Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.
1
vote
1answer
46 views
A loan is being repaid by 12 annual payments of 3000…determine the principal and interest portions of the tenth payment
A loan is being repaid by 12 annual payments of 3000 followed by 8 annual payments of 5000. If i=0.10, determine the principal and interest portions of the tenth payment and the 15th payment.
I am ...
1
vote
1answer
43 views
Find the accumulated value of an investment fund
Find the accumulated value at the end of six years of an investment fund in which \$100
is deposited at the beginning of each quarter for the first three years and \$50 is deposited at the beginning ...
1
vote
1answer
29 views
Cost for hedges under a Wiener process
I'm trying to estimate the hedging costs relating to a financial derivative which moves like a Wiener process, and I'm struggling to find the correct setup to solve the problem.
Suppose I have a ...
1
vote
1answer
78 views
Compound interest quarterly
I know the financial formula for calculating compound interest:
Compound Interest Multiple = [1+(Annual Interest in decimals/365)]^(number of days).
I have a initial and final date. I calculate the ...
1
vote
1answer
64 views
Calculate Compounding Interest Rate From Total Interest Rate?
I would like to be able to calculate the interest rate that is compounded for a given total interest rate, and number of compounding events.
TotalInterestRate = ...
0
votes
1answer
32 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
1answer
41 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
54 views
Random Stock Stop-Loss/Stop
Assuming a Stock's price changes in a random manner. If you buy this Stock, you are required to set a stop-return and stop-loss price. I am looking for the equation that shows the probability for ...
0
votes
1answer
15 views
Find the relative shares of B,C and D in the estate, if it is assumed that the estate will earn a 7% annual eff
Person A leaves an estate of $100,000. Interest on the estate is paid at the end of the year to beneficiary B for the first 10 years, to beneficiary C for the next 10 years, and to charity D ...
0
votes
1answer
50 views
European Calls: arbitrage
I have following question, it should be pretty easy, but this subject is still pretty new for me.
Given a market where calls of any strike price can be bought and sold. Assume that the interest rate ...
3
votes
0answers
106 views
Algorithm/Formula to compute adding and/or removing compound and/or non-compound percentages from a value?
I will first start with a scenario, I have to apply some adjustments to a particular value. These adjustments are either compound or non-compounded and they can either be added or subtracted to the ...
1
vote
0answers
10 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, ...
1
vote
0answers
13 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 ...
1
vote
0answers
24 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
0answers
35 views
Doob Decomposition of American Option
I am trying to figure out the Doob decomposition of an American put option in a discrete time binomial model.
I know how to price the American put, but I'm having trouble expressing it as the sum of ...
1
vote
0answers
39 views
Interest % and final payment
I dont get these two questions? How should I calculate the answer?
A) Sam intends to retire in 6 yrs. To supplement his pension he would like to receive $\$234$ every 2 weeks for 10 yrs. If he is ...
1
vote
0answers
144 views
Analogue of Leibniz Rule for Stochastic Integrals
Suppose $$f(t,u)=f(0,u)+\int_0^t{\mu (w,u)dw}+\int_0^t{\sigma(w,u)dB_w}$$, where $B_w$ is a standard Brownian motion. I would like to calculus the drift and diffusion of $Y_t=-\int_t^s{f(t,u)du}$ ...
1
vote
0answers
82 views
Uniform convergence of series with utility function
Let $u(x)$ be a real function with the properties
$u(x)$ is continuous and non-decreasing in $x$
$u'(x)$ is non-increasing in $x$
$u(0)=0$
$u'(0)=1$.
In other words, $u(x)$ is a utility function.
...
1
vote
0answers
65 views
Compactness of the set of densities of equivalent martingale measures
Consider an incomplete market $(\Omega,\mathcal F,\mathbb P)$ driven by a semimartingale $S=(S_t)_{t\in[0,T]}$. Under the no free lunch under vanishing risk (NFLVR) assumption, the set $\mathcal ...
1
vote
0answers
74 views
Good reference on sample autocorrelation?
I'm not a statistician but I'm writing my thesis on mathematical finance and I think it would be neat to have a short section about independence of stock returns. I need to get better understanding ...
1
vote
0answers
24 views
Standard practice for identifying outlying spend amounts
Hope this is mathematical enough to qualify as a question - I'm no mathematician!
I have a set of individuals travel & entertainment credit card spend, and I'd like to highlight any outliers that ...
1
vote
0answers
63 views
Portfolio optimization - problem with a proof
I'm trying to proof Proposition 1 in this Paper about Markowitz Portfolio Opitimization on page 6/7 but I can't figure out how to do this. The author wrote "The proof of Proposition 1 can be found ...
1
vote
0answers
222 views
Reading advice: Mathematical finance for a student of pure mathematics
Which books/lecture notes should a student with a background in pure mathematics (in my case it was geared towards algebraic geometry) read in order to do financial math? I have done one basic course ...
1
vote
0answers
121 views
Immunization and Sensitivity Analysis
Frequently a company wants to match its assets and liabilities. However, perfect matching is not practical due to fluctuations in interest rates. So they hedge their risk using immunization. This can ...
1
vote
0answers
123 views
Dividend Discount Model
The current price of a stock can be modeled by $P_0 = \frac{D_{1}}{r-g}$ where $D_1$ is the expected dividend, $r$ is the rate of return, and $g$ is the expected growth rate in the perpetuity. If ...
