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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2answers
61 views

Future Value of Annuity Compounded Daily?

(a) What is the future value of $4$ payments of $\$300$ made at the end of each year with interest rate being $11\%$ p.a. compounded daily? I did $300 (1 + 0.11/365)^{365}\cdot 4 -1)/0.11/365 = ...
0
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0answers
24 views

Exact solution to nonlinear backward SDE

I have read a paper about numerical SDE. After deriving the method, it uses the method to calculate the following nonlinear cases: $$\begin{cases} dX_t=ud\tau+\sigma ...
1
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0answers
26 views

Annunity calculation with and without tax

I'm doing a annunity calculation: payment = 331880*( 0,002458333 /( 1-(1+0,002458333)^-84) ) This will return me the payment per. month of the loan ...
0
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0answers
24 views

Cumulative Return between two dates

I have a table that carries data with cumulative return of some instrument. Data is described with start date, end date and cumulative return for date range (start-end): ...
0
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1answer
41 views

Black-Scholes: solve for $\sigma$ given $d_1$ and $d_2$

Black Scholes valuation for european call option is: $$C_0=S_0N(d_1)-Xe^{-rT}N(d_2)$$ where $d_1=\dfrac{\ln(\frac{S_0}{x})+(r+{\sigma^2\over2})T}{\sigma\sqrt{T}}$ and ...
1
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5answers
63 views

Continuously Compounded Interest

What exactly does it mean? By continuously compounded it makes me think it is almost like multiplied as time goes on. Could someone also explain what the constant e is and how it originated? Also how ...
3
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1answer
64 views

What's the purpose of this unknown (financial) math formula?

I am maintaining an old piece of financial software. In the source code I have found an implementation of the following formula: $$p2 \over (p1 + 1) - (p1 * p2)$$ The formula is used as part of some ...
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0answers
10 views

Calculation the affect of inflation on investments

Does inflation affect how you calculate interest in a term deposit, appreciation of collectibles and depreciation of a motor vehicle?
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1answer
46 views

Calculate payoff time for PV system

I want to calculate the payoff time for a photovoltaic system. Some constants: Current electricity price per kWh: 0,122 EUR Electricity production per yearh: 4427 kWh Annual electricity price ...
1
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0answers
33 views

Looking for a Formula for ROI, couldn't get an answer in Finance

This is honestly a pretty simple problem, but for whatever reason I am not able to pull it all together. I was talking theoretically with a friend and neither of us can nail down the maths so I coming ...
0
votes
1answer
65 views

Rate of Return / Standard Deviation / Correlation Coefficient - Mathematical Finance

Consider these two stocks: AT&T Inc. (T) and Verizon Communications Inc. (VZ). Use the daily adjusted closing prices from March 1, 2015 to August 12, 2015 as historical data. Estimate the mean ...
0
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0answers
67 views

Ito's Lemma / Expected Value / Variance - Mathematical Finance

Assume an asset price $S_t$ follows the geometric Brownian motion $$\Bbb dS_t = \mu S_t\Bbb dt + \sigma S_t\Bbb dWt,$$ where $\mu$ and $\sigma$ are constants and $r$ is the risk-free rate. ...
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1answer
41 views

Rearrange and solve for $N: 16 = \frac{1}{n}\cdot 25 + \frac{n-1}{n} \cdot 218.75$

I need to solve for $N$ to get $16$ with the following formula, I'm very bad a re-arranging though, so does anyone have an answer to this? $$16 = \frac 1 n \cdot 25 + \frac{n-1} n \cdot218.75$$ ...
2
votes
3answers
179 views

A double call option problem

A $(K_1, t_1, K_2, t_2)$ double call option is one that can be exercised either at time $t_1$ with strike price $K_1$ or at time $t_2$ ($t_2 > t_1$) with strike price $K_2$. Argue that you would ...
2
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0answers
84 views

Linear combination of Geometric Brownian Motions

Let $X_t= e^{\left(\mu-\sigma^2/2 \right)t+\sigma W_t}$ be a geometric Brownian motion with drift $\mu$ and volatility $\sigma$. I am trying to derive an analytical solution to $$\mathbb{E}\left[ ...
0
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1answer
57 views

How to calculate interest rate given cash flows and period in days instead of years.

I am presented with an investment opportunity where I am given #481,000 on day 1. Thereafter, every 10 days, I am required to give back #50,000 every for 100 days (10 * 50000 = 500000). How do I ...
1
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2answers
86 views

For what fixed interest rates is a certain single-period, finite-state market arbitrage free?

A single period market with three states of nature $\omega_1$, $\omega_2$ and $\omega_3$ is given, in which a single asset is available, namely a stock that is worth $8$ units today, and whose payoff ...
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3answers
38 views

Interest Question [closed]

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 ...
1
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1answer
41 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 ...
1
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1answer
27 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 ...
0
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0answers
28 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 ...
0
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2answers
48 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.
0
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0answers
17 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
100 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 ...
0
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1answer
98 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
28 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 ...
4
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0answers
65 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 ...
1
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0answers
100 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 ...
0
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1answer
36 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 ...
0
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2answers
56 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 ...
0
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0answers
36 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 $11$ ...
0
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1answer
31 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
56 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 ...
0
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1answer
29 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 ...
1
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2answers
221 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 ...
0
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1answer
72 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
39 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 ...
1
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1answer
238 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 ...
0
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1answer
37 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
votes
0answers
22 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 ...
0
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0answers
41 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
76 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
44 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 ...
2
votes
3answers
56 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 ...
0
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2answers
99 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
40 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 ...
0
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1answer
20 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{ ...
0
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1answer
86 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 ...
0
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1answer
77 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 ...
0
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1answer
66 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 ...