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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2answers
62 views

Financial Mathematics problem

$i^{(p)}$ is the nominal interest converted p-thly i.e the total interest per unit of time paid on a loan of amount 1 at time 0 where interest paid in p equal installments at the end of each p-th ...
0
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0answers
23 views

Feynman-Kac for dividend stream

Suppose an asset value process $V_t$ that solves the PDE $$dV_t=\mu V_tdt+\sigma V_tdW_t \text{ with }\mu\in\mathbb{R},\sigma>0, W \text{ Brownian Motion}.$$ I want to price a dividend stream ...
1
vote
1answer
24 views

What was the Shopkeepers Loss

Here is the problem : A lady buys goods worth 200 from a shop where the goods are sold non-profit.The lady gives the shopkeeper a 1000 rupee note . The shopkeeper gets the change from the next ...
1
vote
0answers
29 views

Proof of “Law of one price” multi period market

I'm struggling with the proof of the LOP. The task is the following: There are two self financing strategies $\psi$ and $\theta$ in a multi period Market $(S^0,S^1,...,S^d)$ and $V_T^\psi$ = ...
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0answers
23 views

Theory of Interest example on annuities (need some clarification)

I'm going through Theory of Interest by Kellison in preparation for actuary exam FM. I'm wading through chapter 3 on annuities right now and I'm completely confused on how this example from the ...
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0answers
21 views

Ito rule for a given ratio and exponential

Helo, I have trouble performing the following differentiation following Ito calculus $$d(e^Z/B)$$ Given that $Z_t$ is a logarithm of a certain process and follows $$dZ=mu_zdt+sigma_zdW$$ $$dB=rBdt$$ ...
1
vote
2answers
35 views

Max price of a share

Company is planning to pay a dividend of 5\$ per share (dividend for previous year). Investor that wants to buy a shares of this company assumes that dividend will be stable (Thus will not change in ...
1
vote
1answer
30 views

Compound Interest : Clarification Of The Given Solution To This Problem.

I was solving some problems on CI from my textbook, there's a problem whose solution is given in my book but I can't understand it. Here is the problem - A man borrowed a sum of money and agrees ...
0
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0answers
23 views

Black Scholes partial differential equation; Derivation

I have an exam tomorrow and the issue is, my notes just really briefly mentions it. It doesn't even take a full 2 pages to mention the partial differential equation. I haven't even seen it in ...
2
votes
1answer
21 views

Annuity and Loan Repayment Question. Show the amount of Loan.

A loan was taken out on 1 September 1998 and was repayable by the following scheme: The first repayment was made on 1 July 1999 and was £1000. Thereafter, repayments were made on 1 November 1999, 1 ...
0
votes
1answer
23 views

Nominal Rates/Effective rate computation, confusion.

Given a nominal rate of 6% per annum. Change it to an effective rate per month. What I do is: $$(1+\frac {0.06}{12})^{12}=(1+i)^{12}$$ where $i$ is the effective interest rate per month. Now what ...
4
votes
1answer
62 views

Annuity that pays $t^2$ at time $t$ in arrears annually.

I am asked to show that such an annuity for $n$ years will be expressed as, $$\frac{2(Ia)_{\bar n|} - a_{\bar n|}-n^2u^{n+1}}{1-u}$$ where $u=\frac{1}{1+i}$ and $i$ is the annual effective ...
0
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1answer
24 views

How to price a supershare option; expected value of a payoff function?

I thought I'd be able to do this but evidently not. Let $S_t=S_0e^{(r-\frac{\sigma^2}{2})t+\sigma W_t}$ for all $t$. $W_t$ is a standard brownian motion. We have the following function for payoff ...
0
votes
1answer
24 views

Confused with “nominal” “convertible” rates; How to calculate a rate for an $n^{th}$ of a year?

The terms and how they're calculated is very unclear to me. My understanding of "nominal" is that this is a rate which isn't in unit time. i.e. $5\%$ per annum "is" in unit time (year) but $5\%$ ...
0
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0answers
21 views

Log-normally distributed variable; finding the distribution, mean and variable

The question here might be "when do you know it's best to use moment (generating) functions, when do you know you should integrate"? Basically, sometimes, we use "moment functions" and compare the ...
0
votes
2answers
48 views

Loan calculation; what went wrong?

I am attempting a question given as follows A loan is payable over 20 years by level installments of $\$1000$ per annum made annually in arrear. Interest is charges at $5\%$ per annum effective ...
1
vote
2answers
39 views

Annuity calculation; what is wrong with my calculation to the following question?

