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

1
vote
1answer
51 views

Ranking $ d, i, d^{(m)}, i^{(m)}, \delta$

Any actuary or anyone studying mathematics of finance out there? Please help me out. How can I prove or show that $ d< d^{(m)}< \delta< i^{(m)}<i,$ for $m > 1$. Thanks a lot !!!
1
vote
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 ...
1
vote
1answer
55 views

Bonds … whats is it and what is a discount?

I am studying about bonds and I am a bit puzzled. So far my understanding is that bonds are loans issued by the government or a company and it works very similarly to loans. However, I have a ...
0
votes
1answer
39 views

Black-Scholes formula is a monotonic increasing function of the volatility. Proof?

I'm trying to show this statement: that Black-Scholes formula is a monotonic increasing function of the volatility ($\sigma$). I need to proof it from the Black-Scholes formula which is: ...
0
votes
0answers
25 views

Suppose the nominal spot rates for the next four years from now $(t=0)$ are $s_1=6.40\%$, $s_2=7.00\%$, $s_3=7.50\%$ and $s_4=7.80\%$

Suppose the nominal spot rates for the next four years from now $(t=0)$ are $s_1=6.40\%$, $s_2=7.00\%$, $s_3=7.50\%$ and $s_4=7.80\%$ a) find the spot rates $s_1$, $s_2$, $s_3$, and $s_4$ for annual ...
0
votes
0answers
25 views

Financial mathematics: asion option

I've got a forward starting asian call option: $V_N = max\left( 0,\left(\sum_{j=m+1}^{N}{S_j} - K \right) \right) $ So the payoff is determined by the average stockprice over de latest N-m days and ...
0
votes
0answers
16 views

Black-Scholes model problem

Consider the Black-Scholes model with $S_0 = 11$, $σ = 0.2$, $r = 0.1$, where the stock will pay dividends $D = 2$ in one month. Compute the price of a European put with strike $10$, that matures in ...
0
votes
1answer
37 views

Derivatives pricing w/ squared and cubed stock prices

I have an assignment in which $S_t$ is a stock price following a geometric Brownian motion. The task is now to show that at time t the risk-neutral price of a derivative on $S_t$ that pays $S_T^3$ at ...
0
votes
0answers
15 views

Shrinkage of variance

I have a sample of N variables, and a sample period of length T. At each time $t$, I have the following information: For each variable i, I have an estimate of variance $\widehat{\sigma^2_{i,t}}$. ...
0
votes
2answers
48 views

Draw the price-yield curves for bonds, B1 and B2 on the same yield-price plane

Consider a bond B1 which matures in 30 years and a bond B2 which matures in 15 years. Both have a facevalue $100 and semi annunal coupon pmt 7%(2). Draw the price yield curves for B1 and B2 on the ...
0
votes
1answer
22 views

How is Excel's `RATE(nper, pmt, pv)` evaluated?

I am trying to come up with the same answer as using the function RATE. I've tried several formulas to no avail. As an example, if I plug in ...
1
vote
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 ...
1
vote
1answer
28 views

What does it mean to be an equivalent repay scheme? (sinking fund vs. amortization)

I am having trouble solving the following problem which seems simple, but I cannot quite get it right. Smith can repay a loan $L=250,000$ in one of two ways 1), 30 annual payments based on ...
0
votes
2answers
30 views

annual and effective annual interest rate

Can anyone help me to find the answer to the question below? I am taking the Engineering Economics exam and need to be sure about the correctness of my answer. Here is the question: Smart Visa, ...
2
votes
0answers
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?
0
votes
0answers
10 views

$\frac{L}{a_{\overline{n}\rceil i}}(n-a_{\overline{n}\rceil i})$ vs. $Li \frac{n-1}{2}$ which is larger?

I am having trouble deciding which of the expression is larger. The following is the original problem and I may not have the expression entirely correct, but I am pretty confident. A loan of $L$ ...
0
votes
1answer
14 views

As stock prices travel down what formula would you use to break out of a position

Suppose you are trading stock and you do not enforce a stop loss. Instead, you allow the stock to go where it wants. At some point, the value of your stock has dropped significantly and when the ...
0
votes
0answers
10 views

I want to prove Determine the coupon rate $r$, such that the price of the bond, at $T_0$, equals its face value.

