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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29 views

Interest Question

If somebody owes \$55k and pays it back in four years with 6.4% interest p.a, how much would it be if its compounded quarterly? So I used $$A=P(1+i/4)^{4(4)}$$ and plugged it in as ...
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0answers
16 views

What kind of stock returns is that? [on hold]

I have a question. I have a file with stock returns for example the stock of 3M corporation from 3rd of September 1996 till 1st of October 1996. Can someone tell me what kind of returns are this? MMM ...
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1answer
24 views

About the boundary conditions of the Black-Scholes-Merton PDE

I have a question about the solution of the Black-Scholes PDE for the European call option when I read the book Stochastic Calculus for Finance II of Steven E.Shreve. Let $c(t,x)$ be the value of the ...
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1answer
16 views

Evaluating NPV caluclators

I'm working on a Net Present Value set of problems and would appreciate someone else's insight as my Excel calculations are coming up differently than other online calculators for NPV. I've read on ...
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0answers
17 views

Net Present Value [on hold]

If you see after each question, I've put the answer I have arrived at with the work I used to get there. It seems that I am coming up with the wrong answer and I'd like guidance as to what needs to ...
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0answers
24 views

Strange Monte Carlo Sampling Phenomena

I am running a Monte Carlo simulation to price call and put options, and observe a strange correlation between the number of sampling points and the standard deviation. It makes sense that as the ...
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0answers
14 views

Lower semicontinuous risk measure

I am looking for some risk measures that hold the lower semi-continuous property. I am not sure whether Expected Shortfall is a such a measure or not. Can anyone give me some help? Thanks.
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0answers
11 views

Not monotonically decreasing Net Present Value for increasing interest rates

Considering the Net Present Value as the discounted sum of all future cash flows, intuitively I expected that the NPV function would always be monotonically decreasing for any increase in the discount ...
2
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1answer
64 views

A more theoretical than computational interest theory problem involving amortization

I am working on the following problem: A borrower has a mortgage that calls for level annual payments of 1 at the end of each year for 20 years. At the time of the seventh regular payment an ...
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1answer
37 views

Calculate interest over multiple years with added value every year?

I'm trying to calculate the interest and total of money when : Someone is loaning $3600 every year over 11 years with an interest of 10% ? Like : 3600 + 10% = 3960 first year, 3960+3600+10% = 8316 ...
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0answers
21 views

Compounded and Simple Interest Rates

Suppose we have a loan worth 10000 that is being repaid late as a lump sum on a given day 30 days after the due date. Suppose the original interest rate is 5% so that the amount owed before late ...
3
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0answers
50 views

Asymptotic Expansion Method for Pricing American Option

In this Article I faced with Asymptotic Expansion method for pricing American option. the price $P(S,t)$ of this option satisfies the partial differential equation (PDE): $${{P}_{t}}+(r-\delta ...
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0answers
61 views

A question of odds

Consider an experiment with four possible outcomes, and suppose that the quoted odds for the first three of these outcomes are as follows. What must be the odds against outcome 4 if ...
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1answer
30 views

identifying sudden change in value given a list of values over time

I have a list of the average price of an item in a game over time. Things don't tend to move much. I am wondering how I can detect whether a new value inserted is a surprising movement in price. I ...
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2answers
21 views

Intuition - For every % point that rates rise, a bond’s value will decline by its duration in years.

[Source:] Generally speaking, for every percentage point that rates rise, a bond’s value will decline by its duration (stated in years). So if rates climb by one percentage point, the value of a ...
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0answers
21 views

Question about the conditional value-at-risk

I have a question about CVaR (Expected Shortfall) An investment who gives a certain amount of cash with a certain probability : A loss of $20$ millions with a probability of $0.0016$ A loss of $11$ ...
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1answer
24 views

Getting VAR parameters from a research paper.

