Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

learn more… | top users | synonyms

0
votes
2answers
54 views

Compound interest with penalty in withdrawal amount

Carl puts $10000$ into a bank account that pays an annual effective interest rate of $0.04$ for $10$ years. If a withdrawal is made during the first five and a half years, a penalty of $5\%$ of the ...
1
vote
1answer
21 views

Expectation equals to Black-Scholes Equation

Let $S_t$ be ageometric brownian motion with parameters $\sigma$ and $r$ and fix $T,K\in (0,\infty)$. How can I show that: \begin{align} \mathbb{E}[e^{-rT}max\{(S_T-K),0\}] & = ...
1
vote
1answer
32 views

How do you calculate the breakeven amount for two credit cards with different fees and rebates?

Credit Card (CC) M offers a rebate of cash back of $a$ dollars, with NO annual fee. CC S offers a rebate of cash back of $b$ dollars, but charges an annual fee of $f$. How much must I ...
0
votes
1answer
36 views

Empirical Formula for Financial problem

I have a financial problem, which is strictly related to math of course. The problem states that on the last year the steel market price was about $450$ \$, and a company, that sells steel, used to ...
2
votes
0answers
24 views

Under which conditions on $\sigma_1, \sigma_2$ and $\rho_{12}$ the minimum variance portfolio involves no short selling?

If $\rho_{12} \lt 1$ or $\sigma_1 \ne \sigma_2$ then $\sigma_{V}^2$ representing the variance of the portfolio with weights $(w_1, w_2)=(s, 1-s)$ as a function of $s$ attains its minimum value at ...
3
votes
2answers
57 views

Does the term “selling price” mean the “cost price” or the “sale price” of a product/commodity?

I have been told that the idiom "selling price" is the same as the cost price of an item, that is the amount which a seller pays to, e.g. a wholesale merchant. The seller later sells the commodity at ...
1
vote
5answers
35 views

How to calculate the price of a product without the sales tax, if we know the price including the tax and the rate of the tax?

The question is The price of a mobile phone is $8800 inclusive of a 10% GST (General Sales Tax). What is the original price of the mobile phone? This is how I approached it: The Sale Price ...
1
vote
2answers
34 views

Determine the weights in the minimum variance portfolio.

Consider three securities with the following expected returns, standard deviations of returns, and correlations between returns: $$ \begin{matrix} \mu_1=0.20, & \sigma_1=0.31, & ...
1
vote
0answers
24 views

Describe a process mathematically

I am simply wondering how to explain this process mathematically: Lets say that we have a set $A_j$ of sets $B_i$ such that $A_j$ is the set off all $B_i$ where $i\leq j$ Now lets say that set ...
1
vote
1answer
34 views

Annuity payments $2n = n$

I'm having trouble with this question: For an annuity of $3n$ payments of equal amount at periodic interest rate $i$, it is found that one period before the first payment the present value of the ...
0
votes
0answers
12 views

Is complete market or not if appreciation rate is random?

Consider the stock price process satisfies the following SDE: $dS_t=\mu_t S_tdt + \sigma S_t dW_t , S_0=s $ and the appreciation rate process $\mu_t$ satisfies the following SDE: ...
2
votes
0answers
40 views

Mean-variance portfolio probelm

So the question asks: Consider three uncorrelated stocks in the market. Each stock has variance 1. The expected returns are given by $2, 3 $ and $ 5$ respectively. Find the optimal mean-variance ...
0
votes
1answer
48 views

Minimum variance portfolio problem

So the question asks: There are N (N > 1) stocks with the same variance $σ^2$ and the same pairwise correlation coefficient γ (i.e. $c_ij$ = γ for all i = j. γ is a given constant such that 0 ≤ γ < ...
1
vote
1answer
23 views

Compute the risk measured by the standard deviations $\sigma K_1, \sigma K_2, \sigma K_3$, does this have to do with weights?

