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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119 views

In stochastic calculus, why do we have $(dt)^2=0$ and other results?

I'm doing actuarial problems of Exam MFE and it covers some of the stochastic calculus (like Ito's Lemma). One of the frequently used results are the so-called "multiplication rules": $(dt)^2=0$ ...
3
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91 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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0answers
158 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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0answers
34 views

Simplifying $\sum_{t=1}^{n}t^2v^t$ using actuarial notation.

In financial mathematics involving immunization, I encounter situations where I am trying to calculate $$(A) \quad v+4v^2+9v^3+ \cdots +n^2v^n=\sum_{t=1}^{n}t^2v^t $$ where $v$ is the present value ...
2
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24 views

Are these two option valuation formulas equivalent? Why?

I have been reading a finance paper that claims that the following function, which is a value for a financial derivative (1): $$V(s,t)=E_{Q} \left[\zeta\big(S(T)\big)e^{-\int_t^T r_F(\nu) ...
2
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0answers
31 views

What is this sort of optimisation called?

I am reading a book in mathematical finance. There is something about constrained optimisation. They have specialised it for the financial market, but I am wondering what the general name for this ...
2
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0answers
33 views

Pricing/Valuation of American Options

Hi i'm a litte bit confused by the pricing valuation of American options. For simple Assumtions on the Blacksholes Model and no dividends, and constant rates else one can show, that for a given ...
2
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13 views

How to calculate present value with changes interest

How to calculate present value with period of 5 years and 6 months? Besides that, there is interest changes and compounded differently. Is there any formula?
2
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198 views

numerical method (implicit , backward difference or forward difference) for nonlinear pde

$\newcommand{\lbar}{\underline{\lambda}}$ In this linear PDE: \begin{cases} B_t+b^Q(r,t)B_r+\frac{1}{2}d^2(r,t)B_{rr}+(\mu(\lambda,t)+\alpha \sigma (t))(\lambda -\lbar)B_{\lambda} \\ ...
2
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0answers
127 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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143 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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43 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 ...
2
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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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0answers
83 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 ...
2
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0answers
28 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 ...
1
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0answers
14 views

Macaulay duration for a coupon bond. Proof

I am working on showing the following. There is a coupon bond redeemable at par with annual coupon rate $r$ per year. The yield to maturity is $i$. The total number of coupons is $n$. Show ...
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0answers
21 views

Calculate year for a provided yield

\$146.25 will yeild \$46.25 at 7.5% per annum. How to get the number of years? Answer is 6 but how do you get it? What is the formula?
1
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12 views

Finite expectation of bank account with CIR interest rate model

The CIR interest rate model is $$dr_t=(\theta-ar_t)\,dt+\sigma\sqrt{r_t}\,dW_t\;.$$ The money account with this interest rate is $$e^{\int_0^tr_s\,ds}\;.$$ It is known that ...
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0answers
38 views

Help with integrating stochastic calculus expression from yield curve model

I am very rusty on stochastic calculus, and I am having trouble integrating the following simple term from a yield curve model: $$z(t)=\int_0^t\exp(-k(t-s))dW(s)$$ Any suggestions appreciated. ...
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0answers
24 views

Force of interest for simple interest

I am struggling to work out what the force of interest for simple interest is when using differential equations. I know that it is $\delta=\frac{r}{1+rt}$ where $r$ is the interest rate, but when I ...
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0answers
85 views

Help writting financial distribution formula

I need help writing a function to calculate the financial contribution of a product subscription into a given month. Not so straight forward however, since it has to consider months with fixed length ...
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0answers
30 views

Finding drop payment with varying interest rates..

Person A is accumulating a 10,000 fund by depositing 100 at the end of each month starting September 1,2002. If the nominal interest rate on the fund is 12% convertible monthly until May 1,2005, and ...
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0answers
21 views

Black and Scholes solution

Consider the Black and Scholes equation. What is the (financial) interpretation of the solutions S and $e^{rt}$? They both satisfy the equation.
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24 views

Finding the annual withdrawal, given initial and final amounts, and interest rate

I am working on the following problem and I keep getting a different answer. The principal $P=10,000$. The annual interest rate is $i=4\%$. The money is deposited at time 0 and the interest is ...
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0answers
35 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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36 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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0answers
60 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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0answers
30 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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0answers
14 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
51 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
41 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
58 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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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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0answers
56 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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0answers
40 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
38 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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0answers
24 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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0answers
218 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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57 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
25 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
172 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
115 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
40 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
37 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
299 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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251 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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0answers
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 ...