Consider a coupon bond, starting at $T_{0}$ T0, with face value $K$, coupon payments at $T_1, . . . , T_n$ and a fixed coupon rate $r$. Determine the coupon rate $r$, such that the price of the bond, ...
0
votes
0answers
18 views

Refinancing an amortized loan - find the maximum value of $k\%$

The following problem is quite complex for me to see what I am solving for and I would appreciate to receive a bit of help. Jenny borrows $L$ at $i^{(12)}=12\%$ from Bank A, requiring level ...
0
votes
1answer
11 views

Reinvestment calulators

I was wondering if someone can direct me to, or explain, calculations regarding reinvestment. For instance, say your initial investment is \$15,000, and via investing in stock you typically have a ...
0
votes
0answers
22 views

Loan Repayments - Sinking Funds

Cindy borrows $ 13500 $ for $12$ years at an annual effective interest rate of $i$. She accumulates the amount necessary to repay the loan by a sinking fund. Cindy makes a payment of $P$ at the end of ...
0
votes
1answer
18 views

Loan Repayments and Yield Rates

Jose loans Martin $12000$. Martin repays the loan by paying $5000$ at the end of two years and $10000$ at the end of $4$ years. The money received at time $t=2$ is immediately reinvested at an annual ...
1
vote
2answers
31 views

Stochastic Calculus For Finance: Conditional Expectation of Binomial Tree Model

I'm reading through Stochastic Calculus For Finance Volume 1, page 32. The conditional expectation of $S_2$ knowing $1=H$ is $p*S_2(HH) + q*S_2(HT) = 0.5*16 + 0.5*4 = 10$ But how do I calculate ...
0
votes
1answer
45 views

How to convert an interest rate from bank discount basis to continuous compounding

I read on Investopedia that a 360-day-count convention is being used in the case of Bank Discount Basis. And I found the following formula on Wikipedia: ...
1
vote
1answer
30 views

Calculating the yearly payment in a loan. Amortization with unequal payments.

The following is the problem that I am working on. A 30-yr loan of $1,000$ is repaid with payments at the end of each year. Each of the first ten payments equals the amount of interest due. Each ...
-2
votes
1answer
33 views

Differential of two geometric brownian motions

I am currently taking a finance course which includes some math that is currently above my level, it is however not a pure math class and we are just supposed to be able to apply the math to the given ...
0
votes
0answers
12 views

Amortization problem with yeild rates from Exam FM.

I am tackling the following problem. I have a tendency to not do well with yield rates, and I am thinking that that's the part that I am not getting. Betty borrows $19,800$ from Bank X. She ...
0
votes
0answers
17 views

Calculating the loan from amortization.

I was not quite sure what the question was asking and I would like to have some input. a), Is it asking us to actually calculate knowing what each principal paid? or b), Working from almost complete ...
2
votes
1answer
36 views

CI for the expected value of the sum of two dependent normal RVs

Let's consider 2 dependent, normally distributed R.V.s, $X_1$ and $X_2$. The means, $\mu_1$ and $\mu_2$ are known, as well the covariance matrix $\Sigma$. Let's consider the following random ...
0
votes
2answers
45 views

Basic annuity loan problem

I've got a loan of $\$32000$, which I need to repay in $36$ monthly payments, with annual rate of $10\%$. What is the amount of monthly payment, which I need to pay? There will be $36$ payments, thus ...
0
votes
1answer
18 views

Reinvestment using $(Is)_{\overline{n}\rceil i}$… calculate $i$

I am working on the following problems which should not involve a difficult polynomial, but I tried a couple of times without success. Victor invests $300$ into a bank account at the beginning of ...
1
vote
1answer
23 views

Using $(Da)_{\overline {n} \rceil i}$ or $(Ia)_{\overline {n} \rceil i}$ in this problem?

I am trying to solve the following increasing (decreasing?) annuity problem from exam FM. A perpetuity costs $77.1$ and makes annual payments at the end of the year. The perpetuity pays $1$ at ...
0
votes
0answers
14 views

Using $(Ia)_{\overline {n} \rceil i}$ from Exam FM.