Many econometrics papers provide the parameters used in their VAR model. If I notate my VAR model as $$z_{t+1} = c + B z_{t} + \Sigma \epsilon_{t+1}$$ where $\epsilon \sim N(0, I)$, then I need to ...
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1answer
20 views

Using IRR to calculate future value of cashflow

Discounting a cashflow using given forward rates will result in the following present value: PV = 102.875 = ${5\over (1+3\%)}$ + ${5\over (1+3\%)(1+4\%)}$ + ${105\over (1+3\%)(1+4\%)(1+5\%)}$ where ...
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1answer
12 views

Semi Annual Deposit Compounded Quarterly

A son planned to endow 1000000 to his son on his son's 21st birtthday. How much is his semi-annual deposit in a special account that earns 5% compounded quarterly if the first deposit was made when ...
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2answers
38 views

Retirement Fund with Interest

A young woman 22 years of age has just graduated from college. She accepts a good job and desires to establish her own retirement fund. At the end of each year thereafter she plans to deposit 2000 in ...
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1answer
27 views

Interest with Inspection Fee in Promissory Note

A man borrowed from a bank a promissory note that he signed in the amount of 25000 for a period of one year. He received only the amount 21915 after the bank collected the advance interest and an ...
0
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1answer
22 views

Compounded Quarterly

Money borrowed today is to be paid in 6 equal payments at the end of 6 quarters. If the interest is 12% Compounded Quarterly. How much was initially borrowed if quarterly payment is $2000 Answer is ...
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1answer
230 views

Where does this characterization of an annuity immediate come from?

I'm looking through my notes, and I don't see anywhere that an annuity immediate can be defined as $a_n = \frac{1}{a(1)} + \frac{1}{a(2)} + \cdots + \frac{1}{a(n)}$. I've always seen it as $a_n = v ...
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1answer
35 views

Money doubling in value

I understand this maybe a question for http://quant.stackexchange.com/; but I believe the math is simple enough to understand. In How many months at an interest rate of 1% per month does money have ...
2
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0answers
13 views

Mean and variance regime-switching model

Suppose we have the following model for stock price: $$ X_{t}=X_{0}\exp\left(\int_{0}^{t}(r-\frac{1}{2}\sigma_{\epsilon(s)}^2)ds+\int_{0}^{t} \sigma_{\epsilon(s)}dW_{s}\right) $$ This follows a normal ...
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0answers
30 views

What math preparation is needed before reading the mathematical method in financial markets?

What math preparation and books are needed before reading the mathematical method in financial markets by Marc Yor if i need to study the whole book? This is one of the advanced finance book
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1answer
23 views

Understanding the solution to a basic annuity problem involving an unknown interest rate

The following is the problem and the solution: Before looking at the solution, here is how I approached the problem: Let $X$ be the amount that each child receives. (i) and (ii) imply that ...
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1answer
24 views

Question related to profit/loss.

Guys see this question: For what sum should goods worth Rs. 1150 be insured at 8% so that in case of loss the owner may recover the premium as well as the goods? I can't understand the meaning ...
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3answers
43 views

Is this equation a parabola or a hyperbola?

In a 1972 paper by Robert Merton, the following equation is derived: $$\sigma(\mu;A,B,C,D)=\sqrt{\frac{A \mu^2-2B\mu+C}{D}}$$ This is known as the Markowitz frontier in finance. When this is ...
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2answers
64 views

Simon invests $\$6000$ and it's compounded semi-annually for ten years

Simon invests $\$6000$ and it's compounded semi-annually for ten years, at $8\%$ per annum. What is the amount of the investment at maturity? I did $(6000)(1.08)^{20}$, and got a completely different ...
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1answer
25 views

Looking for a “Black-Scholes-esque” expression for $E[\max(V-K,Y)]$

In Hull (2008, p. 307), the following equation is found (Eq. 13A.2): $$E[\max(V-K,0)]=\int_{K}^{\infty} (V-K)g(V)\:dV$$ Where $g(V)$ is the PDF of $V$, $K$ is a constant, and both $V,K>0$. He ...
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1answer
10 views

Show that for martingale and predictable process, it is not possible to gain almost surely in some step

Let $X_t, t = 0, 1,\ldots, T$ be a martingale and $V_t, t = 1,2,\ldots, T$ a predictable process, I want to show that for $t = 1,2,\ldots, T$ we have $$ V_t\cdot (X_t - X_{t-1}) \ge 0 \textrm{ ...
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1answer
30 views

Currency Conversion Math

Here is my question. If I have the following exchange rates: 1 Euro = 1.13 USD 1 British Pound = 1.56 USD Is it possible to calculate the value of Euros to British Pounds given that I only have ...
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0answers
22 views

Annuity formula proof $\frac{a_{\overline{n}|}}{a_{\overline{k}|}}$

I have the actuarial exam FM in 2 days and there is one more thing that I would like to understand. I cam across a problem having to do with identities and this is the following. A perpetuity ...
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1answer
41 views

Distribution of Black Scholes call option price at time 0<t <T

Does anyone know how to find the probability law (distribution) under P* of a Black Scholes Call Option price $C_t$ for $0 < t < T $? (Under P*, $ dC_t = \frac{\partial c}{\partial s}\sigma S_t ...
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0answers
33 views

Compound Interest Calculation (Years + Months)

My question is with regards to the calculation of "Compound Interest". I have the formula below where I would get an answer to the total value of the investment over a period of "years". $A$ = ...
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0answers
19 views

How to do fixed point iteration with matrices?

