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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3
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80 views

How to get interest in the mathematics of tax

In a similar vein to my previous thread, I will also be teaching about the mathematics behind taxation - to a lot of people, this is very mundane - but that is not true of everyone. The practicality ...
3
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133 views

Algorithm/Formula to compute adding and/or removing compound and/or non-compound percentages from a value?

I will first start with a scenario, I have to apply some adjustments to a particular value. These adjustments are either compound or non-compounded and they can either be added or subtracted to the ...
2
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76 views

Engineering Economics Cash Flow Diagram

I have the following question and solution below. What I don't understand is why is the 100,000 seen as savings/revenue when clearly it is coming out of pocket? Additionally, the monthly loan payment ...
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63 views

What does it mean to “pass to the limit” in mathematics?

I've been reading a finance paper and stumbled upon this phrase. What does passing to the limit mean in this context (or overall in mathematics)? Here is an excerpt from the paper: It is ...
2
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38 views

Reinvesting the interest (generalized version)

If I deposit \$1 at $t=0$ into an account which credits interest at the end of each year at a force of interest $\delta_t$ (assume it's integrable.) Then, if I reinvest the interest at an annual ...
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34 views

Stochastic control, numerical, need expectations given coupled SDEs

I'm looking at a trio of processes which arises in a stochastic control situation. I have a process $(V_t)$ which I may control, and $(V_t)$ influences a diffusive stock price process $(S_t)$. The ...
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16 views

financial mathematics: n financial assets in p states of the world.

Suppose there are two dates, $0$ and $1$. Suppose the world will be in one of $p$ states at date $1$, but the true state of the world at date $1$ is unknown at date $0$. Let there be $n$ financial ...
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21 views

Expected value of multiplied and squared Wiener Process

May someone help me how to calculate the following thing: E0[z^2[2] Exp[-2 z[2]] ] Where z[2] is Wiener process. How to find exact expected value? I am new to this stuff, not sure how to do this. ...
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28 views

Why does the price term in Vega disappear for a European call option?

In my course, I have been asked to prove a number of statements about "the Greeks" from the Black-Scholes model for pricing a European call option with no dividends and a strike price of $K$. One of ...
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21 views

On finance problem: saving money

First of all, sorry for my pour English. Consider the situation: I'd like to save an amount $P$ of money every month for $240$ months consecutively ($m_1,\ldots,m_{240}$). The gain with money is ...
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6 views

Partial differential of sharpe ratio of a portfolio with n ( =4 )equities with respect to the allocation for each equity.

Sharpe ratio is the mean of the daily returns from the portfolio divided (minus a constant )by the standard deviation of the return from the portfolio. Daily return of the portfolio is calculated by ...
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66 views

What do two number on top of each other in square brackets mean?

Im currently going through "Universal Portfolios with Side Information" by Cover and Ordentlich [96]. Near the end of the paper, they provide a formula for calculating weights of a Universal Portfolio ...
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45 views

Need help with partial derivatives

So here's the question: The monthly payment $P$ on a mortgage loan of $A$ dollars at an APR of $r$ (as a decimal) for $t$ years is given by this formula. $$P(A,r,t)$= ...
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0answers
24 views

How to sum correlation, or, calculate correlation of disjointed variables

I'm trying to calculate the correlation of 2 array of variables, but the array is disjointed in the middle - but I'm trying to obtain one correlation coefficient See the excel file I uploaded: ...
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0answers
19 views

Average Interest Payment For Specific Period of Ammortization Schedule

I would like to derive an equation that calculates the average interest payment x for an amortized mortgage loan in the first m ...
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0answers
108 views

Compound annual growth rate for negative values

How to compute a compound growth rate when some values are zero or negative? Example 1: A company has 0 money in first year, 5 money in second year and -2 money in third year. All previous year ...
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32 views

Financial mathematics 2

I've been given the following information: MR bob borrows 50000 now and promises to repay it in monthly installments over the next eight years. Interest is compounded monthly at 18% per year. ...
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0answers
18 views

How to find sigma-algebra over omega3 generated by the log-return ln(S2/S1) and ln(S3/S2)?

