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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Several options using Black-Scholes equation(s)

Could someone provide me some information about the modelling of several options at the same time by using Black-Scholes (probably coupled) equations? Any reference to papers and/or books shall be ...
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17 views

Money-Business Stocks [on hold]

Let's say I work in retail and at the beginning of the month, my stock ownership is \$350,000.00. Over time, my sales are \$78,000.00 and my stock is reduced by \$32,000.00 worth of markdowns. my ...
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2answers
19 views

Investment in simple interest

Consider an investment with nonzero interest rate $i$. If $i_5$ is equal to $i_{10}$, show that interest is not computed using simple interest. Answer is If $i$ is a simple interest rate, then ...
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1answer
19 views

Effective rate of interest

An investor purchases $1000$ worth of units in a mutual fund whose units are valued at $4.00$. The investment dealer takes 9 % front-end-load (deduction) from the gross payment. One year later the ...
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1answer
28 views

method/technique for finding arbitrage

I was able to solve this problem and find the arbitrage but only after spending a long time on it and trying out different possibilites, is there a method or technique that can help me find the ...
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1answer
26 views

Finding the accumulated profit.

The above project is financed by a loan. The company pays 6.25% on the money borrowed and earns 4% on money invested in its deposit account.(Spare funds can't be used to repay the loan at any time) ...
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2answers
85 views

Can someone explain what a portfolio is in financial math?

I took mathematical probability last semester and now I am taking financial mathematics, but only probability was a pre requisite for financial math (no finance classes were required). These types of ...
2
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0answers
21 views

Stock Price Dynamics correlated with Bond market returns

I am currently working on to derive the following form of the stock price dynamics: $$dS_t = S_t[(r_t + \psi\sigma_S)dt + \rho \sigma_S dz_{1t} + \sqrt{1-\rho^2}\sigma_S dz_{2t}$$ where the ...
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3answers
25 views

interest being compounded annually

What sum would amount to 31,104 in three years at 20% p.a Compound interest, interest being compounded annually ? (Ans: 18,900) Solution: \begin{align*} C I &= A – P \\[1ex] P &= 31104 – ...
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32 views

Black Scholes Constant Implied Volatility

I hope someone can clarify my ideas about the constant implied volatility in the classical Black Scholes framework. As well known, market practitioners quote the prices of vanilla call and put ...
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2answers
34 views

Amount of interest

Find the amount of interest earned between time t and n where $t<n$; if $I_r=r$ for some positive integer r. Answer is $\frac{1}{2}(n^2+n-t^2-t)$ $I_{[t,n]}=A(n)-A(t)$ $I_{[0,r]}=A(r)-A(0)=r$ ...
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0answers
16 views

Formula for contingent claim similar to European call option but with two dates for option to buy

So in a normal European call option with one maturity date, you'd buy a share of a stock if the price of the stock at the maturity date was higher than the exercise price. How would you come up with a ...
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2answers
39 views

The Simple Interest accurued on an amount.

The Simple Interest accurued on an amount of 24000 at the end of 2 years is 11,520. Find the C I accrued on the same amount at the same rate of interest, for the same period? Ans: C I = 12,902.40 ...
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1answer
30 views

Solving for n in Present Value and Annuity formula

I derived the formula for n=.... of the following formula P = $\ 525 $ A = $\ 15 $ i = $\ 0.015 $ Answer: $\ 50 $ P = $\ A [\frac{((1+i)^n - 1) }{ ...
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3answers
24 views

interest being compounded half yearly.

What is the compound interest on $15000/-$ at $12\%$ P.a for one and half years, interest being compounded half yearly? (Ans: $C I = 2865.24$) I Selected this Procedure to solve: If a sum of $x$ is ...
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1answer
22 views

how to show that definition for stochastic process in continuous time applies to stock prices

I know that the formal definition of a stochastic process is: {$X(t,\omega)\,\,t\ge0$} is a stochastic process if: For any fixed $t\ge0$, $X(t,\omega)$ is a random variable For any fixed $\omega$ ...
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2answers
50 views

What is the maximum expected Sharpe ratio by combining two assets into a portfolio?

