Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.
3
votes
2answers
63 views
Speculating on the stock exchange
Imagine you model each stock as a random walk (fractal) and also that you can buy and sell at any price. Suppose also that it 'walks' with the pace of 1.
If you buy, for example, 1000 shares of ...
0
votes
0answers
12 views
Hedging a long position-one period
Consider a one period binomial stock model with $S_0=4$, $S_1(H)=8$ and $S_1(T)=2$. The interest rate is $25$%. Let's say I buy a call option for $1.20$ with strike price $K=5$ which expires at time ...
0
votes
0answers
23 views
Help with accumulation and amount functions
Consider the amount function $A(t) = A(0)(1 + i) t$: Suppose that a deposit $1$ at time $t = 0$ will increase to $2$ in $x$ years, $2$ at time $0$ will increase to $3$ in $y$ years, and $3$ at time ...
0
votes
0answers
23 views
Split a debt into growing parts
Suppose that at the present day I owe a friend a certain amound of money, say $ P_1 $ . This debt will linearly grow at a fixed (and known) rate, so that there will be a time in the future at which my ...
0
votes
1answer
57 views
Black-Scholes PDE to heat equation, nonconstant coefficients
Can someone provide me with details or a reference on how to transform the Black-Scholes PDE with nonconstant coefficients (i.e. $r=r\left(S,t\right)$, $\sigma=\sigma\left(S,t\right)$) to the heat ...
0
votes
0answers
28 views
Black-Scholes application of heat transfer
I cannot find an explicit application of the heat transfer equation to convert the Black-Scholes partial differential equation
into the result
Please show me how or a better alternative.
0
votes
3answers
63 views
$1500=P \times { (1 + 0.02) }^{ 24 }$, what is the value of $P$?
Hey guys could you please tell me what is the faster why to solve this equation. It's a compound interest equation and I'm stuck at the ${ (1 + 0.02) }^{ 24 }$ I really don't know how to proceed in ...
1
vote
1answer
27 views
I'm looking a compound interest formula.
Admittedly, I just finished physics and calculas but some of my more basic math skills escape me.
I'm looking for a formula that will give me a total compounded value after x number of weeks.
So for ...
1
vote
0answers
30 views
Easy proof of Black-Scholes option pricing formula
I use this Book to read the option princing in Black-Scholes model in pages 93-99, The poof of the formula given by
$$c(s,t)= N(d_1(s,t)- Ke^{-rT}N(d_2(s,t)))$$
where
$$d_{1,2}=\frac{\ln(s/K)+(r\pm ...
1
vote
0answers
36 views
Why does Black-Scholes equation hold on continuation region of American Option? [migrated]
Explanation for Put Option:
$ \frac{\partial V}{\partial t}+ \mathcal{L}_{BS} (V) = 0 $, where
$\mathcal{L}_{BS} (V) = \frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + (r-\sigma) S ...
1
vote
2answers
98 views
Calculating interest rate of car financing
I want a new car which costs $26.000.
But there's an offer to finance the car:
Immediate prepayment: 25% of the original price
The amount left is financed with a loan: Duration: 5 years, installment ...
0
votes
1answer
20 views
Difference between Bi-annual and semi-annual in Financial Maths
I was wandering what the difference was between compounding interest when they use bi-annual and semi-annual and hence how to change your value of i
I think semi-annual means twice in 1 year so your ...
0
votes
1answer
50 views
Early-exercise point of American Put
Could you please help me?
In book Rüdiger Seydel "Tools for Computational Finance" in Chapter 4.5 "American Options as Free Boundary Problem" it is provided the following explanation for case ...
1
vote
1answer
42 views
Deferred Annuity not working
A simple financial math problem:
Mack obtains $500\ 000$ repayable over $20$ years. If interest is compounded monthly at $9.25\%$ per annum, determine the monthly repayments if the repayment ...
1
vote
0answers
41 views
Notation in Financial Math
I am very close to showing part b of this question and think that the reason my solution doesn't match up is because I don't understand a piece of notation.The notation I don't understand is ...
4
votes
1answer
39 views
Arbitrage opportunity
Given odds $o_i$ for $i=1,2,\ldots,n$ and the possibility to bet the amount $b_i\in \mathbb{R}$ on each event such that if event $i$ occurs you receive $b_io_i$ and if it doesn't you recieve $-b_i$. I ...