I am trying to solve the following problem which I am having a bit of trouble with. Olga buys a 5-yr increasing annuity for $X$. Olga will receive $2$ at the end of the first month, $4$ at the end ...
0
votes
0answers
11 views

Arbitrage-free market for continuous distribution

Is it true, that a one-period market say $(0,t)$ is arbitrage-free if $S_t$ is continuously distributed on $\mathbb{R}$? I.e., for continuous distributions on $\mathbb{R}$, there always exists a ...
0
votes
0answers
18 views

Increasing annuity problem

I learned increasing/decreasing annuity and am tackling the following problem for hours now without success. Amy deposits $Z$ into a bank account that has effective annual interest rate of $5\%$ ...
0
votes
0answers
16 views

Pension calculation with annuity and a geometrically progressing deposits.

I am a bit confused regarding how to solve the following problem. An employee serves $37$ years before retiring on a pension. His initial salary was $18,000$ per year and increased by $4\%$ each ...
0
votes
1answer
61 views

Geometric progression in annuity

I am working on the following problem that involves annuity which deposits form a geometric progression. Stan elects to receive his retirement benefit over $20$ years at the rate of $2,000$ per ...
0
votes
0answers
18 views

Calculating the interest rate for an annuity (Exam FM)

I have been searching for a way to solve for the interest rate given the monthly payments of a loan. I would like to set up a problem as the following. $X$=monthly payment , $i$=effective ...
0
votes
0answers
19 views

Reinvestment problem involving finding loan payments given the yeid rate (From Exam FM)

I am having trouble computing the interest rate for the following problem. Sally lends $10,000$ to Tim. Tim agrees to pay back the loan over 5 years with monthly payments at the end of each ...
1
vote
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 ...
0
votes
1answer
44 views

need help calculating the interest “i”

A regular deposit of 120 dollar made at the beginning of each year for 20 years. Simple interest is Calculated at a rate of i per year for 22 years. At the end of the 22-year period, the total ...
1
vote
1answer
40 views

Annuity/Finance

I'm trying to determine the question below: Mr. Learnwell wants to setup a scholarship of $4500 paid at the end of every six months. If the interest rate is 6.4% compounded semi-anually, how much ...
0
votes
2answers
96 views

current value of a forward contract

Suppose we hold a forward contract on a stock with expiration 6 months from now. We entered into this contract 6 months ago so that when we entered into the contract, the expiration was T=1 year. The ...
2
votes
1answer
23 views

Annuity problem, calculating the accumulated value.

the following is the problem I am trying to work on. Kathryn deposits 100 into an account at the beggining of each 4 year period for 40 years. The account credits interest at an effective annual ...
-1
votes
1answer
25 views

Sunk Costs NonRefundable Deposit

A young couple has made a nonrefundable deposit of the first month’s rent (equal to 1,000 dollars) on a 6-month apartment lease. The next day they find a different apartment that they like just as ...
0
votes
1answer
38 views

Hard to understand the strategy of the following investment.

Upon attempting to solve a problem regarding annuities, I am a little puzzled regarding the following strategy of investment. $10,000$ can be invested so that one can purchase an annuity-immediate ...
0
votes
2answers
35 views

Annuity problem from Exam FM

I am working on the following problem and I was wondering if someone could help me solve it. Chuck needs to purchase an item in 10 yrs. The item costs $\$200$ today, but its price inflates $4\%$ ...
1
vote
1answer
71 views

books on the application of linear algebra on statistics/finance/machine learning

I am reading "linear algebra done right" by Axler and like it a lot. One thing though, in the end I would like to put these theory to use and as a math textbook it doesn't cover much application. ...
2
votes
2answers
35 views

Identity of $I_t$ under annuity with principal $1$

I am trying to prove an identity and quite not get there. The following is the premise. One deposits $\$1$ at time $t=1,2, \cdots ,n$. evenly spaced. The effective interest per payment is $i$. ...
0
votes
0answers
21 views

finance ( call option for the European)

Consider a 1-period binomial model with R=1.02, S_0=100, u=1/d=1.05. Compute the value of a European call option on the stock with strike K=102. The stock does not pay dividends. i know that the call ...