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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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
47 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
16 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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0answers
38 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
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: ...
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1answer
40 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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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
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1answer
41 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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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 ...
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1answer
59 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
75 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
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 ...
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1answer
133 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 ...
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0answers
21 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 ...
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1answer
43 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 ...
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1answer
20 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 ...
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1answer
49 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 ...
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1answer
69 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 ...
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0answers
40 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 + ...
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0answers
16 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: ...
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1answer
53 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 ...
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0answers
64 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$
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1answer
84 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 ...
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2answers
59 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) ...
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0answers
10 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 ...
3
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0answers
36 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
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1answer
64 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 ...
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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
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1answer
136 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 ...
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1answer
31 views

Splitting profits based on quantity of work when work is reused

General Problem We (a small organization) want to split all profits for a project based on the quantity of work invested into that project (thus, if Person A invests 40h and Person B invests 60h, A ...
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1answer
48 views

Discrete Dynamical Systems & Credit Card Debt: How to solve for payment

I have the following problem, taken out of Giordano, Fox, and Horton's A First Course in Mathematical Modeling: Your current credit card balance is $\$12,000$ with a current rate of $19.9\%$ per ...
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1answer
56 views

Differential of stochastic term

Question 1: How does one come up with the equation in the red box below? It looks like some kind product rule, but I'm not sure how to apply Ito's lemma here. Bjork doesn't seem to explain it ...
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23 views

Zero coupon bond is without discounting coupons?

How much should you pay for a zero coupon bond due in 10 years with a YTM 7%? I simply did 1000/(1.035)^20, without discounting the coupons. Is this correct? Or am i missing something? Thanks!
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1answer
69 views

YTM and YTC. how do you discount the coupon rate?

A corporation sold a 30-year bond with a coupon rate of 8% (4% semiannually) two years ago. The bonds are callable at 105% of par value 5 years after issue and 103% of par value 10 years after issue. ...
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1answer
16 views

Finantial Math problem verification: price of a product, devaluation and type of change

The problem is: "Which would be the price, in Mexican Pesos (MXN) that would have a car in five years, if its actual value is US 28,567? Consider that its price increments in a 1.2% each semester and ...
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0answers
21 views

Mixed Lognormal Model Calibration

Any ideas as to how to calibrate a mixed lognormal volatility model (Brigo and Mercurio 2002) for arbitrary N < 10? The paper seems vague with respect to implementation.
3
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2answers
157 views

Book request: Mathematical Finance, Stochastic PDEs

I'm a math student, starting a PhD in the near future. My field of research will be mostly in the field of applied mathematics / numerics. Topics will deal with Kinetic Theory, Moment Equations, ...
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1answer
32 views

Exam FM problem using force of interest. Calculate $P-Q$ [closed]

The foce of interest at time $t$ is given by $\delta_t=.01t$. $P$ is the present value of a 12 yr annuity due of $100$ payable annually. $Q$ is the present value of a 12 yr annuity immediate of ...
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1answer
48 views

House loses value each year. How long will it take for the house to be worth $150000

A house purchased for $\$226000$ loses $4\%$ of its value each year. How long will it take for the house to be worth $\$150000$? The way I set up the equation was $150000=(226000)(.96)^x$. I just ...
0
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1answer
31 views

Covariance in normal lognormal (NLN) mixture

Let $u = \epsilon e^{\frac{1}{2} \eta}$ where \begin{equation*} \left( \begin{array}{c} \epsilon \\ \eta \\ \end{array} \right) \sim N\left( \left( \begin{array}{c} 0 \\ 0 \\ ...
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0answers
20 views

Is there a goodness-of-fit chi-square test for muli-factor SDE models?

I read in the book 'Modeling with Itô Stochastic Differential Equations' by Edward Allen about a chi-square test for SDE models. In section 5.5 this test is explained for a one-factor model. Can this ...
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1answer
27 views

Find probability that payoff function is in $[10,20]$

In moment $t=0$ we bought option with expiration date $T=2$. The payoff function of this option is given by: $$f=(\max_{t\in[0,T]} S_t -110)^{+}$$ where $S_t$ satisfies $$dS_t=15dW_t$$ $$S_0=95$$ ...
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1answer
49 views

Hypothetical scenario with economics

You have been assigned to purchase a new molding machine. One vendor offered a machine that will cost $200,000$, with an estimated installation of $10,000$. The machine has an expected life of $10$ ...
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1answer
39 views

Discount rate of an annuity

The formula for the present value of an annuity is: $$p = \frac{a[1-(1+r)^{-n}]}{r}$$ Where: p = present value r = discount rate n = number of payments I would like to find the discount rate, since ...
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0answers
27 views

Linear Algebra for fund allocation logic

I am writing a program which automatically calculates the trade allocations. Imagine we have a 3 funds, Fund A, B and C. They current asset allocations (so-far-percentages) are 10%, 20%, 70% ...
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1answer
57 views

cash flow diagram, in/outflow series

I have a econ midterm coming up soon and stumbled upon this question. I know this is the math section but it appears not many use the finance one. My approach is: 2C=800/(1.12^2)+1200/(1.12^6)=125.71 ...
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2answers
60 views

Why does PERT work?

e is the limit of (1+1/n)^n. So how come we do Pe^rt to calculate continuously compounded interest? The regular formula for compound interest is (1+r/n)^tn, with rate being part of the base, not the ...
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1answer
32 views

Find the accumulated value at time 8 of $1600 invested at time 6

Given: $a(t) = xt^{2} + yt + z $ $100a(2) = 152$ and $200a(4) = 240$ Using that, I found that $z = 1, $ $x = -0.105 $, and $y = 0.47$ The question asks for the accumulated value at time 8 of 1600 ...
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2answers
57 views

Need help and clarification in Exam FM problem, future value.

The problem that I am working on is the following. Jim began saving money for this retirement by making monthly deposits of 200 into a fund earning 6% interest compounded monthly. The first ...
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2answers
26 views

The Present Worth of $169 due in 2 years at 4% Per Annum Compound Interest

The present worth of $\$169$ due in 2 years at $4\%$ per annum compound interest is The choices are as follow: $\$150.50$ $\$154.75$ $\$156.25$ $\$158$ I tried to solve this by multiplying $169$ ...