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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74 views

Theory of Interest - Going from discount rate - annual effective and nominal to force of interest

[![Force of Interest & Discount Rate][1]][1] Hi there guys, I'm new to Theory of Interest and I might have started studying a bit too late, but I really need to just grasp this before the end of ...
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0answers
15 views

Proving implications of equations

I'm currently working on the finance problem: If we define $I_k$ = A(k)-A(k-1) then $\sum_{k=1}^n I_k$ = A(n) - A(0) show that this implies $\sum_{k=1}^n i_ka(k-1)$ = a(k)-1 So I know that our top ...
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1answer
23 views

Finance and effective interest rate

I'm trying to solve a finance question, and am getting slightly confused. The question is as follows: On Jan. 1st, 2000, 3500 dollars is deposited into a bank account. On Jan. 1st 2005, 4000 dollars ...
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3answers
46 views

What is the Future Value of a $\$5{,}000$ loan paid back at $\$1{,}000$ per month, with a $6\%$ nominal interest rate?

I'm trying to figure out a problem with the formulae I have, but I'm having some difficulty. The problem is: Susan borrows $5{,}000$ dollars from a finance company at a nominal interest rate of $6.6\%...
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0answers
24 views

Coupon Bond Pricing and YTM Question

We started working on this problem, and we got $\frac{-c+\sqrt{c^2+4p}}{2}-1$ for part b. However, the solution that was given to us in class was $r = 1-\frac{\sqrt{4+c}}2$. We don't know where we are ...
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2answers
35 views

Exchange rate conversion

If the EUR/USD exchangerate fell by -0,96%, how much has the USD/EUR exchange rate increased? According to the below charts the number would be +0,97% (currently) but I cant figure out how these ...
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1answer
111 views

History of the power series for $e^x$ and compound interest

As discussed in How did Bernoulli approximate $e$?, Bernoulli showed that $2\frac{1}{2} < e < 3$ in this paper: https://books.google.com/books?id=s4pw4GyHTRcC&pg=PA222#v=onepage&q&f=...
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0answers
25 views

Forward contract pricing

A stock $S$ with price $S(t)$ at time t pays dividend of $D$ dollars at time $T$. Suppose that to borrow it until time $T$ from a broker you have to pay at time T a borrowing rate of $b$ of the final ...
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0answers
33 views

lognormal and expected stock prices?

Suppose that S is a stock that is lognormally distributed and that S satisfies the following: • S(0) = 22. • The expected price of the stock in 16 months is E∗(S(4/3) = 24. • The volatility of S is ...
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0answers
21 views

Determine Var[Y(3)/Y(1)]? Fin Math

Let Y (t) = 2e^(0.07t+0.5z˜(t)) Determine Var(Y(3)/Y(1)) under the risk free measure. So I found E*(Y(3)), E*(Y(1)), E*(y^2(3)), and E*(y^2(1)) and divided and subtracted, ect, for variance and got ...
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0answers
28 views

Mathematics of portfolio rebaance

I would suspect that a financial maths book would introduce the following, but I am only a novice and so would cherish your recommendations. The following is motivated by pp 304-305, ETFs for ...
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1answer
32 views

Aggregating exponential growth rates

I'm working on a simple forecast model that uses Cumulative Annual Growth Rate (CAGR) to project future growth, and I've run into an apparent paradox. The model includes multiple lines of business ...
2
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1answer
41 views

Pricing a Europen style put option

So I'm enrolled in a Mathematics for Finance course, and we received this question on the last Problem Set. I'm completely stuck on how to solve this problem. I tried applying the formula xS(t) + yA(t)...
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1answer
23 views

Proove the approximation for risk premium

Exercise comes from Bowers' "Actuarial Mathematics". I'm self-studying and have virtually no clue how to approach it. We make no assumptions about either utility function or distribution of X. Let $w$...
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1answer
42 views

Simple discounting rate question and finding unknown time:

The thing is to solve for n. This is how far I got: $FV=PV(1-d)^{-t}$ So, $1000(1-0.05)^{-10} + 2000(1-0.05)^{-5}= 1000(1-0.1)^{-(10-n)}+2000(1-0.1)^{-(10-2n)}$ $\Longrightarrow\;\; 2584.71=1000(0....
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2answers
57 views

Is there a more rigorous way to show the expected price of a stock?