Compute the risk measured by the standard deviations $\sigma K_1, \sigma K_2, \sigma K_3$ for each of the investment projects, where the returns $K_1, K_2$, and $K_3$ depend on the market scenario: ...
-1
votes
1answer
15 views

Calculating retirement amount and time

I am asking for three inputs from the user: How much money do you want to retire?(Savings goal) Initial Investment Annual contribution Interest rate And I want to calculate the amount you end up ...
1
vote
0answers
23 views

Incompatibility of Libor and Swap Market Models

I'm trying to see why the Libor and Swap Market Models are incompatible with each other. I have found numerous sources such as the book of Brigo and Mercurio but my main source is a paper of ...
0
votes
1answer
66 views

Proportion of Stock investors owning stocks in companies

Suppose stocks of companies A, B, and C are popular among investors. Suppose $18$% of the investors own A stocks, $49$% own B stocks, $32$% own C stocks, $5$% own all three stocks, $8$% own A&B ...
1
vote
1answer
36 views

The three year bond has face value $100, and pays \$5 coupons annually, the last one at maturity. Assume that the continuously compounding rate is 7%.

The three year bond has face value USD 100, and pays USD 5 coupons annually, the last one at maturity. Assume that the continuously compounding rate is 7%. (a) Find the price of this bond. (b) ...
2
votes
1answer
34 views

Is this the correct continous compounding equivalent to daily compunding of 90%?

Find the rate of continuous compounding equivalent to daily compounding of 90%, if we assume that a year has 365 days. P=principle daily = $P(1+(\frac{0.9}{365}))^{365}$ continuous = $Pe^x$ ...
1
vote
2answers
31 views

why does this answer on paying a mortgage two years earlier make sense?

Suppose that you took a mortgage of 100000 on a house to be paid back in full by 10 equal annual installments, each consisting of the interest due on the outstanding balance plus a repayment of a part ...
1
vote
1answer
26 views

How to find arbitrage for forward rate of exchange?

Assume that $S(0)$ is the current rate of exchange for foreign currency. Assume that and $K_h$ and $K_f$ are rates of return on home and foreign currency if it is invested over a period $T$. (A) ...
1
vote
1answer
26 views

can someone explain how bonds work and how to calculate the value of a bond?

I am taking financial mathematics and in class I learned a formula to calculate the value of a bond, $B=\frac{F}{1+r}$ if one payment or if coumpund $B=\frac{F}{(1+r)^n}$ where $B$ is the value of the ...
0
votes
1answer
28 views

Models for Financial Economics: Determining The Amount to Lend in Synthetic Assets

You are given: (i) The price of a stock is 43.00$ (ii) The continuously compounded risk-free interest rate is 5% (iii) The stock pays a dividend of 1 three months from now (iv) A 3-month European ...
1
vote
1answer
39 views

Question About Representation of Brownian Motion

In Stochastic Calculus with Financial Applications by J. Michael Steele he makes a specific representation of a Brownian Motion using wavelets. At one point he calculates the covariance, and he uses ...
0
votes
0answers
58 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 ...
1
vote
2answers
21 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 ...
1
vote
1answer
23 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 ...
1
vote
1answer
43 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 ...
0
votes
1answer
35 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) ...
4
votes
2answers
116 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 ...
3
votes
0answers
31 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 ...
0
votes
3answers
30 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 – ...
0
votes
0answers
43 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 ...
1
vote
3answers
47 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 $\frac{1}{2}(n^2+n-t^2-t)$ $I_{[t,n]}=A(n)-A(t)$ $I_{[0,r]}=A(r)-A(0)=r$ ...
0
votes
0answers
21 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 ...
-1
votes
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 ...
1
vote
1answer
42 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) }{ ...
-1
votes
3answers
32 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 ...
0
votes
1answer
24 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 $\omega$ ...
0
votes
2answers
209 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} ...
1
vote
1answer
19 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 ...
0
votes
1answer
48 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, ...
0
votes
1answer
63 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 ...
0
votes
2answers
43 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 ...
0
votes
0answers
27 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 ...
0
votes
1answer
53 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
votes
1answer
28 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
vote
1answer
69 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
votes
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 ...
1
vote
0answers
55 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 ...