Given two assets that have expected excess returns of 7 and 4. Also, given their expected co-variance matrix $$ \begin{bmatrix} 2 & 1 \\ 1 & 1 \\ \end{bmatrix} ...
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1answer
15 views

Confirmation of Interest and financial mathematics problem

I'm having trouble with two questions A fund earns a nominal rate of interest of 6% compounded every two years. Calculate the amount that must be contributed now to have 1000 at the end of six ...
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1answer
33 views

Black-Scholes SDE solution help

I am trying to solve the Black Scholes SDE, but got really stuck. I have done most of the derivation but the integral seem intractable to me. The integrals look bit like the Normal Distributions PDF, ...
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1answer
59 views

How do I go about finding effective interest/discount please?

How do I go about solving this please? I solve a lot of interest questions but this looks different. I'm just trying to solve as many as questions as possible. Am I ought to use the compound interest ...
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2answers
35 views

How do i solve compound interest questions like this?

How do i solve compound interest questions like this? Do I just use the compound interest formula directly? If I have lets say $500 in a savings account for 5 years and it earns 2.5% Annual ...
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0answers
17 views

Parallel Shifts of Forward Curve and Arbitrage Opportunities

I came accross a phrase in the Paul Glasserman, Monte Carlo Methods In Financial Engineering, page 153 : "a model in which the forward curve makes only parallel shifts admits arbitrage opportunities ...
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0answers
34 views

Effective Rate of Discount and Continuous Interest

I have two problems that I am having trouble with Using an interest rate of 5%, find the present value of 5000 payable in 10 years and the effective rate of discount between the 7th and 8th year. ...
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1answer
24 views

How to solve this question related to interest rate?

An investor would like to have £5,000 at the end of 20 years. The annual effective rate of discount is 5%. How much should the investor deposit today to reach that goal? I tried- PV = ...
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1answer
57 views

Financial Mathematics, interest problem

Determine the amount of interest earned from time $t=2$ to $t=4$ if $240$ is invested at $t=1$ and an additional $300$ is invested at $t=3$. Given, $a(1)=1.2$, $a(2)=1.5$, $a(3)=2.0$, $a(4)=3.0$ I ...
2
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1answer
50 views

HJM model - Differentiation Problem

starting from the folowing SDE (HJM model): $$df(t,T)=\left(\sigma(t,T)'\int_t^T{\sigma(t,u)du}\right)dt+\sigma(t,T)'dW_t$$ And having $r(t)=f(t,t)$, I have two questions : 1) how do we obtain the ...
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0answers
49 views

converting to math from economics major

Recently, i'm majoring in honour track of economics taking econometrics statistics courses and minoring in mathematics taking advanced calculus, real analysis ,linear algebra courses. Upon research on ...
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2answers
34 views

Financial mathematics problem. ( Deferred annuities ).

We need to calculate present value(value at t=0) of the payments of amount $1$ made at $t = m+1 , m+2 , ...... , m+n$ and no payments are made between $t=0$ to $t=m$ , effective rate of interest is ...
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0answers
25 views

Mathematical proof solving an accounting issue

For whom it may concern, Consider the following situation, a parent company "P" holds two subsidiaries (i) A1 which in turn has a subsidiary, A2, and a sub-subsidiary A3 (lets call these the A-chain) ...
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2answers
36 views

What does it mean when a letter has both superscript and subscript?

I have a formula for Bond Valuation of a Level Coupon Bond, but I don't understand the notation. It looks like: It's the bottom formula in the image below, starting with PV = What does it mean ...
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1answer
32 views

self financing strategy

how could one prove the following proposition from stochastic calculus applied to finance? Proposition : Let $\Phi$ a trading strategy. Then, $\Phi$ is self financing if and only if ...
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23 views

Conditional expectation in continous markov chains

I am trying to understand the double integral in calculating the conditional expectation. In calculating $V_i$, the second and third equalities are due to the law of total probability. I have the ...
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27 views

Mathematics of finance - reference - Exercise, Problem books for High schools [duplicate]

Please, could you give me any examples of books (Problem books with exercises) of Mathematics of finance for High schools? Thanks for any advice.
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2answers
20 views

Total Present Value of Multiple Cash Flows

I understand how to calculate the total accumulated and present values of multiple cash flows over n years, but I don't quite understand how this works when m of those n years aren't included. For ...
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1answer
37 views

Discount factor problem.

