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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Calculating a Forward Starting Swap with Forward Equations

I have been trying to resolve this problem for some time but I cannot get the correct answer. The problem is the following one. Compute the initial value of a forward-starting swap that begins at ...
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9 views

Calculating forward rate

I have to find nominal and effective forward interest rate for 3M-9M term, knowing that current interest rates are: 3M - 2.05% 6M - 2.04% 9M - 2.03% 12M - 2.02% For a nominal interest rate I just ...
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1answer
25 views

Loan Interest Discrepancy

Suppose that I have a loan value $x$ and interest rate $r$. The simple interest is then $x\cdot(1+r)$. If I take out a loan compounded annually and paid monthly for $12$ months the amount at the end ...
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12 views

What is the minimum variance portfolio, for all possible returns?

The data I was given is: ...
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1answer
28 views

Inequality of an expectation (here: perpetual put of an american option)

for a given function $u(x):=\sup_{\tau \in T_{0,\infty}}E[(Ke^{-r\tau}-xe^{\sigma B_{\tau}-(\sigma^{2}\tau)/2})_{+}1_{\tau <\infty}]$ and $x \in [0,\infty)$, K a positive real number, $(B_{t})$ a ...
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1answer
16 views

Exam FM problem: Financial calculator necessary for finding $i$ from $a_{\overline{n}\rceil i}$? Edited

I am currently studying for the Exam FM for actuaries, and the calculator that I have is a TI 30X IIS, which was very helpful for me during the Exam P. I cam as far as studying bonds, and the ...
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1answer
13 views

Finding out the minimum yield of a premium bond with a different redemption fee. ($F=100, r^{(2)}=10\%, i^{(2)}=8\%, C=110$)

I am working on a specific problem regarding price of bonds and it is the following. A 10% bond with face amount $F=100$ is callable on any coupon date from $t=15.5$ years after issue up to the ...
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1answer
51 views

Forward Starting Swaps and Forward Equations

Hi all I have a problem when I have to calculate swaps/swaptions. n=10-period binomial model for the short-rate, ri,j. The lattice parameters are: r0,0=5%, u=1.1, d=0.9 and q=1−q=1/2. 1.Compute the ...
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1answer
33 views

Why would an investor want the minimum yield?

I am puzzled by a problem related to bonds. When a bond is callable, the purchase price (present value of the bond) can fluctuate and I also understand the difference when the bond is purchased at a ...
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1answer
48 views

Portfolio VaR with Copula?

Let the portfolio be given by: $$X=X_1+X_2$$ $(X_1,X_2)$ are dependent through a Copula function $C(u_1,u_2)$, such that the joint distribution is given by: $$F(x_1,x_2)=C(F(x_1),F(x_2))$$ What is ...
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1answer
18 views

Annuity Depreciation Problem from Exam FM

A manufacturer buys a machine for 20, 000. The manufacturer estimates that the machine will last 15 years. It will be depreciated using the constant percentage method with an annual depreciation rate ...
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Question on Annuities [closed]

Is the negative of an increasing annuity equal to a decreasing annuity?
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What is the formula for FvSchedule & Ispmt functions in excel? [closed]

What is the actual formula behind the FVSCHEDULE & ISPMT function in MS OFFICE Excel? From where can we find reference for that.
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24 views

Why is the money factor defined the way it is? [migrated]

In some loan situations, especially car leases, people like to talk about the money factor, which is a number given by $$ \frac{\text{interest percentage}}{2400} $$ Where does the $2400$ come from? I ...
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2answers
39 views

What is an alternative book to oksendal's stochastic differential equation: An introduction?

What is an alternative book to oksendal's stochastic differential equation: An introduction? But also An alternative that is over 300 pages and at the same level? Some professor refer that book as a ...
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1answer
40 views

Will this well enough to serve as a prerequisite to oksendal's book?

Will this well enough to serve as a prerequisite to oksendal's stochastic differential equations: an introduction with applications book? I refer to shiryeav's probability, but i guess it still miss ...
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2answers
20 views

Help for calculating the correct marked price?

A) For this equation I need help calculating the marked price. A retailer wants to make a 22% profit on the sale of a television set. The television set cost the retailer $560. What should the ...
2
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1answer
19 views

Total MSRP given monthly payment, downpayment %, and term of autoloan

I want to buy a car. I know the following: - monthly payment - interest rate - # of months of loan - downpayment % How can I calculate the total MSRP I can get for my monthly payment? So for ...
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2answers
50 views

What is an elementary yet important application of matrix in finance?

What is an elementary yet important application of matrix in finance? I have difficulty to read anything intermediate/advanced associated with this topics, hopefully I can find something interesting ...
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1answer
17 views

Are yield rates different from rate of return? (Bonds)

There is a puzzling thing that is bothering me regarding bonds and I would like to have some help. The following is the situation I am dealing with. A 20-yr 8% bond has semi=annual coupons and a ...
3
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1answer
22 views

Zero-coupon vs. $10\%$ coupon problem

I am working on Bonds and I am having trouble solving this problem. A zero-coupon bond pays no coupons and only pays a redemption amount at the time the bond matures. Greta can buy a zero-coupon ...
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1answer
26 views

Time required to make money 6 times of itself

A sum doubles itself in one year at a certain rate of interest, compounded annually. In how many years will a sum become six times itself under the same investment scheme? I got confused in this ...
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1answer
13 views

Bond prices and how to compare

I have a couple of basic questions regarding bonds that I would like to ask and the following problem is what I used. Find the "price" of the following bonds "redeemable at par". Let $F=100$ be ...
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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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1answer
50 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 !!!
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23 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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1answer
54 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 ...
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1answer
34 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: ...
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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 ...
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23 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 ...
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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 ...
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1answer
32 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 ...
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0answers
14 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 $\widehat{\sigma^2_{i,t}}$. ...
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2answers
46 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 ...
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1answer
20 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 ...
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0answers
84 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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1answer
25 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 ...
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2answers
27 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, ...
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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?
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9 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 $L$ ...
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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 ...
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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, ...
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0answers
13 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 ...
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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 ...
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21 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 ...
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1answer
17 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 ...
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2answers
25 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 ...
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1answer
37 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: ...
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1answer
29 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 ...
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1answer
25 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 ...