Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

learn more… | top users | synonyms

0
votes
2answers
407 views

A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual…

A farmer buys a used tractor for Rs $12000$. He pays Rs $6000$ cash and agrees to pay the balance in annual installments of Rs $500$ plus $12 \%$ interest on the unpaid amount. How much will be the ...
0
votes
2answers
11 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
votes
1answer
20 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
votes
1answer
693 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 ...
0
votes
1answer
513 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 ...
0
votes
1answer
23 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 ...
0
votes
0answers
15 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 $11$ ...
2
votes
0answers
12 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 ...
1
vote
1answer
197 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
votes
1answer
18 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
votes
1answer
9 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 ...
0
votes
2answers
20 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 ...
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
20 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 ...
0
votes
1answer
15 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 ...
0
votes
1answer
34 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 ...
0
votes
0answers
28 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
1
vote
1answer
19 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 ...
-1
votes
1answer
19 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
42 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
votes
2answers
58 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 ...
2
votes
0answers
34 views

European Call/Put Option of a jump difussion Process

Lets have the next jump difussion Stochastic Process: $$S_t = S_0 e^{\sigma W_t + (v-\frac{\sigma ^2}{2})t}\prod_{i=1}^{N_t}(1+J_i)$$ where $W_t$ is the Brownian Motion, hence $G_t \equiv e^{\sigma ...
1
vote
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 ...
0
votes
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{ ...
0
votes
1answer
25 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
votes
1answer
263 views

Determining Total Assets, Total Liabilities From a Financial Statement with Missing Values [closed]

I at a loss trying to figure out the total assets and liabilities from what is given. K-Os Corporation Beginning of year Total ...
0
votes
0answers
54 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
votes
0answers
18 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 ...
2
votes
1answer
89 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: ...
0
votes
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 ...
1
vote
0answers
29 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". $A$ = ...
0
votes
0answers
18 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 ...
0
votes
0answers
34 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
votes
1answer
25 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: $$dr_t = b(a-r_t)dt + \sigma dB_t$$ ...
3
votes
0answers
69 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 ...
1
vote
1answer
38 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
63 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 ...
1
vote
0answers
36 views

Matlab Optimization problem with Matrices

I'm trying to solve an optimization problem in Matlab. The expressions you will find below. Problem is it is all matrices, and I have no idea which solver to use for that. $w$ is of size $n \times 1$, ...
0
votes
0answers
29 views

European option and American option are equivalent in this case? [migrated]

This is Question No.11 from 2007 May MFE Exam. For a two-period binomial model for stock prices, you are given: (1) Each period is 6 months. (2) The current price for a nondividend ...
-1
votes
0answers
33 views

Pricing a zero coupon bond when the intersest rate is the Cox Ingersoll Ross (CIR) model using Green's function.

I have been trying to find the Fundamental solution of the Partial differential equation of the CIR model. \begin{equation}\ f_t (t,r) + (\alpha_1 - \alpha_2 r_t)f_r (t,r) + \dfrac{1}{2} \sigma^2 r_t ...
1
vote
3answers
46 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 ...
0
votes
0answers
11 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 ...
-1
votes
1answer
33 views

Why are $dw_1(t) dw_1(t)$=$dt$ and $dw_1(t)dw_2(t)=0$ in shreve's stochastic finance II? [closed]

Refer to http://i.stack.imgur.com/doQuT.png on example 4.6.6 How come $dw_1(t) dw_1(t)$$=$$dt$ and $dw_1(t)dw_2(t)=0$?
2
votes
1answer
248 views

How to compute ideal investment leverage ratio to maximize median return? [closed]

If I had an investment that with 50% likelihood quadruples your investment on a given day and you lose it all also with 50% likelihood, what percent of your money should you invest each day to ...
0
votes
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 ...
-1
votes
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
vote
0answers
22 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) ...
1
vote
3answers
57 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 ...
0
votes
1answer
26 views

Find probability that payoff function is in $[10,20]$

In moment $t=0$ we bought option with expiration date $T=2$. The payoff function of this option is given by: $$f=(\max_{t\in[0,T]} S_t -110)^{+}$$ where $S_t$ satisfies $$dS_t=15dW_t$$ $$S_0=95$$ ...
0
votes
1answer
161 views

Compound interest

I've watched the khan academy pre-calculus playlist about compound interest and constant e on youtube Khan Academy. First he said that you can compute the final payment like this: Let P = Principal, ...