1
vote
0answers
20 views
The impact of jump on the returns of portfolio and asset pricing
There exsits jumps in financial market. What will be the impact of jump on the returns of portfolio and asset pricing?
Please explain it both academically and plainly. If you can give some excellent ...
-1
votes
2answers
62 views
How to find the amount to added every month or year to get the required amount after certain years?
I want to do a Java application for which after giving the current savings, and the rate of interest and and required amount after specified no of years, it has to show how much a person has to earn ...
0
votes
0answers
14 views
Present value, an interest rate to give zero
Say you have a series of future payments $-1000,-1000,700,750,800$.
$\displaystyle\text{PV}=\sum\limits_{i=0}^4 C_i \exp{(-r t_i)}$
Say $r=0.02$ and each $t_i=0,1,2,3,4$
Expanding that ...
0
votes
0answers
43 views
Why are call options necessary?
My question is actually less ambitious and more specific then the title may have lead you to believe.
Suppose the interest rate is $25\%$ you have a stock at time zero price of $S_0=50$ and at time 1 ...
0
votes
0answers
35 views
Replicating portfolio under the Black-Scholes model
I have a two-asset Black-Scholes model:
$dB_t = B_t r dt$
$dS_t = S_t (\mu dt + \sigma dW_t)$
I introduce a European claim $\xi = \max(K,S_T)$ with maturity $T$, for some fixed $K$. I have ...
1
vote
1answer
62 views
if you invest $ 500 at 6 % compounded annually,
Please help me with this problem. It needs to be done in the same format as below
if you invest $500$ dollars at $6$ percent compounded annually, how many years to the nearest tenth would it take your ...
0
votes
1answer
27 views
Suppose you invest \$10 at 10.2% per annum compounded annually. How many years would it take for your investment to grow to \$15 000?
I'am solving a simlar equation to this and just trying to figure out how they did it?
the only part I don't understand is how they got the number.... 1.102
15000 = 10(1.102)n ¬1 mark
1500 = 1.102n
2
votes
1answer
49 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
votes
2answers
61 views
Probability related finance question: Need a more formal solution
You are offered a contract on a piece of land which is worth $1,000,000$ USD $70\%$ of the time, $500,000$ USD $20\%$ percent of the time, and $150,000$ USD $10\%$ of the time. We're trying to max ...
0
votes
0answers
68 views
A few finance probability and logic questions. Help? I did some work, but I'm stuck on a few. [closed]
I'm currently trying to study for some probability questions for a job interview that I have a couple weeks and I was wondering if you could help me refresh... to be honest this is kind of fun. It's ...
1
vote
0answers
12 views
What is a rolling par-swap?
I am trying to understand the hedging strategy mentioned in the paper below on p.17 (set of rolling par-swaps). Can anyone explain how this works?
Moreover, if anyone is familiar with this paper, ...
0
votes
1answer
34 views
Can anyone show me how this was derived?
So here is all the slide says and I'm and trying to see the steps for derivation. Can someone please show me how this is derived? Essentially I'm trying to go from 1 to 2. Pi is the profit function.
...
4
votes
1answer
62 views
Calculating interest rate for a payment plan
I really should know this from high school so I'm a bit ashamed to ask... :)
I've been offered several cars for lease and want to compare the offered interest rates.
E.g. I have:
...
1
vote
0answers
14 views
Programming in R: How do I switch the X and Y axes?
I have a distribution plot of the daily drawdowns of the Dow Jones Industrial Average index; however, it has the drawdowns on the y-axis and the frequency on the x-axis... I'd like to switch that so ...
2
votes
5answers
140 views
Game Theory Question about Financial Markets
This is a recent quote from one of the outstanding bond portfolio managers:
"First of all, for every buyer there is a seller. Therefore, in order for someone to sell their bonds and buy stocks means ...
0
votes
1answer
19 views
Find the transaction cost-adjusted expected return of the stock
Let $W^b_i$ denote the weight of stock i in the existing portfolio and $W^a_i$ denote the weight of stock i in the new portfolio to be created. Let $c_i$ denote the transaction cost of stock $i$.
If ...
2
votes
0answers
25 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 ...
