annualized volatility from monthly return?

Suppose the average monthly return is $\mu$, the monthly standard deviation is $\sigma$ and denote the autocorrelation of monthly returns by $corr(r_i,r_{i+h}) = \rho(h)$ Prove that, when $\sigma$ ...
2
votes
2answers
240 views

Bonds and Yield Rate

I came across the following problem on bonds: Suppose we are given the following term structure of annual effective yield rates for zero coupon bonds: $(1, 2 \%)$, $(2, 6 \%)$, $(3, 7 \%)$, and ...
2
votes
2answers
137 views

Solve for level payment with a twist

Reworded trying to clarify. Also corrected example to correctly state 4 years and 150 days. I'm struggling with how to solve for a level withdrawal that will reduce a starting balance amount to zero ...
2
votes
0answers
13 views

Mean and variance regime-switching model

Suppose we have the following model for stock price: $$ X_{t}=X_{0}\exp\left(\int_{0}^{t}(r-\frac{1}{2}\sigma_{\epsilon(s)}^2)ds+\int_{0}^{t} \sigma_{\epsilon(s)}dW_{s}\right) $$ This follows a normal ...
2
votes
1answer
84 views

Stochastic calculus book recommendation

I'm a quantitative researcher at a financial company. I have a PhD in math, but I'm an algebraist, so I only took the two required analysis courses in grad school (measure theory for the first, and I ...
2
votes
0answers
32 views

Term Structure and short rates

If I have a term structure/yield curve given by: $$f(t, T) = f(0, T) + σ^2t(T − \frac{t}{2}) + σB_t $$ and want to find the short/spot rate $r_t$, is this simply: $$f(t,t) = f(0,t) + ...
2
votes
2answers
46 views

Brownian motion and covariance

Show that for $B = (B_t)$ Brownian motion, its covariance is $cov(B_s, B_t) = min(s, t)$. The solution I was given was: For $s ≤ t$, $B_t = B_s + (B_t − B_s)$, $B_sB_t = B_s^2 + Bs(Bt − Bs)$ ...
2
votes
1answer
44 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 ...
2
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0answers
41 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 ...
2
votes
1answer
62 views

Whats the formula to work out the minimum monthly payment of a loan?

I'm a developer, and i'm building a snowball debt calculator. I want a formula to work out what the minimum monthly repayment would be on a debt with a given interest. And I really want to get the ...
2
votes
1answer
37 views

Pricing a riskless asset in the Black & Scholes market

Consider a Black&Scholes Market where a risky asset evolves according to: $$\frac{dS_t}{S_t}=\mu dt+\sigma dB_t$$ $$S_o=s$$ Riskless asset is associated with risk free rate r. I want to represent ...
2
votes
0answers
62 views

Simplifying $\sum_{t=1}^{n}t^2v^t$ using actuarial notation.

In financial mathematics involving immunization, I encounter situations where I am trying to calculate $$(A) \quad v+4v^2+9v^3+ \cdots +n^2v^n=\sum_{t=1}^{n}t^2v^t $$ where $v$ is the present value ...
2
votes
0answers
36 views

Are these two option valuation formulas equivalent? Why?

I have been reading a finance paper that claims that the following function, which is a value for a financial derivative (1): $$V(s,t)=E_{Q} \left[\zeta\big(S(T)\big)e^{-\int_t^T r_F(\nu) ...
2
votes
0answers
43 views

Macaulay duration for a coupon bond. Proof

I am working on showing the following. There is a coupon bond redeemable at par with annual coupon rate $r$ per year. The yield to maturity is $i$. The total number of coupons is $n$. Show ...
2
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0answers
38 views

What is this sort of optimisation called?

I am reading a book in mathematical finance. There is something about constrained optimisation. They have specialised it for the financial market, but I am wondering what the general name for this ...
2
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0answers
64 views

Pricing/Valuation of American Options

Hi i'm a litte bit confused by the pricing valuation of American options. For simple Assumtions on the Blacksholes Model and no dividends, and constant rates else one can show, that for a given ...
2
votes
1answer
22 views

Total MSRP given monthly payment, downpayment %, and term of autoloan

I want to buy a car. I know the following: - monthly payment - interest rate - # of months of loan - downpayment % How can I calculate the total MSRP I can get for my monthly payment? So for ...
2
votes
0answers
20 views

How to calculate present value with changes interest

How to calculate present value with period of 5 years and 6 months? Besides that, there is interest changes and compounded differently. Is there any formula?
2
votes
1answer
42 views

CI for the expected value of the sum of two dependent normal RVs

Let's consider 2 dependent, normally distributed R.V.s, $X_1$ and $X_2$. The means, $\mu_1$ and $\mu_2$ are known, as well the covariance matrix $\Sigma$. Let's consider the following random ...
2
votes
2answers
79 views

Are there other accumulation functions that holds $a(n-t)={a(n) \over a(t)}$?