I calculated {S2/S1} = {u, u*u/d, d, d*d/u}, and then get ln(S2/S1)= {ln(u),ln(u*u/d), ln(d),ln( d*d/u)}. I am not sure my way of doing this question is right, because i m confuse about how to get ...
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172 views

Calculate sell(sales) price from margin and cost price

Slight finance question, trying to program the calculation of sell price when we have %margin and cost price. ((CostPrice / ((1 - %Margin) / 100)) * 100) / 100 ...
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183 views

Notation in Financial Math

I am very close to showing part b of this question and think that the reason my solution doesn't match up is because I don't understand a piece of notation.The notation I don't understand is ...
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23 views

The impact of jump on the returns of portfolio and asset pricing

There exsits jumps in financial market. What will be the impact of jump on the returns of portfolio and asset pricing? Please explain it both academically and plainly. If you can give some excellent ...
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0answers
16 views

What is a rolling par-swap?

I am trying to understand the hedging strategy mentioned in the paper below on p.17 (set of rolling par-swaps). Can anyone explain how this works? Moreover, if anyone is familiar with this paper, ...
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0answers
40 views

Programming in R: How do I switch the X and Y axes?

I have a distribution plot of the daily drawdowns of the Dow Jones Industrial Average index; however, it has the drawdowns on the y-axis and the frequency on the x-axis... I'd like to switch that so ...
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62 views

Doob Decomposition of American Option

I am trying to figure out the Doob decomposition of an American put option in a discrete time binomial model. I know how to price the American put, but I'm having trouble expressing it as the sum of ...
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0answers
57 views

Interest % and final payment

I dont get these two questions? How should I calculate the answer? A) Sam intends to retire in 6 yrs. To supplement his pension he would like to receive $\$234$ every 2 weeks for 10 yrs. If he is ...
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0answers
258 views

Analogue of Leibniz Rule for Stochastic Integrals

Suppose $$f(t,u)=f(0,u)+\int_0^t{\mu (w,u)dw}+\int_0^t{\sigma(w,u)dB_w}$$, where $B_w$ is a standard Brownian motion. I would like to calculus the drift and diffusion of $Y_t=-\int_t^s{f(t,u)du}$ ...
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92 views

Uniform convergence of series with utility function

Let $u(x)$ be a real function with the properties $u(x)$ is continuous and non-decreasing in $x$ $u'(x)$ is non-increasing in $x$ $u(0)=0$ $u'(0)=1$. In other words, $u(x)$ is a utility function. ...
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88 views

Compactness of the set of densities of equivalent martingale measures

Consider an incomplete market $(\Omega,\mathcal F,\mathbb P)$ driven by a semimartingale $S=(S_t)_{t\in[0,T]}$. Under the no free lunch under vanishing risk (NFLVR) assumption, the set $\mathcal ...
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0answers
81 views

Good reference on sample autocorrelation?

I'm not a statistician but I'm writing my thesis on mathematical finance and I think it would be neat to have a short section about independence of stock returns. I need to get better understanding ...
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0answers
27 views

Standard practice for identifying outlying spend amounts

Hope this is mathematical enough to qualify as a question - I'm no mathematician! I have a set of individuals travel & entertainment credit card spend, and I'd like to highlight any outliers that ...
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0answers
76 views

Portfolio optimization - problem with a proof

I'm trying to proof Proposition 1 in this Paper about Markowitz Portfolio Opitimization on page 6/7 but I can't figure out how to do this. The author wrote "The proof of Proposition 1 can be found ...
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340 views

Reading advice: Mathematical finance for a student of pure mathematics

Which books/lecture notes should a student with a background in pure mathematics (in my case it was geared towards algebraic geometry) read in order to do financial math? I have done one basic course ...
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150 views

Immunization and Sensitivity Analysis

Frequently a company wants to match its assets and liabilities. However, perfect matching is not practical due to fluctuations in interest rates. So they hedge their risk using immunization. This can ...
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139 views

Dividend Discount Model

The current price of a stock can be modeled by $P_0 = \frac{D_{1}}{r-g}$ where $D_1$ is the expected dividend, $r$ is the rate of return, and $g$ is the expected growth rate in the perpetuity. If ...
0
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0answers
29 views

