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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89 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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151 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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113 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 ...
2
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0answers
98 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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40 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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37 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 ...
2
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73 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
25 views

Markov property question

In every book I can find, the Markov property for ito diffusions, $E[f(X_{t+h})\mid F_s] = E^{X_t}f(X_h)$ is stated for $\textbf{bounded}$ Borel functions. However, I have the following statement ...
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23 views

Locate proof of Second Fundamental Theorem of Asset Pricing

Where can I find a $\textbf{rigorous}$ proof of the Second Fundamental Theorem of Asset Pricing. That is, A market is complete if and only if it has a unique risk neutral measure. Please do not ...
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27 views

Intuition behind American option pricing

The price of an American option is given by $V_n = \max\{G_n, \frac{1}{1 + r}(pV_{n +1}(H) + qV_{n + 1}(T)\}$, where $p$, $q$ are the risk neutral probabilities. I have two questions. How can ...
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56 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 ...
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25 views

Matlab Optimization problem with Matrices

I'm trying to solve an optimization problem in Matlab. The equations 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 x 1) mu_BL (1 ...
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13 views

Finding the continuity of the mapping of a solution to a PDE to its partial derivative

Here is a modified version of the Black-Scholes PDE: $\frac{\partial \phi(t,S,i)}{\partial t}$ + $r_iS\frac{\partial \phi(t,S,i)}{\partial S}$ + $\frac{1}{2} \sigma^2_i S^2 \frac{\partial^2 ...
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0answers
42 views

Calculating VaR, CVaR

I am supposed to calculate the value at risk and expected shortfall of an asset with revenue given by a density function: $f(x)=0.5\exp{(-|x-0.05|)}$. My workings: If I understand it correctly, than ...
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0answers
37 views

Construct an arbitrage opportunity in a multi-period model

I am currently revising for my exam in Financial Mathematics, and I could not solve this question: For $T > 1$, consider a $T$-period model with a single risky asset and a bank account which pays ...
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0answers
53 views

Show that the risk-neutral probability of a European call option ending in money is N(d2)

Show that the risk-neutral probability of a European call option ending in money is N(d2). I was trying to using Risk-Neutral Valuation Formula, but how to show the result is N(d2)? Thanks
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0answers
23 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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41 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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35 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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0answers
34 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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17 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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196 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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54 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
26 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
23 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
151 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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0answers
91 views

Intensity Function of Stochastic process`

I'm fitting some financial data to a model based on a stochastic process and evaluating the fit of it by looking at the compensator. However, I cannot understand well what does it mean to take the ...
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0answers
37 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
32 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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0answers
249 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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0answers
215 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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24 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
18 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
44 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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0answers
59 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
311 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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94 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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0answers
95 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
83 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
78 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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0answers
399 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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0answers
162 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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0answers
145 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 ...
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0answers
17 views

compounding interest annuity

In the following ordinary annuity, interest is compounded with each payment, and the interest is made at the compounding period. An IRA earns tax deferred interest. Tim and Karen both make deposits ...
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25 views

Solving Black scholes PDE using Laplace transform

I'm trying to obtain the Laplace transform of Call option price with repect to time to maturity under the CEV process. The well known Black scholes PDE is given by $$ ...
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0answers
47 views

numerical method (Implicit) for nonlinear pde

$\newcommand{\lbar}{\underline{\lambda}}$ I need a numerical method (implicit , backward difference or forward difference) for estimate $A$ in this nonlinear PDE: $$ A_t + \mu(\lambda -\lbar ) ...
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0answers
30 views

Reverse Engineer Math(financial) Answer.

I'm starting to question the Payment amount generated by the software my lender is using, but it could be my calculations that are wrong. I would like confirmation before I proceed. Is my approach ...
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0answers
10 views

Confused about Effective Rate of Discount and Effective rate of Interest - Theory of Interst

Question: If $A(0)=500$ and $A(1)=525$, find $i_1$ and $d_1$. From what I understand the equation for $i_n$ is $i_n = \frac{a(n) - a(n-1)}{a(n-1)}$ and the equation for $d_n$ is $d_n = \frac{a(n) - ...
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0answers
28 views

How to find out when the profit of a transaction will hit $500,000

The question I have been trying to wrap my head around is a little complicated. Supposing you buy ten contracts worth 62,500 each and you double the total number of contracts each time you make a ...