This might be a beginner's question regarding accumulation methods and their functions, but so far I have learned that compound interest satisfy $$a(n-t)={a(n) \over a(t)}$$ Which allows nice ...
2
votes
1answer
33 views

Saving for retirement - how much?

I'm working through a problem in the book "An Undergraduate Introduction to Financial Mathematics" and there is an example I can follow. The problem is: Suppose you want to save for retirement. The ...
2
votes
1answer
50 views

Understanding APR - can it be calculated as a dollar amount

If the APR (as used in the US Truth in Lending Act) is considered "the cost of your credit as a yearly rate," can an APR be converted to a dollar amount? For example 10% simple interest per year on a ...
2
votes
1answer
33 views

the relationship between fractional difference and ACF of a time sequence

When reading the GARCH modeling part of book Analysis of Financial Time Series, I read the following statement. In specific, I do not understand how does the author ...
2
votes
2answers
118 views

Understanding basic stochastic differential equations

This is from a physics course in economics, the literature provides a bare minimum of mathematical explanations. I am trying to understand how to work with stochastic differential equations given in ...
2
votes
1answer
35 views

Find APR with loan balance

Here is the problem: L: original loan amount B: current balance after P periods P: number of periods that have been paid A: period payment **you do not know the number of periods remaining, so ...
2
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0answers
168 views

Engineering Economics Cash Flow Diagram

I have the following question and solution below. What I don't understand is why is the 100,000 seen as savings/revenue when clearly it is coming out of pocket? Additionally, the monthly loan payment ...
2
votes
0answers
265 views

What does it mean to “pass to the limit” in mathematics?

I've been reading a finance paper and stumbled upon this phrase. What does passing to the limit mean in this context (or overall in mathematics)? Here is an excerpt from the paper: It is ...
2
votes
0answers
45 views

Reinvesting the interest (generalized version)

If I deposit \$1 at $t=0$ into an account which credits interest at the end of each year at a force of interest $\delta_t$ (assume it's integrable.) Then, if I reinvest the interest at an annual ...
2
votes
2answers
58 views

quartely payment

A Loan of R65 000 with an interest rate of 16% per annum compounded quartely is to be amortised by equal quartely payments over 3 years Question : how do I calculate the size of the quartely payment? ...
2
votes
1answer
80 views

first order differential question

Mr. John want to buy a house and he must borrow $150,000 from the bank. He wants a 30-year mortgage and he has 2 choice. Choice #1, he can borrow money at 7% per year with no point ( each point is ...
2
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0answers
39 views

Stochastic control, numerical, need expectations given coupled SDEs

I'm looking at a trio of processes which arises in a stochastic control situation. I have a process $(V_t)$ which I may control, and $(V_t)$ influences a diffusive stock price process $(S_t)$. The ...
2
votes
1answer
60 views

Financial Bonds 500 $1,000 bonds with stated rate of 5% issued at par. 10 year term and pay interest semi-annually.

Every time I try and calculate this problem something comes up wrong. Either from working it out by hand or using my BA II plus, I cannot get the answer shown below. Am I wrong or is this book answer ...
2
votes
0answers
90 views

Doob Decomposition of American Option

I am trying to figure out the Doob decomposition of an American put option in a discrete time binomial model. I know how to price the American put, but I'm having trouble expressing it as the sum of ...
2
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0answers
445 views

Analogue of Leibniz Rule for Stochastic Integrals

Suppose $$f(t,u)=f(0,u)+\int_0^t{\mu (w,u)dw}+\int_0^t{\sigma(w,u)dB_w}$$, where $B_w$ is a standard Brownian motion. I would like to calculus the drift and diffusion of $Y_t=-\int_t^s{f(t,u)du}$ ...