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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2
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2answers
28 views

To mark up in retail by $20$%, do I add $0.20$ times the original cost, or divide by $0.80$?

Why is it that when I take a cost of say $\$15.60$ and want to mark the item up at retail 20% that I'm being told two different ways with two different answers? The first way (my way) would be to ...
1
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0answers
11 views

The Law of One Price in a discrete model

The following question assumes familiarity with the discrete model described in chapter 5 of Steven Roman's "Introduction to the Mathematics of Finance", 2nd edition, Springer 2012. I will not ...
0
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1answer
38 views

Recurrence relation for a mortgage

Find a recurrence relation for the amount of money outstanding on a \$40,000 mortgage after n years. The interest rate on the mortgage is 10% and the yearly payment is \$2,000( the yearly payment is ...
-4
votes
0answers
24 views

Bad and doubtful debts [on hold]

A company keeps a provision for doubtful debts of $\$1000$. At the end of the year, the required provision is $\$500$. During the year, debts of $\$1500$ are written of and $\$100$ is received in ...
0
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1answer
459 views

compound interest with geometric series

Were studying geometric sequences in maths and this came up as one of the questions: A mortgage is taken out for 150000 and is repaid annually with 20000 installments. Interest is charged on the ...
-5
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0answers
48 views

Show that for a European put on a stock which pays continuous dividends [on hold]

Proof that for a European put on a stock which pays continuous dividends, P(S,t ) = Ker(T-t)N(-d*2)-Se-q (T-t)N(-d*1). Here d*1 and d*2 are the usual d1 and d2 but with r replaced by r-q.
-2
votes
0answers
12 views

Financial Mathematics-Bond(Current Yield and Capital Gain Yield) [on hold]

Bond A is a 10-year bond with par=1000. Coupon rate =10% and interest payable semiannually. I buy Bond A today when Yield-to-maturity(YTM) is 8%. I hold the bond for one year and sold it when ...
-1
votes
0answers
36 views

American and European option [on hold]

I've been stuck on these 2 parts for a long time, can't find anything on the internet that is even the slightest bit connected to the question. Hoping someone here can provide some help. Let $C(t)$ ...
-1
votes
0answers
17 views

Isolate n in Compound Interest Formula

How would one isolate n in this comound interest formula? Another forum says that it is impossible and can only be estimated with a series but I'm wondering if anyone can confirm that or knows how. ...
0
votes
1answer
13 views

Equivalent Interest Rates

Suppose that the APR on a certain product $x$ whose dollar value is $x_1$ is 5%. Now suppose we subtract some amount $x_2$ from $x_1$ where $x_2 < x_1$. Call this new amount $y$. How does one ...
0
votes
1answer
606 views

Comparing annualised volatility from monthly and annual data

I fear there is a very simple answer to this question and its killing me that I can't see it. I am interested in calculating historical volatility: I have monthly index values starting in Jan 2005 ...
1
vote
0answers
22 views

Find the highest price which an investor can pay and still be certain of a yield of:

I'm having trouble understanding this example in Kellison's Theory of interest: Consider a 100 par value 4% bond with semiannual coupons callable at 109 on any coupon date starting 5 years after the ...
3
votes
1answer
119 views

Altering a Lease Calculation to take into account an upfront payment

I am trying to find the interest rate of a lease if we know the monthly payment amount but have an advance payment. I have found a site with part of the calculation we need (Scenario 2 on the link ...
2
votes
1answer
39 views

Is there any interpretation to the imaginary component obtained when computing the geometric mean of a series of negative returns?

When computing returns in finance geometric means are used because the return time series of a financial asset is a geometric series: $\mu_r = \sqrt[T]{\prod_{t=1}^T r_t}$ where the return is computed ...
2
votes
4answers
13k views

Most efficient method for converting flat rate interest to APR.

