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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32 views

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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0answers
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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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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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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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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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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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 ...
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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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0answers
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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1answer
943 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 ...
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1answer
22 views

How to solve this question related to loan payments? [closed]

A bank issues a loan of £5,000. Level repayments are made annually in arrears for 5 years. The bank charges an effective annual rate of interest of 6%, so that each annual repayment is ...
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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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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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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
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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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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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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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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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 ...
4
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3answers
537 views

Independent math learning

I'm an undergraduate math and econ major and I'm planning on graduating relatively soon and I am very limited to the number of math classes I have left (very sad about this fact). So far I have ...
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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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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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1answer
742 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 ...
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1answer
63 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 ...
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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. ...
0
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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 = ...
1
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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 ...
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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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1answer
436 views

Redington vs full immunization?

I understand that the present values and duration of liabilities and assets are required to be equal to each other under both cases, and furthermore for Redington immunization the convexity must also ...
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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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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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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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0answers
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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0answers
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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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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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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3answers
62k views

What is the formula for the difference between CI and SI?

if principal, time and rate are given how do i find the difference between Compound interest and Simple Interest? P=12,000 n=1 and a 1/2 yrs. R=10% per year ...
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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 $$X_t-X_0=\int_0^t\mu X_s \, ds+\int_0^t \sigma X_s \, dZ_s, \tag{*}$$ ...
3
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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 ...
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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 ...
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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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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 ...
2
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2answers
62 views

Financial Mathematics problem

$i^{(p)}$ is the nominal interest converted p-thly i.e the total interest per unit of time paid on a loan of amount 1 at time 0 where interest paid in p equal installments at the end of each p-th ...
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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; ...