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
0answers
10 views

Are these two option valuation formulas equivalent? Why?

I have been reading a finance paper that claims that the following function, which is a value for a financial derivative (1): $$V(s,t)=E_{Q} \left[\zeta\big(S(T)\big)e^{-\int_t^T r_F(\nu) ...
0
votes
0answers
4 views

Liabilities and Immunization problem

I am working on a certain basic problem which is puzzling me. Liabilities of $1$ each are due at the ends of periods 1 and 2. There are three securities available. Bond A: due at the end of ...
1
vote
1answer
20 views

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 ...
8
votes
1answer
347 views

Modelling risk when market making

I'm interested in learning about algorithmic trading, particularly in bitcoin. Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest ...
0
votes
1answer
325 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 ...
1
vote
0answers
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
0answers
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?
0
votes
1answer
569 views

How to calculate APR using Newton Raphson

I'm have a computer program to calculate apr using Newton Rhapson. I imagine most mathletes can code so i dont imagine the coding being an issue. The solution is based on this initial formula ...
0
votes
1answer
30 views

How can I show that $u=e^{\sigma\sqrt{\Delta t}}$ in the binomial option pricing model

Given that $e^{r\Delta t}(u+d)-ud-e^{2r\Delta t} = \sigma^2\Delta t$ I would like to show that $u=e^{\sigma\sqrt{\Delta t}}$ I know I must somehow use Taylor's approximation $e^x = 1 + x + ...
3
votes
4answers
71k views

What is the formula to calculate Profit Percentage?

Let cost price of an item be $C$, selling price be $S$. Assume the seller makes a profit. Then profit would be: $P = S - C$. Now, what is the formula for calculating Profit Percentage? $P \% = ...
1
vote
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 ...
0
votes
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 ...
1
vote
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?
-4
votes
0answers
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 ...
-2
votes
0answers
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?
0
votes
0answers
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
0answers
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
1
vote
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 ...
0
votes
1answer
476 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 ...
2
votes
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 ...
0
votes
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 $s_0(1)=.15,\ s_0(2)=.10,\ \text{and} \ s_0(3)=.05$ ...
1
vote
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 $8.4\%$ ...
1
vote
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 ...
1
vote
2answers
32 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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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. ...
1
vote
1answer
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 ...
1
vote
0answers
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 ...
2
votes
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
2answers
285 views

A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual…

A farmer buys a used tractor for Rs $12000$. He pays Rs $6000$ cash and agrees to pay the balance in annual installments of Rs $500$ plus $12 \%$ interest on the unpaid amount. How much will be the ...
1
vote
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 ...
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
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 ...
0
votes
2answers
52 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 ...