Second Fundamental Theorem of Asset Pricing

It seems that there is a step missing in the proof of the second Fundamental Theorem of Asset Pricing in Shreve's Stochastic Calculus for Finance II: Does anyone know how to show the following: If ...
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0answers
16 views

Proposition from Oksendal Stochastic Calculus

I am reading Oksendal's Malliavin Calculus with applications to Finance and there is a part that I do not understand. First we have a proposition which is fine: If $\zeta_1$,$\zeta_2$,... are ...
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0answers
15 views

Financial Mathematics - Security Market Line and CAPM

not sure if this is the correct place to be posting this but I couldn't find a relevant stack exchange site (albeit this is part of my financial mathematics university course.) I have to write a ...
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0answers
22 views

Application of Ito's formula

I recently learned about Ito's formula and integral and now i have to do the following exercise, but I actually don't really know, how to start: Apply Ito's formula to prove that $$Z_t=exp(\sigma ...
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34 views

Black-Scholes derivation assumption contradiction

In many books and derivations of the Black-Scholes PDE one sees that $$\Pi=V-\Delta F \Rightarrow d\Pi=dV-\Delta dF$$ which implicitly assumes that $d\Delta=0$. Somewhere down the road one then ...
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18 views

Calculate breakeven point for business

I have a question with which I am somewhat stuck. Specifically I need to calculate the break-even figure for the following scenario. Peter is a business consultant. As well as providing ...
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0answers
11 views

Parameter estimation using characteristic function

Is it possible to do parameter fitting using log-returns data & the characteristic function(CF) in Matlab? I have been trying it on the Variance Gamma Scaled Self-Decompasable (VGSSD) model CF for ...
0
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0answers
33 views

Girsanov's theorem and simulation of bond prices

Assume that we want to calculate the time $t=0$ price of a bond: $B(0,T) = E_P[\exp(-\int_0^T r_s ds)]$, where $r$ is the interest rate following the SDE $dr_t=k(\theta-r_t)dt+\sigma ...
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0answers
7 views

Quantitative Finance/Financial Mathematics - What are the areas of research?

I've just finished my first year of a quantitative finance course. It was hard going but I got there in the end! More to do with the fact that I haven't got much of a background in maths though ;) ...
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0answers
5 views

Tangency portfolio in multiple periods model (Finance)

This might be a bit specific, but i'm stuck at this "little" problem. I've got a little problem now that i'm writing my BA thesis in dynamic asset allocation. It might be a very specific question, but ...
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0answers
25 views

Put-Call-Parity of Asian Options

I could need some help with deriving the put-call-parity for asian options. Let $S_t$ be the price of the underlying asset at time $t$ and set $Y_t = \int_0^t S_t dt$. Then the payoff of an asian ...
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0answers
10 views

dividend payout ratio??

Laurel company expects $3.81 earnings per share, has a 30% retention rate which is constant. It's equity cost of capital is 9%, which is also its expected return on new investment. Its earning are ...
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0answers
12 views

How can I show that $u=e^{\sigma\sqrt{\Delta t}}$ in the binomial option pricing model

Given that $e^{r\Delta t}(u+d)-ud-e^{2r\Delta t} = \sigma^2\Delta t$ I would like to show that $u=e^{\sigma\sqrt{\Delta t}}$ I know I must somehow use Taylor's approximation $e^x = 1 + x + ...
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0answers
25 views

Corporate Finance Problem

A recent college graduate has taken a new job at Work LLC and since the company does not offer a traditional pension plan, she plans to take advantage of a tax-free investment account backed by a ...
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0answers
8 views

How to solve for maturity and interest when only given future borrowing & annual debt service

Consider this example: Debt Issued in 2015: 250,000 Projected Annual Debt Service due to Future Borrowings: 16,441 Debt Issued in 2016: 270,000 Projected Annual Debt Service due to Future ...
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0answers
20 views

What is the present value of the annuity?

The effective annual interest rate is 3%. A perpetuity pays $3000 at the end of the first year and the payments are increasing 5% each year for the first 10 years. From then on, the payments remain ...