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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Exam FM Portofolio problem: Using Macaulay Duration

The following problem is what I am working on and I cannot solve it. Under the current market conditions Bond 1 has a price (per 100 of face amount) of $P_1=88.35$ and a Macaulay duration of ...
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13 views

Macaulay duration for a coupon bond. Proof

I am working on showing the following. There is a coupon bond redeemable at par with annual coupon rate $r$ per year. The yield to maturity is $i$. The total number of coupons is $n$. Show ...
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1answer
11 views

Calculating interest on changing principal amount

I'm writing software and I'm trying to calculate interest on a principal value that changes daily in a predictable way. For example, if you saved $5 each day for five years at a 4% annual interest ...
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19 views

Calculate year for a provided yield

\$146.25 will yeild \$46.25 at 7.5% per annum. How to get the number of years? Answer is 6 but how do you get it? What is the formula?
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1answer
26 views

Advice inquiry: Financial mathematics

I am a math instructor at an education center studying to become an actuary. Currently I am studying for Exam FM and practicing problem from a book. Some of the problems in the book says "use a ...
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0answers
26 views

Solving for an interest rate on BA II Plus [closed]

I have the equation: $$ 32 = 40v{_j}^{100} + a_{100|j} $$ where $a$ is present value annuity, and $v$ is present value factor. How can I solve for interest rate $j$ on BA II plus?
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1answer
12 views

How to solve a Compound Interest Question with yearly withdrawals?

The current period is January 2015 A Principal wants to make 3 deposits in the bank: Start of 2015, Start of 2016, Start of 2017, And wants to give a $5000 scholorship for to the best student at ...
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25 views

Interest Theory [closed]

A 20-year annuity certain provides payments annually of \$200 at 1 year, \$180 at 2 years, \$160 at 3 years, and so on, until the payments have reduced to \$60. Payments then continue at \$60 per year ...
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27 views

Logs math problem [closed]

Two investments A and B each quadruple. Investment A was paid 7.5% interest compound annually, investment B was paid 10% compounded annually. How much longer did it take for A to quadruple than B?
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19 views

A calculation for short term loans with different periods

I'm trying to come up with an equation that will allow me to calculate interest for short term loans. These are normally compounded monthly, however, they can be compounded weekly, and the periods ...
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0answers
32 views

Why doesn't this interest calculation add up

I'm trying to develop a calculation for returning the monthly payment for short term loans. Thanks to mardat, I've got an equation like this: 200=x*(1-(1+0.22)^-3)/0.22 = 97.93 Where 300 is the ...
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1answer
21 views

Find expected present value of a continuous payment stream

I have a question for the financial part of my course which I am struggling to answer as i am not sure my answer makes sense. Question: Time is counted from the present t = 0 in years. Suppose for ...
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19 views

Finding Joint Probability of a Binomial Tree Model given the stock price , then Conditional Probability

Consider a T-period binomial tree model with stock price $S_{t,n} = S_0u^nd^{t-n}$ at each node $(t,n)$ of the binomial tree for every $n = 0,1,...,t$ and every $t = 0,1,...,T$. a) Let $v,t \in ...
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1answer
26 views

Prove the process is a martingale with respect to the natural filtration

Let $\{M_n\}_{n\ge 0}$ be a symmetric simple random walk. Fix a real $b$. Prove that the process $S_n = e^{bM_n} (\frac{2}{e^b + e^{-b}})^n$, $n = 0,1,2,....$, is a martingale w.r.t. the natural ...
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1answer
23 views

How to differentiate the standard normal deviation w.r.t. a parameter inside the upper bound

Given that $$N(x)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^x e^{-\frac{s^2}{2}}\:ds$$ And that $$d=\frac{1}{\sigma\sqrt{\tau}}\ln\left({\frac{S}{e^{-r\tau}K}}\right)+\sigma\sqrt{\tau}$$ How do I take the ...
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1answer
49 views

How do I calculate interest on short term loan?