I am studying for the Society of Actuaries' Financial Math exam and I found the solution to this practice problem to be not convincing enough: Is there a more mathematical / rigorous way of showing ...
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1answer
75 views

How to construct a linear demand equation? and obtain the weekly revenue

Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center, but are not sure how much to ...
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1answer
21 views

Continuous Sigma-martingales and local martingales are equivalent sometimes?

I was reading through this paper, and they mentioned in the beginning-most portion of it that $\sigma$-martingales and local-martingales are equivalent if they are continuous. Why must they be ...
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1answer
35 views

Currency conversion using available rates

I have the following rates available: USD -> USD = 1 USD -> EUR = 0.887662 USD -> GBP = 0.654514 I want to calculate the following rates ...
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1answer
23 views

Clarification on the set-up of this interest theory problem

The following problem and solution is taken from an actuarial exam (financial math) study manual: I would set this problem up completely different. I think it would be necessary to consider the ...
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1answer
47 views

Isolate Costs in NPV equation

Hey can anyone help with this? This is the classic NPV equation: NPV = -CapEx + ∑ (Revenue − Costs) / (1+Discount)^i The partial sum is from i = 0 to n years. For my purposes all the elements ...
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1answer
31 views

A credit model. Default time.

In a paper, I find the following situation: Let $(\Omega,\mathcal{G},\mathbb{Q})$ be a probability space. $\mathbb{Q}$ is supposed to be a risk neutral measure. Suppose that $\left(\mathcal{F}_t\...
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2answers
123 views

Geometric progression (compound interest)

"A man, who started work in 1990, planned an investment for his retirement in 2030 in the following way. On the first day of each year, from 1990 to 2029 inclusive, he is to place £100 in an ...
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0answers
29 views

In an incomplete market does every payoff function admit at least two arbitrage-free pricings?

Consider an arbitrage-free (not necessarily complete) market. Prove or disprove the following assertion. If the market is incomplete, then every payoff function $A : \Omega \rightarrow \mathbb{R}$ ...
2
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1answer
39 views

Clarification on a collared stock being equivalent to a bull spread?

The following is a question on financial math from the financial math actuarial exam: Earlier in the manual, the author stated that a collared stock is equivalent to a bull spread. Therefore, in ...
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1answer
147 views

What equal installment of annual payment will discharge a debt which is due as 848 at the end of 4 years at 4% per annum simple interest?

What equal installment of annual payment will discharge a debt which is due as Rs. 848 at the end of 4 years at 4% per annum simple interest? The above question can be calculated by using the ...
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2answers
31 views

Bank interest but reversed problem - how much was the first money deposited?

Suppose I have money ($x$) in a bank account bank with compound interest of $5\%$ annually paid monthly. Bank gives me $20,000$ usd a month and the money $x$ finishes in $20$ years ($240$ months). How ...
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0answers
41 views

Are these Finance-related calculations correctly solved?

1)A car costs R130 000 is advertised:'no deposit necessary and first payment due three month after date of purchase'.The interest rate is 18% p.a compounded monthly. 1.1)Calculate the amount owing ...
0
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1answer
68 views

Quick Finance Question?

I have just signed a lease that requires me to repay $100,000 over 10 years with payments starting today. What is my annual repayment if the effective interest rate is 7% p.a.? I did (100000)/(1-(1/...
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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 = $...
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0answers
25 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 dW_t,\\X_0=X_0,\\dY(t)=\big(rY_t+\...
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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 (4.337,...
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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
42 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 $d_2=\dfrac{\ln(\frac{S_0}{x})...
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5answers
70 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
65 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 ...
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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 ...
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1answer
66 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 ...
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0answers
70 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
42 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
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3answers
183 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
90 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[ \...
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1answer
58 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 ...
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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 $$A=55000(1+.064/...
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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 ...
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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 ...
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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 ...