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

1
vote
1answer
12 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 ...
-2
votes
0answers
18 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 ...
0
votes
0answers
25 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
35 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
32 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
18 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
33 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
33 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
24 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 ...
-3
votes
0answers
35 views

Price per share problem. [closed]

Last year the company paid a dividend of 3.40 dollars. It expects zero growth in the next year. In year 2, 5 % growth is expected, in year 3 and 4 the company is not paying any dividends. In year 5 ...
0
votes
0answers
20 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
36 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
53 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 ...
-3
votes
0answers
57 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 ...
0
votes
0answers
51 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
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 ...
0
votes
0answers
17 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
30 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
0answers
23 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
1answer
51 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. ...
0
votes
1answer
25 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
39 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
21 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
11 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
30 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
18 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
30 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
36 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
41 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
35 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
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 ...
1
vote
1answer
106 views

Tangent portfolio weights without short sales?

Consider a mean-variance investor in a world with a risk-free asset. Let $R_f>0$ be the return of the risk-free asset, $\mathbb{E}(R_i)>R_f$ the expected return of the risky asset $i$ and ...
0
votes
0answers
16 views

Book to learn foundation mathematics for finance

I come from engineering background, but been more than 10 years since I passed out - have forgotten most of the mathematics! I am trying to find a good book to rebuild my mathematical foundation ...
1
vote
1answer
23 views

Portfolio Theory - Finance Riskless Assets Return

A market consists of two risky assets and one riskless asset. Asset 1 has a return of 8% and a risk of 10%. Asset 2 has a return of 16% and a risk of 30% The correlation between the returns of the two ...
0
votes
1answer
17 views

load repayment with increasing annuity

Question is : A loan of $10,000 is to be repaid in ten years by payments at the end of each year. The payments grow by 3% per year, so if the first payment is P, then the second payment is 1.03P and ...
0
votes
1answer
45 views

Value of an Asian option with squared integral

Is it possible to find a closed form solution of the value of an asian option paying $(\int_0^T S_u du)^2 $ at maturity? I know there is no closed form solution if the payoff is of the type $(\int_0^T ...
0
votes
1answer
31 views

Deriving the difference between compound interest and simple interest

What is the derivation for the formula that gives the difference between compound interest and simple interest after three years: $P\left(\frac R{100}\right)^2 \left(\frac R{100} + 3\right)$? It is ...
0
votes
4answers
373 views

Why do Fibonacci numbers appear in stock market tick charts? [closed]

I've been reading about stocks trading and noticed Fibonacci numbers are preferred as the time frames for tick charts. I was immediately very curious about why that happens. Does anyone know? Thanks! ...
0
votes
0answers
36 views

How to calculate the daily late fee?

Due to my ignorance, I owe the mobile service provider $701. The penalty is 3% per day. That means on day 1, I should pay $701 + 701\times0.003$ On day 2, I should pay $701 + ...
0
votes
0answers
13 views

FM question: Price call option with dividend paying?

In a binomial tree model with dividends, if stock price goes up in the latest period, then a dividend of $0.5 will be paid out;otherwise, no dividend is paying out. The stock price at time n is: ...
0
votes
1answer
20 views

How to test if two sets of data are closely related?

As part of my masters thesis i am 'Examining the Reliability of Markov Chains and The Kalman Filter as Stock Market Forecasters'. I will be using the daily returns from the s&p500 over a 5 year ...
0
votes
0answers
36 views

Eurpean call option is a convex function of the strike price - proof

I need to show that the price of a plain European call option is a convex function of the strike E of the option i.e. show that $ \frac{\partial^2 C}{\partial E ^2} \geq 0$
1
vote
1answer
76 views

Exam FM question. Bonds with loss at the last moment.

I was working on the following problem and the answer that was given to me looks a little shady and I wanted someone to confirm my thoughts. As of 12/31/2005, an insurance company has a known ...
0
votes
2answers
44 views

Variance and diversification of a portfolio

Suppose I have a portfolio composed by $n$ assets and fixed total size, with stochastic returns. I'm looking for a result stating that as $n$ increases the variance (or any other measure of riskiness) ...
1
vote
0answers
7 views

Convergence under rank correlation

I have a following setup: Let $c\in{\Bbb R}$, $R^2\in [0,1]$ and $\Psi,\varepsilon_1,\varepsilon_2,\ldots$ independent random variables on a probability space $(\Omega,{\cal A},{\Bbb P})$. Define the ...
2
votes
0answers
31 views

Stochastic control with stopping times

Given a wealth process that evolves as $$d w_t = r w_t dt + \theta_t ( \sigma dW_t + (\mu-r) dt) - c_t dt.$$ and smooth functions $u,F: [0, +\infty) \rightarrow \mathbb{R}$, how can we optimise the ...
3
votes
1answer
60 views

Isolating for i

So this might seem a bit fundamental, but in financial math the following equation gives you the price for a bond $$ P = C \frac {1-(1+i)^{-n}} {i} + B(1+i)^{-n} $$ where $P$ is the price of the ...
-3
votes
1answer
27 views

How much should they have in the account?

The Meek brothers are planning a trip around the world. They hope to work some as they go, but believe that they should have accessible $\$800$ per month so they can live in relative comfort for the ...
3
votes
1answer
88 views

Reference Request - Introductory book on Mathematical Modelling in Economics and Business

I have to take a compulsory course named Mathematical Modelling in Economics and Business this semester and have absolutely no background on the subject. I also noticed there is no post on this site ...