I'm trying to work out interest on short term loans - these are loans that extend to months not years, and are typically repaid in monthly chunks, but I also know that some are repayable in weekly ...
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1answer
19 views

How to differentiate the Black-Scholes formula w.r.t. volatility

The Black-Scholes-Merton formula for determining call option value is given as: $$C(S,K,\sigma,r,\tau)=N(d_1)S-N(d_2)Ke^{-rT}$$ where $N(d_i)$ is the standard normal distribution and ...
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1answer
30 views

Construct a strategy to profit: Problem involving term structure and interest rates.

I am currently studying about term structure and interest rates such as forward rates, swap rates, etc... The following problem seems like an actual actuarial problem that I might see in the future ...
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0answers
31 views

What is this sort of optimisation called?

I am reading a book in mathematical finance. There is something about constrained optimisation. They have specialised it for the financial market, but I am wondering what the general name for this ...
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1answer
23 views

Find the annual yield rate. Exam FM problem.

I'm trying to solve for the following problem and I cannot get the right #. You are given the spot rates at time $t=1,\ 2 \ \text{and} \ 3$ as $s_0(1)=.15,\ s_0(2)=.10,\ \text{and} \ s_0(3)=.05$ ...
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1answer
22 views

Forward rate example, switching the investment.

I need explanation regarding forward rates for the following specific example. A zero coupon with spot rate $s_0(1)=.08$ and $s_0(2)=.09$ are available. a), Smith borrows $1$ and is obliged ...
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3answers
69 views

How long an investment will take to compund to a target amount

A man with $\$20,000$ to invest decides to diversify his investments by placing $\$10,000$ in an account that earns $7.2\%$ compounded continuously and $\$10,000$ in an account that earns $8.4\%$ ...
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2answers
31 views

Calculating monthly compounded interest

To solve the problem How long does it take for an investment to double in value if it is invested at 8% compounded monthly? I figured like this: $$2P = P(1 + 0.08)^t$$ where $P$ is an ...
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0answers
9 views

Purchasing a unit on fund $X$ calculating the dollar weighted and the time weighted rate of return.

I am currently working on the following problem trying to figure out the rate of return. Fund $X$ has unit values which are $1.0$ on Jan 1 05, $0.8$ on Jul 1 05 and $1.0$ on Jan 1 06. A fund ...
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0answers
12 views

Payoff on Call Option

Mr Draper makes an investment: for $C$ pounds he buys a call option on $1$ share with strike price $K$ and expiration time $T$. He also deposits $K^{e−rT}$ pounds in a bank account where interest is ...
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1answer
10 views

Dollar weighted method vs. Time weighted method Problem. Exam FM

The following is the problem that I am working on and I am having trouble. On Jan 1 2005, an investment account is worth 100. On Apr 1 2005, the value has increased to 103 and 8 was withdrawn. ...
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12 views

Finite expectation of bank account with CIR interest rate model

The CIR interest rate model is $$dr_t=(\theta-ar_t)\,dt+\sigma\sqrt{r_t}\,dW_t\;.$$ The money account with this interest rate is $$e^{\int_0^tr_s\,ds}\;.$$ It is known that ...
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1answer
20 views

Dollar weighted return. Formula or definition?

I was learning dollar-weighted return and I was a bit puzzled by the following and I would like to have some advice. I understand that it's basically the internal rate return, but using simple ...
2
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0answers
33 views

Pricing/Valuation of American Options

Hi i'm a litte bit confused by the pricing valuation of American options. For simple Assumtions on the Blacksholes Model and no dividends, and constant rates else one can show, that for a given ...
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0answers
20 views

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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1answer
26 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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42 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
27 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
60 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
34 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
58 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
23 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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0answers
25 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
51 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
44 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 ...
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1answer
20 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
54 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
18 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 ...
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1answer
31 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
27 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
16 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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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. ...