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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4
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0answers
50 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
68 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
29 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
235 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 ...
0
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1answer
44 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 ...
1
vote
1answer
94 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 ...
1
vote
1answer
73 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 ...
-1
votes
1answer
112 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. ...
0
votes
1answer
23 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 ...
0
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0answers
27 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
votes
2answers
279 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, ...
1
vote
1answer
46 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 ...
1
vote
1answer
52 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
votes
1answer
63 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 \\ ...
1
vote
0answers
35 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 ...
0
votes
1answer
29 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 $$dS_t=15dW_t$$ $$S_0=95$$ ...
1
vote
1answer
68 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 $10$ ...
1
vote
1answer
50 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 ...
0
votes
1answer
196 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: ...
0
votes
2answers
196 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 ...
0
votes
1answer
47 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 ...
0
votes
2answers
98 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 ...
1
vote
2answers
31 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 $169$ ...
2
votes
1answer
156 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 ...
0
votes
1answer
70 views

Exam FM problem. What does this problem mean?

Danny borrows 4,000 from Genevive at an annual effective rate of interest i. He agrees to pay back 4,000 after 14 years and 5,440.32 after another 14 years. Danny repays the ...
2
votes
2answers
48 views

Methods of solving this exam FM problem with geometric-investments.

The problem I am working on is as follows. Matthew makes a series of payments at the beginning of each year for $20$ years. The first payment is $100$. Each subsequent payment through the tenth ...
2
votes
1answer
57 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 ...
0
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1answer
32 views

Can someone check my answers to this problem?

This is from Discrete Mathematics and its Applications Definition of recurrence relation from book From my understanding, compounded annually means that every year(annually) the account will ...
-1
votes
1answer
92 views

Exam FM problem with loans. $(1.0075)^2$ or $(1.0075)^3$?

I am a bit confused about the following problem and I would like to have clarification. A loan of $12,000$ was made with annual rate of $12\%$ convertible quarterly. Smith plans to make a ...
1
vote
1answer
25 views

Calculating the yield of a bond purchased at a lower price.

I am working on the following problem. A 10 year bond bearing a $7\%$ coupon rate payable semiannually is bought to yield $5\%$ semiannually. The bond is redeemable at par. If the bond is ...
1
vote
1answer
26 views

Algebraic representation of how values are calculated in TI BA II+?

In order to understand how the BA II+ works, I would like to know the algebraic representation of it. For example, for the problem below Present value of an annual coupon bond that pays 80 per ...
1
vote
1answer
108 views

Exam FM problem. Bonds

the following problem is what I am working on. Suzan can buy a zero coupon bond that will pay $1000$ at the end of $12$ years and is currently selling for $624.60$. Instead she purchases a $6\%$ ...
1
vote
1answer
59 views

How do you compute such a limit? (Where the variable is the upper limit in a definite integral)

I have computed limits rigorously before but I have never come across an example where the variable is located in the upper limit of a definite integral. The exact question is attached. It's shown ...
8
votes
1answer
135 views

Heavy-tailed distributions

I have encountered the following two definitions of heavy-tailedness (right tail) for a $[0,\infty)$-valued random variable $X$ satisfying $\mathbb{E}[X]<\infty$: (i) ...
2
votes
2answers
80 views

Interest rates. What is the difference between $I=I_0(1+r)^t$ and $\frac{dI}{dt}=rI$?

When I was in school, we used this method for generating the amount of money would be in a bank account after $t$ years with interest rate $r$: $$I=I_0(1+r)^t \text{ where }I_0\text{ is the initial ...
1
vote
1answer
56 views

Conditional likelihood of continuously-combounded returns

The simplest possible asset pricing model ist the geometric brownian motion for asset price. Here the price $S_t$ solve the familar $$dS_t = (\mu +0.5 \sigma^2)S_t \, dt + \sigma S_t \, ...
1
vote
1answer
43 views

Find compound growth rate from cumulative totals

I'm a bit out of my depth here, so please feel free to correct any errors in terminology, etc. I'm looking to solve for a percentage growth rate. I know the starting population, the number of ...
1
vote
1answer
95 views

How to calculate savings over the life of a car loan?

I'm working through the maths in this, only the relevant parts of which I quote: ...On a \$25,000 car loan through the manufacturer for four years, your monthly payment would be about [1.] \$520 ...
2
votes
0answers
66 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
48 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) ...
1
vote
1answer
198 views

Exam FM Portofolio problem: Using Macaulay Duration

The following problem is what I am working on and I cannot solve it. Under the current market conditions Bond 1 has a price (per 100 of face amount) of $P_1=88.35$ and a Macaulay duration of ...
3
votes
1answer
124 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 ...
0
votes
1answer
35 views

Calculating interest on changing principal amount

I'm writing software and I'm trying to calculate interest on a principal value that changes daily in a predictable way. For example, if you saved $5 each day for five years at a 4% annual interest ...
1
vote
0answers
28 views

Calculate year for a provided yield

\$146.25 will yeild \$46.25 at 7.5% per annum. How to get the number of years? Answer is 6 but how do you get it? What is the formula?
0
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1answer
79 views

How to solve a Compound Interest Question with yearly withdrawals?

The current period is January 2015 A Principal wants to make 3 deposits in the bank: Start of 2015, Start of 2016, Start of 2017, And wants to give a $5000 scholorship for to the best student at ...
1
vote
1answer
250 views

Find expected present value of a continuous payment stream

I have a question for the financial part of my course which I am struggling to answer as i am not sure my answer makes sense. Question: Time is counted from the present t = 0 in years. Suppose for ...
0
votes
1answer
192 views

Prove the process is a martingale with respect to the natural filtration

Let $\{M_n\}_{n\ge 0}$ be a symmetric simple random walk. Fix a real $b$. Prove that the process $S_n = e^{bM_n} (\frac{2}{e^b + e^{-b}})^n$, $n = 0,1,2,....$, is a martingale w.r.t. the natural ...
0
votes
1answer
175 views

How to differentiate the standard normal deviation w.r.t. a parameter inside the upper bound

Given that $$N(x)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^x e^{-\frac{s^2}{2}}\:ds$$ And that $$d=\frac{1}{\sigma\sqrt{\tau}}\ln\left({\frac{S}{e^{-r\tau}K}}\right)+\sigma\sqrt{\tau}$$ How do I take the ...
1
vote
1answer
403 views

How do I calculate interest on short term loan?

I'm trying to work out interest on short term loans - these are loans that extend to months not years, and are typically repaid in monthly chunks, but I also know that some are repayable in weekly ...
1
vote
1answer
284 views

How to differentiate the Black-Scholes formula w.r.t. volatility

The Black-Scholes-Merton formula for determining call option value is given as: $$C(S,K,\sigma,r,\tau)=N(d_1)S-N(d_2)Ke^{-rT}$$ where $N(d_i)$ is the standard normal distribution and ...