A while ago, a rather sneaky car salesman tried to sell me a car financing deal, advertising an 'incredibly low' annual interest rate of 1.5%. What he later revealed that this was the 'flat rate' ...
1
vote
1answer
28 views

Properties of brownian motion

I was doing some revision and had an admittedly elementary question. My lecture notes say, the following are properties of Brownian Motion {$B_t$} (Normal or Gaussian increments) For all $s < t, ...
1
vote
0answers
86 views

Expected value of multiplied and squared Wiener Process

Can someone help me how to calculate the following: $E0[z^2[2] \mathrm{Exp}[-2 z[2]] ]$ Where $z[2]$ is Wiener process. How to find exact expected value? I am new to this stuff and not sure how to ...
1
vote
1answer
20 views

Savings account interest rate

Just a brief question regarding bank interest rates, my apologies if this is a duplicate, I did a quick search but came up with no results relating to my question, surprisingly. Also, please excuse ...
-2
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0answers
21 views

prove why expected utility better than expected value in terms of unlimited value of expected

Why expected utility is better than expected value? i was asked by my supervisor to prove that expected utility is needed in mixed strategy and i need to prove it's better than expected value. i have ...
1
vote
1answer
1k 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 ...
0
votes
1answer
36 views

Continuous Annuity Question

I need to calculate the present value of a level continuous annuity which pays $1000/mo. for 10 years. The force of interest is 5/(3+2t). I tried taking the integral of e^(integral of force of ...
0
votes
0answers
26 views

Method for finding a arbitrage opportunity when market price of call is incorrect

The solution of the Black-scholes equation is the price of a European call. And the option price assumes the underlying stock is a geometric Brownian motion with volatility $\sigma_{1}>0$. ...
0
votes
2answers
36 views

How to find the actual doubling time with the rule of 72.

I have a programming assignment in C# from my professor that involves the Rule of 72. He clearly says that in order to find the amount of time in years it will take for an amount to double, you have ...
1
vote
3answers
26 views

Finding the probability of loss from standard deviation in normal distribution

I am unsure how to approach the following question. The returns from a project are normally distributed with a mean of \$220,000 and a standard deviation of \$160,000. If the project loses more than ...
-3
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0answers
60 views

Price of derivative contract with payoff at time $2$ or $S_2/S_1?$

What is the price of a derivative contract with payoff $X_2=S_2/S_1?$ The question requires price $V_t$ for when $0 < t < 1$ and $1<t<2$? Really can't get my head around this, any help ...
0
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1answer
34 views

How to calculate inverse of Variance Gamma call price formula using Newton-Raphson search

The Variance Gamma call price formula is given by: $$C(0)= \int\gamma(R) e^{-rT} \int f\left(S(0) e^{\theta R+\omega T+\frac12 \sigma^2 R} e^{rT-\frac12 \sigma^2 R+\sqrt{T}\sqrt{R/T} \sigma ...
0
votes
1answer
35 views

Factorals with exponents. Is their a way?

I know of multiplication factorials with the 4! = 4*3*2*1 and I know of the addition with the nth triangle. I am busy deriving my own equation for something, and i am getting stuck on how to furthur ...
0
votes
0answers
27 views

Gaussian distribution finite population with unknown cardinality

I have taken a sample population of a population with unknown size. The sample size is 54 trades. The sample mean is 2.1% (1.021) return per trade. The sample standard deviation is 0.01. 100% of ...
0
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0answers
28 views

Optimization of stochastic differential equations

Is there a way to optimize or maximize a set of differential equations. such that each equation is represented by a time series S_((t+1),μ) = μ*(S_(t+1)-S_t) + S_t and μ = 2/(i+1), i=1,...,n. Then I ...
2
votes
1answer
38 views

Market Making Card Bet Game

In an interview I received the follow question: We have 3 cards face down, and we give each card in a deck of 52 a numeric score ( A = 1, 2=2, .... , J=11, Q=12, K = 13). The interviewer asked me to ...
3
votes
3answers
53 views

Rule of 72 doubling time

I need some help understanding this. So as far as I can tell. The rule of 72 is used to determine when prices will double in years. This is done by 72 divided by the rate, or interest. So it would ...
0
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0answers
52 views

Estimating the value of a stock

I need a way to know the value of my stock. Let $(x_1, \dots, x_n)$ be the quantity of the products $1$ to $n$ I have in stock, such that, for example, if I have $8$ units of the product $2$, $x_2 = ...
0
votes
2answers
43 views

Loan and annuity (prospective methods)

The question is a loan of $10,000 is to be repaid over 10 years by level annual repayment of capital and interest. The interest rate to be charged on the capital outstanding will be 6% per annum for ...
0
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0answers
20 views

Spectral Analysis: How to interpret a periodogram.