We need to state whether the given statement is true or false : $$ v(t_2) = v(t_1)v(t_2 - t_1)$$ where $v(t)$ is the discount factor. I found it ti be true as $v(t) = (1 - d)^{t}$ where $d$ is the ...
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1answer
26 views

Compounding cash, at a gambling game with certain payout and your certain win rate.

Say there is a gambling game that pays $p=.70$ of bet per win and your win rate is $w = .70$. What is an expression for your account balance $P$, given a starting balance of $P_0$ if you're betting ...
5
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1answer
61 views

$dX_t/X_t=\mu+\sigma \, dZ_t$, does this notation make sense?

I understand that the notation $$dX_t=\mu X_t \,dt + \sigma X_t \,dZ_t,$$ where $Z_t$ is Brownian Motion, is a shortcut to $$X_t-X_0=\int_0^t\mu X_s \, ds+\int_0^t \sigma X_s \, dZ_s, \tag{*}$$ ...
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2answers
26 views

Where the constant comes from in the Compound Interest formula?

I want to understand where the 1 constant comes from in the Compound Interest formula. I'm a programmer, I can find a logical way to calculate it using a programming language, this is a way I can ...
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1answer
30 views

A 39-year annuity-immediate will pay 13 in each of the first 3 years…

A 39-year annuity-immediate will pay 13 in each of the first 3 years, 12 in each of the next 3 years, etc., until payments of 1 are made in each of the last 3 years. The present value of the payments ...
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0answers
20 views

How much of the loan has been repaid after 2 years and 6 months? (Simple question)

A loan of £2000 is to be repaid over 5 years by a level annuity paid monthly in arrears. The amount of the monthly payment is calculated on the interest rate of 1% per month effective. This implies ...
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0answers
24 views

What are the differences between large deviations theory & extreme value theory?

I need to study both for my Master's thesis in finance. (Probably, I'll have to apply them on the Value at Risk and Conditional Value at Risk estimation, so, on quantile estimation, loosely speaking; ...
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1answer
62 views

How is APR calculated?

I would be extremely grateful if someone could help with this problem. I'm planning a series of lessons on basic finance and wanted to brush up. I will not have to teach this but I like to keep a ...
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0answers
34 views

AR(1) process with exponential noise.

For the AR(1) process defined by $Z_t = aZ_{t-1} + \epsilon_t$, $\epsilon_t \sim Exp(\lambda)$, $a \in (0,1),\lambda >0$, compute $P(Z_t|Z_{t-1})$. I was only able to compute $E(Z_t|Z_{t-1}) = ...
2
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1answer
55 views

How does filtration model information?

Lets say you have a probability space $(\Omega, \mathcal{F},P)$ And a stochastic process on this space $\{X_t, t \in T\}.$ Assume that our process takes vaslues in $\mathbb{R}$. T is a totally ordered ...
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29 views

Proof that no futures trading system always wins

Hopefully someone here has some knowledge in both finance and maths. I am pondering on the existence/impossibility of a trading system (or algorithm) that ALWAYS ends up winning money, no matter how ...
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2answers
34 views

Calculating asset returns by portfolio weights

I have a securities portfolio (Fixed Income) and corresponding information regarding the single issues weights (in %) in the portfolio, sector identifiers (i.e. Industrial, Retail) and Total Return ...
2
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0answers
14 views

optimal derivative position through optimization

So I have the following optimization problem: min. $-E^Q[u(h(x))]$ s.t $\int h(x)q(x)dx \leq \frac{V_0}{B_0}$ Where $Q$ is the subjective probability which then gives: $E^Q[u(h(x))]=\int ...
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1answer
24 views

help with $\nabla$ and Lagrangian in optimization / portfolio theory?

So $\nabla$ as I know it from calculus means gradient. We have $\min \ \ \frac{1}{2}w^T\Sigma w$ $s.t. \ \ \ \ \ w^T1 = V_0, \ \ V_0 = 100$ where $w$ is weights in vector, $\Sigma$ is the ...
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0answers
16 views

Affect of projection matrix on the covariance matrix

Suppose I have a projection matrix $P$ which transforms a random vector $u$ to a new random vector $w $ with a mean of zero. such that the constraint applies $Xw = 0$ $P = I - ...
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1answer
24 views

Correlation and Covariance

The book I'm reading gives this as an example for lognormal variables. Starting at some fixed time, let $S(n)$ denote the price of a security at the end of $n$ additional weeks, $n \ge 1$. A popular ...