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

learn more… | top users | synonyms

0
votes
0answers
29 views

Interpretation of the Snell Envelope wrt European and American options.

In lectures we were taught that the Snell envelope U of a process Z, passes from European to American option prices. I thought that price processes are supposed to be martingales, but the Snell ...
0
votes
1answer
42 views

Promissory note example Financial Math

Brenda owes Cathy $\$8500$ and has signed a promissory note to repay the debt in 15 months from the signing date. The note was signed on December 6, 2009, and the maturity value of the note is ...
3
votes
1answer
66 views

Ornstein–Uhlenbeck SDE.

I am trying to understand the solution to the following exercise, however it is kind of poorly written. Can someone please explain it to me? For $V = (V_t)$ the solution to the Ornstein-Uhlenbeck SDE ...
2
votes
2answers
43 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 $s ≤ t$, $B_t = B_s + (B_t − B_s)$, $B_sB_t = B_s^2 + Bs(Bt − Bs)$ ...
1
vote
0answers
30 views

Common term for “present value” and “future value”

In the past, I have always used the term "present value" for the value of a payment made at some point in time $t$ from the perspective of some other valuation point in time $T$. I did not distinguish ...
1
vote
1answer
30 views

Martingale Properties

Here is a proof of a property of a martingale $X$ relative to the filtration $(F_{n})$: $n\gt m,\\$ $\\ \\ E[X_n|F_m]=E[E[X_n|F_{n-1}]|F_m]=E[X_{n-1}|F_m]=...=E[X_m|F_m]=X_m$ In the definition of a ...
0
votes
1answer
56 views

Redington vs full immunization?

I understand that the present values and duration of liabilities and assets are required to be equal to each other under both cases, and furthermore for Redington immunization the convexity must also ...
1
vote
1answer
15 views

Ito's formula for this stochastic differential - please explain this step?

Referring to those two lines, can someone please explain how those results were obtained? My understanding is, the following formula is being referenced: $$dV_t = dV(S_t,t) = \frac{\partial ...
1
vote
0answers
44 views

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 ...
1
vote
1answer
54 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 ...
0
votes
1answer
68 views

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 $r_i = \alpha + \beta_i\theta + \epsilon_i,$ ...
0
votes
0answers
17 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 ...
1
vote
1answer
41 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?
2
votes
1answer
65 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 ...
1
vote
0answers
29 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 ...
2
votes
2answers
38 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 ...
0
votes
1answer
57 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 ...
0
votes
1answer
14 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 ...
1
vote
0answers
24 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
votes
1answer
43 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 ...
1
vote
1answer
34 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, ...
1
vote
1answer
33 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 ...
1
vote
1answer
40 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 $\sigma_{1}>0$. ...
0
votes
1answer
48 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 ...
0
votes
2answers
64 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 ...
1
vote
3answers
81 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 ...
0
votes
1answer
44 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 ...
0
votes
1answer
37 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 ...
0
votes
0answers
34 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 ...
0
votes
0answers
56 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 ...
2
votes
1answer
42 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 ...
3
votes
3answers
63 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 ...
0
votes
0answers
58 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 = ...
0
votes
2answers
45 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 ...
0
votes
0answers
39 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 ...
0
votes
0answers
62 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 ...
1
vote
1answer
38 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 ...
2
votes
2answers
75 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. ...
-1
votes
1answer
46 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 ...
0
votes
1answer
45 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!
1
vote
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: ...
1
vote
0answers
36 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: $\begin{align*} \text{Call option value} =SN(d_1)-Ee^{-r(T-t)}N(d_2) \end{align*}$ ...
0
votes
0answers
13 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: ...
0
votes
1answer
35 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 ...
1
vote
0answers
19 views

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 ...
2
votes
1answer
39 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 $C(1+i)^n$ ...
2
votes
0answers
40 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 ...
0
votes
1answer
57 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 ...
0
votes
1answer
65 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
0
votes
1answer
25 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 ...