I'm reading a paper that has to do with financial volatility. The author uses a periodogram to estimate the power spectrum density of the volatility time-series. Evidently, the plot (below) is ...
0
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0answers
31 views

Calculate the Value at Risk

Let's have the following example: We have two independent investments. Each of them have: a 94% chance of a profit of 1 million a 3% chance of a loss of 1 million a 2% chance of a loss of 5 million ...
1
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0answers
24 views

Simple Interest Problem Ambiguity in Conventions

I am solving some simple interest problems. Following questions are creating ambiguity with conventions, hope someone will clarify what is going on. In what time does sum of money become 4 times ...
2
votes
1answer
56 views

Book Recommendation for mathematical finance

Does anyone know a book which covers topics on: Brownian Motion Martingales Stochastic Calculus Stochastic Differential Equations Options pricing. Black-Scholes model Fundamental Theorems. ...
0
votes
1answer
27 views

Having trouble solving this Exam FM problem with zero coupon bonds.

You have two 4-year annual-coupon bonds, each one of them has a face value of 8000 and a redemption value of 8000. The coupon rate of first bond is 7% and its price is 7908.57, while the second has ...
0
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1answer
40 views

Annuity present value formula explanation

Could somene please explain me how the formula evolves, ie. how does the fraction flip, etc? Thank you in advance!
0
votes
2answers
108 views

Geometric progression in annuity

I am working on the following problem that involves annuity which deposits form a geometric progression. Stan elects to receive his retirement benefit over $20$ years at the rate of $2,000$ per ...
0
votes
4answers
383 views

Why do Fibonacci numbers appear in stock market tick charts? [closed]

I've been reading about stocks trading and noticed Fibonacci numbers are preferred as the time frames for tick charts. I was immediately very curious about why that happens. Does anyone know? Thanks! ...
1
vote
1answer
108 views

Tangent portfolio weights without short sales?

Consider a mean-variance investor in a world with a risk-free asset. Let $R_f>0$ be the return of the risk-free asset, $\mathbb{E}(R_i)>R_f$ the expected return of the risky asset $i$ and ...
1
vote
0answers
15 views

How to analytically find these rounding issues

Let's say we have a fixed yearly amount that we have to divide equally among an amount of days. For instance for $1,600 we may have: ...
1
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0answers
23 views

Negative option value

I have an exercise where I need to replicate the following graph: with my own parameters. To do this I use: $\begin{align*} \text{Call option value} =SN(d_1)-Ee^{-r(T-t)}N(d_2) \end{align*}$ ...
0
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0answers
11 views

Weighted Std Deviation of Securities

Corporate Finance problem - can't figure out if I'm right or not but here goes: Probability 15% 35% 20% 30% Security A 8% 5% -4% -6% I need to find mean and std deviation for security A. I got: ...
0
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1answer
30 views

Can't Get Present Value Answer?

I've done this problem at least 20 times a number of different ways, but I can't seem to get the correct answer. Please show all work and describe the EXACT formula you used: Find the present value ...
1
vote
0answers
18 views

Financial Mathematics Question - How to approach?

I know the answer, but I'm not sure how to 'approach' the question the right way. The question is "Katarina would like to buy a house in 4.5 years time and requires a deposit of $40000. What ...
2
votes
1answer
32 views

Simple vs compound interest rates and Taylor expansion

I am having trouble deciphering a portion from my finance text. Let $i = \text{interest rate}$, $n = \text{Some arbitrary time period}$ and $C = \text{Cash invested}$ And also $C(1+i)^n$ ...
2
votes
0answers
38 views

Reformulate this PDE in different notation

I would like to rewrite this general PDE \begin{equation} \alpha\partial_tu+\beta\partial_xu+\gamma\partial_{xx}u+\delta u=\varepsilon \end{equation} in this form $$c\left(x,t,u,\frac{\partial ...
0
votes
1answer
43 views

What to read after Shreve's “Stochastic calculus for finance 2”?

I am finishing the last pages of Shreve's Stochastic calculus for finance 2, and I was wondering what would be the best book to follow. I would like to go on with a book introducing more technical ...