0
votes
0answers
11 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 ...
0
votes
0answers
11 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
37 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
26 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 ...
0
votes
0answers
22 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
0answers
25 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
0answers
48 views
Drift equation / Girsanov's Theorem
Define $$\frac{dS_t}{S_t} := \mu \, dt + \sigma^B \, dB_t +\sigma^W \, dW_t,$$ $$dS_t^{(0)} := S_t^{(0)}r \, dt,$$ where the constants $\mu, \sigma^B,\sigma^W$ and $r$ all positive and $\mathcal{F}_t$ ...
0
votes
0answers
20 views
SDE(s) satisfied by Radon Nikodym derivatives of martingale measures?
Given:
Money Market Account: $dR_{t}=R_{t}r_{t}dt, R_{0}>0$
Risky Asset: $dS_{t}=S_{t}(\mu_{t}dt+\sigma_{t}dB_{t}), S_{0}>0$,
where $r, \mu,$ and $\sigma$ are positive processes and $B$ is a ...
0
votes
0answers
27 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 $- ...
0
votes
0answers
78 views
What does the term “scaled by” mean?
Sorry for the simplistic question i"m just not sure where else to turn. I'm reading a math-heavy academic paper (not for a class - for my own edification) that says:
...
0
votes
0answers
18 views
Bond worth given yield to maturity
On 18 February 2010, the bonds were issued with a face value of $1,000. The bonds mature in 15 April 2015 and have an annual coupon rate of 6%.
(a) Assuming today is 15 April 2013, how much is the ...
0
votes
0answers
48 views
Find the present value of a ten-year annuity
Find the present value of a ten-year annuity which pays $400$ at the beginning of each quarter
for the first $5$ years, increasing to $\$600$ per quarter thereafter. The annual effective rate of ...
0
votes
0answers
51 views
Financial Math question. Appreciate you help :)
Correct me if im wrong is the answer $ 21,200 Minus the 10% loan. The book does not provide answers, and I have no one else to help me... Thanks :)
"Compare the potential returns from an all-equity ...
0
votes
0answers
29 views
Market Clearing Prices: find the set for the valuations
We express Gp=(X U Y, E) is the preffered graph where ij in E if j is preferred seller of X=buyers, Y=sellers
--> A vector of prices p is market clearing if Gp has a perfect matching( generally, ...
0
votes
0answers
31 views
Find the time and amount of the final payment, if the final payment is larger than the regular payments? Assume i=4.5%
A load of \$1000 is to be repaid by annual payments of \$100 to commence at the end of the 5th year and to continue thereafter for as long as possible. Find the time and amount of the final payment, ...
0
votes
0answers
54 views
How to calculate VAT in this case?
A manufacturer X sells a TV to a wholesaler Y for 10,500. Wholesaler Y sells it to a retailer Z at a profit of 600 and the retailer Z sells it to a customer at a profit of 4000. If the VAT rate is 4% ...
0
votes
0answers
68 views
Black Scholes PDE for non-constant coefficients
I need to derive the Black–Scholes PDE for non-constant coefficients. I suppose we should also use an appropriate transformation such as $y=\ln S$. I have no idea, please help me.
0
votes
0answers
38 views
On mortagage payment
A mortgage balance of $\$ 9,566.66$ is to be repaid over a 2 term by equal monthly payments at $2\%$ compounded semi-annually. At the request of the mortgagor, the monthly payments were set at $\$ ...
0
votes
0answers
24 views
relation between foward curve and interest rates
I am working through the book "term structure models a graduate course" by damir filipovic. Suppose the interest rate is given by the following sde
$$ dr(t)=(b(t)+\beta r(t))dt +\sigma dW^*(t)$$
...
0
votes
0answers
168 views
Net Present Value Calculation for Construction Project with Initial Capital
I'm having real trouble working out how to do the following question because of the initial capital that the company has at the start of the project, meaning that they can delay taking out a loan ...
0
votes
0answers
56 views
TVaR proof of formula question
I'm trying to prove that $TVaR_p(X) = \frac{\int_{\pi_p}^{\infty} x*f(x)dx}{1- F(\pi_p)}$ is equal to $\frac{\int^1_p VaR_u(X)du}{1-p}$ ?
I obviously see that the denominators are the same since ...
0
votes
0answers
16 views
Boundedness of a payoff
How can i establish the the following arithmetic average payoff function is bounded?
$dS=μSdt+σSdB$
$F(x)=[(1/n)∑x(t\{i\})-K]⁺$
0
votes
0answers
38 views
Regime switching models
I would be extremely grateful if you could point me to any good source on Regime switching, mainly:
What we define as regime switch
Different kinds of regimes (trend, high/low vol)
Attempts at ...
0
votes
0answers
119 views
Portfolio convexity proof
Consider $n$ different fixed-income securities with prices $P_1 , P_2 , \ldots , P_n$
and convexities $C_1 , C_2 , \ldots , C_n$ respectively. Assume that all securities have the same yield. Prove ...
0
votes
0answers
244 views
best revenue to Costs ratio
Would you say for best revenue to costs ratio would be D as cost is 0.4. Thanks in advance for your help.
A) 109 (Sales Revenue) : 141 (Cost) = 0.77
B) 533 (Sales Revenue) : 307.92 (Cost) = 1.73
...