I am trying to follow solution to solve $$\min[\mathbf{z},\mathbf{q+Mz}]=0$$ by fixed point iteration. If $\mathbf{M=C+B}$ then a recursive algorithm with $k$ showing the iteration can be written as ...
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1answer
21 views

Maximizing the Sharpe ratio by finding the optimal weights

In calculating the Sharpe Ratio: $S = (\frac{\bar r_p - r_f}{\sigma_p})$ Where: $\bar r_p$ = Portfolio return (See below) $r_f$ = Risk free rate = 0.03 (for simplicity) $\sigma_p$ = Portfolio ...
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0answers
50 views

Why hold $Stock=(1−Delta_{put})$

You would like to be holding a protective put position on the stock of XYZ Co. to lock in a guaranteed minimum value of USD 80 at year-end. XYZ currently sells for USD 80. Over the next year, the ...
2
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1answer
26 views

how to derive the stochastic differential equation of this process

How can I derive the SDE for the vasicek model : $$r_t = 0.1 + 0.1 e^{-t} + e^{-t}\int_0 ^t e^s dB_s$$ From observation, the SDE vasicek's model is such that: $$dr_t = b(a-r_t)dt + \sigma dB_t$$ ...
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0answers
86 views

What is the name of this symbol ( ┐) and what does it mean

Sorry bout the dumb question, it's just that I'm taking a mathematical finances class and the teacher started using this symbol today but I've never seem it before, was trying to google it but don't ...
2
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1answer
84 views

Stochastic calculus book recommendation

I'm a quantitative researcher at a financial company. I have a PhD in math, but I'm an algebraist, so I only took the two required analysis courses in grad school (measure theory for the first, and I ...
2
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1answer
91 views

Calculus in Economics

A company is planning to manufacture and market a new headphone set. After conducting extensive market surveys, the research department provides the following estimates: Marginal costs function: ...
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0answers
12 views

Sample variance matlab geometric brownion motion

I have a question about the geometric Brownian motion. I want to sample many paths and then showing that the sample variance equals the exact variance: $$\mathrm{Var}\left[S(t)\right]=S_{0}^2 e^{2 \mu ...
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3answers
48 views

Financial Mathematics, Simple interest question. Help.

Laurie deposits $\$60,000$ in a bank at $5\%$ interest per annum. Andrew deposits $\$40,000$ in bank at $8\%$ per annum. How long wil it take, by simple interest, for Andrew to have more money ...
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1answer
14 views

Improper integral confusing step

The following passage is in my textbook: $$A(S) = \int_0^{\infty} f(E) \max(S-E,0)dE$$ This simplifies to $$A(S) = \int_0^{S} f(E)(S-E) dE$$ Now this is from a finance textbook so it might ...
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1answer
66 views

Lemme itô and Martingale [closed]

I want to to find values of $a$, $b$ such that the process: $$e^{W_{t}^2+at+b\int_\limits{0}^{t}W_{s}^2\,ds}$$ be a martingale Could you please help me do that Thank you
1
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0answers
23 views

Estimating compound growth

I have a compound interest function with the following parameters: Value at time 0 = 13.8 Interest rate = 0.05 time interval = 10 I need to check quickly, (without a calculator, only pen and paper) ...
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3answers
65 views

I'm trying to reverse engineer a formula to find answers without trial and error.

As an example, I need to pay €100 to this business, and there are 2 separate fees I need to also pay, the fee for the payment processor and the VAT (Value Added Tax). I know that the fee for the ...
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1answer
39 views

What is the difference between simple interest and simple discounting?

I have been given the following statements: "Simple interest: $C$ now $\equiv (1+in)C$ in $n$ years; $C$ in $n$ years $\equiv \frac{C}{1+in}$ now. Simple discounting: $C$ in $n$ years $\equiv ...