First off, I will be honest that I am rather confused not to much with the concepts but more of the language used in questions in finance. So I must acknowledge the possibility that I have ...
0
votes
1answer
43 views

Application of Integration on Investments

A small business expects an income stream of $\$300$ per month for a period of $9$ years. The income will be invested at an annual interest rate of $17\%$, compounded continuously. How much interest ...
0
votes
1answer
20 views

annuity certain, financial mathematics.

A 20 year annuity certain provides payments of 200 at time 1 year, 180 at time 2 years , 160 at time 3 years, and so on until the payments have been reduced to $ 60. Payments then continue at 60 ...
2
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0answers
42 views

Actuarial : “ Amortization - mortage”

What is the monthly payment for a $800,000 mortgage for the first 119 payments that is due in 10 years, has a 25 year amortization, at 5% interest? What is the amount of the 120th payment? I ...
0
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0answers
19 views

Present Value of an annuity payable with $n^2$ at $t=n$

Find the Present Value of an annuity payable with $n^2$ at $t=n$ , $t\in [0,n]$ What I have is: PV=present value $PV=1u+2^2u^2+3^2u^3+\cdots+n^2u^n$ I don't seem to know how to simplify it to: ...
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0answers
15 views

Have I understood the question properly? Annuities in Actuarial math

I am wondering if I have interpreted the language correctly in the following question The force of interest at time $t$ is given by $\delta(t) = 0.05-0.005t$ for $\leq t < 5$ and ...
0
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2answers
32 views

Investment in a treasury bill

You invested 968 710 in a treasury bill with the face value of 1 000 000 with 91 days left till maturity. After 60 days you have the option to sell it for 989 250. Which option is more profitable? My ...
1
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0answers
30 views

Black Scholes derivation; How and Why

A 15 mark past paper question essentially ask s me to derive the Black Scholes formula for pricing options. Let $S_t=S_0e^{(r-\frac{\sigma^2}{2})t+\sigma B_t}$ where $B_t$ is a standard Brownian ...
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0answers
2 views

Does anyone know about Forced rate of interest and present value $u(t)$? Because it's confusing!

my notes doesn't explain these concepts well and I am very stuck at this example solution. I don't get where the numbers come from at all. Suppose that the forced rate of interest is $\delta(t)$ ...
0
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1answer
17 views

How to determine loan payment and total price of a loan

Let's say, that we have borrowed a $100,000 for a 5 years, with 6% p.a. interest rate. How can one determine the value of a loan payment, if we are making payments every quarter and at the beginning ...
2
votes
1answer
36 views

How to integrate the following geometric brownian motion in Black-Scholes framework

As my previous questions make it obvious, I am very new to this field of mathematics and wondering if I am doing things right in the following question. Let $T \in (0, \infty)$ and consider a ...
-1
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0answers
9 views

After tax cash flow

Consider and asset that costs $360,800$ and is depreciated straight-line to zero over its $7$-year tax life. The asset is to be used in a $3$ year project; at the end of the project, the asset can be ...
0
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0answers
14 views

Are the interest accrued formula the same

Relating to my other post on Stack Exchange http://money.stackexchange.com/questions/56477/correct-way-to-calculating-interest-accrued-with-leap-year I'm wondering is example 1 and example 3 ...
0
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0answers
24 views

Call/Put options for Finance

I'm working with put/call options for a finance class, and am having just a little bit of confusion with the formulae. For call options, I know that the formula to determine price (C(0)) is equivalent ...
0
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2answers
26 views

What is the function $\mathbb{1}_{[t_i,t_{i+1})}$?

Hello, I am wondering if anyone knows what is meant in the picture above, where it says $\mathbb{1}_{[t_i,t_{i+1})}$. I see it is some sort of function probably dependent on $t_i,t_{i+1}$ but it ...
1
vote
4answers
155 views

$ax^{13}+bx^{12}+c=0$ by hand. Is there any chance?