1
vote
3answers
65 views
If you invest $\$1500$ at $7\%$ compounded annually, how many years would it take for your investment to grow
If you invest $\$1500$ at $7\%$ compounded annually, how many years would it take for your investment to grow to $3750$?
Is this right?
$$\text{term } = \frac{\log( \text{overall gain factor})}{ ...
0
votes
1answer
35 views
confusing part to basic accounting question
Directions: Given the information find the weekly and monthly taxable wages (4.3 weeks per month).
This is for federal income taxes.
Weekly Taxable Wages: $\$21.40$ per hour, $40$ hours a week, $47$ ...
0
votes
0answers
23 views
determine the effective annual yield rate
The American Savings Bond of 1958 were 15 year bonds sold and redeemable at par with annual coupons, the first at 3.5% and the remainder at 4.25%. If the bond is help to maturity, determine the ...
0
votes
1answer
29 views
How to Maximise Efficiency With hp12c gold calculator: Equation of Value Loan Schedule
I would like to calculate the net present value of a loan schedule or an equation of value. e.g. "For an investor receives R1 000 after 2 years, R2 000 after 5 years and R4000 after 7 years, how much ...
0
votes
0answers
33 views
Probability Density Function and Eigenvalue Spectrum of Correlation Matrix
My question is in the link...
http://www.flickr.com/photos/88684900@N03/8654322505/in/photostream
0
votes
1answer
52 views
Binomial expansion for solving american put option identity [duplicate]
For american put option I have to prove that:
1) As $D$ tends to $\infty$, $a_n$ tends to $-r/D$ so that $S^*$ tends to $0$.
2) As $D$ tends to $-\infty$, $a_n$ tends to $2D/ \sigma^2$ so that ...
1
vote
1answer
84 views
american put option
For a perpetual american put option $v(s)$, satisfies the following problem:
$$\frac12\sigma^2S^2\frac{\mathrm d^2V}{\mathrm dS^2}+(r-D)S\frac{\mathrm dV}{\mathrm dS} - rV = 0\quad\text{for ...
2
votes
1answer
24 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 ...
1
vote
2answers
23 views
In this situation, how to decrease the payout amount based on the “weighed” constituent parts?
Couldn't think of a better way to explain it in the title, my bad.
This is a problem I'm running into in a programming project.
Here's the situation:
Say a partner is due to be paid $1000 for ...
0
votes
1answer
24 views
How to find breakeven amount when the buy and sell amount has a fee?
With currency exchange they charge 3% when I buy a currency. When I sell they charge 3% on the amount I sell. My question: At which amount do I need to sell to make up for the 3% fees?
I currently ...
0
votes
0answers
29 views
Non-arbitrage theory and existence of a risk premium
Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and isgenerated by $1 d $- ...
2
votes
1answer
79 views
Bonds and Force of Interest
Studying for FM/2 and ran into this problem dealing with bonds;
A 1,000 par value 3 year bond with annual coupons of 50 for the first year, 70 for the second year, and 90 for the third year is bought ...
2
votes
1answer
24 views
Calculating percentage reduction from results only.
I've been looking over some loan repayment statements, and I'm trying to work out:
What the precentage interest is per month.
How long it will be until the final amount reaches 0.
Whether there is ...
0
votes
1answer
47 views
Find the price to yield 10% compounded semi-annually.
A 50,000 par value bond at 8% has semi-annual coupons and is callable at end of 12th through 15th years at par. Find the price to yield 10% compounded semi-annually.
0
votes
1answer
48 views
Calculate the time after which Money doubles
I while solving a problem in banking just thought to form a formula for the time period after which money deposited in bank at a compounded interest rate @$\alpha $ % p.a. .
Amount for compounded ...
1
vote
1answer
109 views
Increasing and decreasing annuity
Going in circles.....
Find an expression for the present value of an annuity-immediate where payments start at 1, increase by 1 each period up to a payment of $n$, and then decrease by 1 each period ...
1
vote
1answer
40 views
Continuous annuity calculation
This is a problem from Marcel Finan's Exam FM/2 course. It is not homework but I am studying for the FM exam and trying to get through this.
You are given $\frac{d}{dt}\bar{s}_t$ = $(1.02)^{2t}$. ...