I'd like to know if is there any way to get an approximation for the roots of the equation below by hand. $$ax^{13}+bx^{12}+c=0.$$ You are allowed to use calculator to calculate powers, logarithms, ...
-3
votes
2answers
66 views

Specific question about investment returns that needs someone smart to answer it! [closed]

OK, so I'm trying to work out the answer to a very specific question and for me it's complex maths. I'm sure for you mathematicians out there it's fairly everyday. If anyone can help I'd be very ...
2
votes
1answer
28 views

Financial Mathematics missing step for solution

I got the first line, but I got lost when they moved to the second step. Can someone please explain to me how they moved from the first to the second line? This I am aware of is just Algebra, but ...
1
vote
1answer
55 views

Kelly Criterion and mean variance optimization

I noticed that the Kelly Criterion resembles a ratio between the mean and variance in a continuous probability distribution. Now the mean and variance are important values in portfolio optimization ...
2
votes
0answers
60 views

Some really interesting problems in Mathematical Finance [closed]

I think this question fits on this forum or otherwise...........I stand to be corrected! I am preparing for my masters thesis in Mathematical Finance, come next year. I am thinking of taking on a ...
2
votes
1answer
65 views

Approximating the compond interest for a loan

A young boy (13 years old), son of friends of mine, is already very dedicated to mathemetics. He told me that, in the classical formula $$A=P\frac{i \,(i+1)^n}{(i+1)^n-1}$$ using his calculator he was ...
0
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0answers
11 views

Calculate portfolio weighted averages - smoothing curve

I'll first off apologize for not knowing how to ask this question properly, but I just can't come up with the right words which is likely why I can't find an answer. I have a fairly simple portfolio ...
0
votes
2answers
31 views

Finding common interest rate

My question is; How can I approach a common interest rate? (See example below for an explanation) Consider the example in the table below ...
0
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1answer
45 views

How would you find the profit maximising level of output of these 2 products?

Suppose a company produces two products A and B which have demand functions \begin{gather*} D_{A}=30-P_{A} \\ D_{B}=25-P_{B} \end{gather*} With $P_{A}$ and $P_{B}$ being their prices. If the combined ...
0
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0answers
15 views

Determination of Bond prices

Two 1000 dollar face value bonds are both redeemable at par, with the first having a redemption date 3 years prior to the redemption date of the second. Both are bought to yield 11 percent convertible ...
0
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1answer
12 views

Duration of a Continuously Compounding Investment

I have been asked to create a formula for the duration, 'd' of a continuously compounding investment for the time interval 0 <= t <= T. I know that the 'force of interest' $\delta$ = ln(1+i), ...
3
votes
1answer
92 views

Riskless Pricing of an European Option; How to calculate?

I don't know if this question could be asked/answered here but since there is a "finance" tag...I'll give it a shot. I am asked to show that the value of an option below obtained by 1. Risk-neutral ...
0
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0answers
20 views

Derive the Black-schole formula by solving the BSDE.

Consider the FBSDE as following: $$ \left\{ \begin{aligned} dS_t &=S_t\mu d_t+S_t\sigma dW_t \\ dX_t &=(rX_t+\frac{\mu-r}{\sigma}Z_t )d_t+Z_tdW_t \\ S_0 &=s\\ X_T &=(S_T-k)^+ ...
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0answers
45 views

How to calculate net % profit PER ANNUM for regular investment

I need to calculate a net % profit over a period of time with regular investments throughout this period. Data is as follows: ...
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0answers
34 views

Show that $e^{-rt}E\Phi(S_T)=S_0N(d_+)-Ke^{-rT}N_{d_-}$

Show that $e^{-rt}\mathbb E[\Phi(S_T)]=S_0N(d_+)-Ke^{-rT}N_{d_-}$ where $S_t=S_0e^{(r-\sigma ^2/2)t+\sigma W_t}$ for $t\in[0,T]$ , $W_t\sim \mathbb N(0,t)$ and $N$ is the cumulative density function ...
0
votes
0answers
10 views

Riskless Portofolio hedging

Consider the following one step model: (all options are EU) We need to find the price of the Call Option Make a portfolio of long $\Delta$ shares and short European Call. Using the portfolio ...
0
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0answers
9 views

Acceptance set is real subset of acceptance set corresponding to its risk measure

$\Omega$ non-empty, $\mathcal X := \{ X: \Omega \rightarrow \mathbb R | X \text{bounded} \}, ~ \mathcal A := \{ X \in \mathcal X | \text{sup}_{\omega \in \Omega} X(\omega) < 0 \}$. Why is the ...
0
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0answers
13 views

Building a riskfree portfolio for a 2step model

I completely understand the idea for a single step model. I simply make a portfolio of long $\Delta$ shares and short European Call. Question 1: In the example they used this portfolio when the ...
0
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0answers
14 views

Implementing a mathematical model of Exponential Moving Average

I learn best my reading about a concept and then trying to implement it using math and a programming language. Right now, I'm trying to implement an Exponential Moving Average indicator, but I'm ...