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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Finding interest rate in simple annuities, without interpolation

How do you solve for i from this equation? 4.37={[(1+i)^4] - 1}/i
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26 views

Bactracking to find compound interest

I'm trying to find what percentage 5000 dollars compounding monthly over 120 months will be if the final sum will be 7000 dollars. So: 7000=5000(1+r/12)^120 When working backwards to find r I ...
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1answer
27 views

Proof of the Black - Scholes pricing formula for European Call Option

I want to prove the following The price of a European call option with strike price $K$ and time of maturity $T$ is given by the formula $\Pi(t) = F(t,S(t))$, where $$F(t,s) = ...
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8 views

EBIT and EPS indifference

how do i find the EBIT indifference level associated with the following to financial proposals and the individual EBIT and EPS of each plan... Plan A- $\$5,000,000$ raised by selling 160,000 shares ...
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2answers
47 views

Vanilla swap payoff

The payoff of a plain vanilla swap with respect to measure $Q$ is : $$V_{\mathrm{swap}}(t) = \beta(t) \sum_{n=0}^{N-1} \tau_n E_t^Q \left( \dfrac{1}{\beta(T_{n+1})} ( L(T_n, T_n, T_{n+1}) - k) ...
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1answer
59 views

Derivation of Black-Scholes equation by riskless portfolio

The following is a summary of the derivation of the Black-Scholes equation as given on wikipedia (http://en.wikipedia.org/wiki/Black-Scholes_equation#Derivation) - I have a question regarding the ...
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1answer
12 views

Formula for fitting step-wise increasing loan payments into a given term

My company is developing a product that helps people project out what-if scenarios for paying down their student loan debt. One of the government options for paying off debt is called the "graduated" ...
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2answers
61 views

How much more than will you pay on a 30 year mortgage than if you paid it all up front?

There are hundreds of loan calculators online but none of them tell me this, Say I take out a 30 year mortgage on a 80,000 dollar house for 4% interest. How much more than $80k will I spend at the ...
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1answer
27 views

Question on interest

I have a question about interest on a loan from a family member, and it is difficult figuring out. I borrowed \$35,000 @ 3.5% in June, 2013, and here's the break down of the payments I've made: ...
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1answer
54 views

What is the purpose of a trailing minus sign?

I cashier at a grocery store and the POS system we use (SurePOS by IBM/Toshiba) uses trailing minus signs for all of its representations of negative numbers. Examples: Coupon being rung up: ...
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66 views

In stochastic calculus, why do we have $(dt)^2=0$ and other results?

I'm doing actuarial problems of Exam MFE and it covers some of the stochastic calculus (like Ito's Lemma). One of the frequently used results are the so-called "multiplication rules": $(dt)^2=0$ ...
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1answer
21 views

Break Even Point

Suppose that x thousand units of a product will be sold when the price is p(x) = 50 - 1.25x dollars per unit and the cost of producing x thousand units is C(x) = 20x + 100 thousand dollars. a) What ...
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19 views

Multi year installment loan. Know monthly compouning rate, wish to find simple equivalent rate

First of all, thank you very much for your time. Since I have no math background whatsoever, please pardon me for my ignorance (which is not bliss here). I am not looking for the formula to get a ...
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1answer
11 views

Deffered annuity with perpetuity

An annuity immediate has $40$ initial quarterly payments of $20$ followed by perpetuity of quarterly payments of $25$ starting in the eleventh year. Find the present value at $4\% $ convertible ...
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0answers
9 views

Time homogeneous asset dynamics model

I'm studying asset process. As i know, Black scholes model and CEV model is time homogeneous diffusion model. Are there time homogeneous model ???
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2answers
26 views

Basic question mathematical finance, law of one price in single period markets.

I am reading Pliskas Introduction to mathematical finance. And I am at single period models. It is the law of one price I am having a hard time of understanding. I have some questions about this: ...
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1answer
30 views

Dynamics of short rate in HJM

According to a simplified HJM framework, we have: Forward Rate: $f(t,T)=\sigma W_t +f(0,T) +\int_0^t{\alpha(s,T)}ds$, where $W_t$ is brownian motion. Dynamics of forward rate: ...
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53 views

Altering a Lease Calculation to take into account an upfront payment

I am trying to find the interest rate of a lease if we know the monthly payment amount but have an advance payment. I have found a site with part of the calculation we need (Scenario 2 on the link ...
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1answer
18 views

Method to calculate the best way to repay two different loans given a set amount of money per month?

Given two (or more) loans of different balances and interest rates and a single amount of funds available per payment period, is there a way to calculate the best way to split the available funds to ...
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1answer
22 views

the intuitive difference between expected utility and utility of expected profit in a gambling game

What is the intuitive difference between expected utility and utility of expected profit in a gambling game ? Which one is the "usefulness of the game" to a player ?
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2answers
64 views

Compound interest with a compounding interest rate

I have an investment which pays 3% interest (r) annually but it also increases the interest rate every year by 5% (g). I re-invest all interest payments at the start of each year. How many years (t) ...
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1answer
40 views

Shape of utility function

I have read in a paper (http://www.public.asu.edu/~kirkwood/DAStuff/refs/risk.pdf) that the shape of the utility function depends on the attitude towards risk. My question is does not it also depend ...
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55 views

Attitude toward risk taking and the exponential utility function [closed]

I want to know some reference/book on the following topic: "Attitude toward risk taking and the exponential utility function". Thanks in advance.
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1answer
39 views

Discrete Fourier Transform Interpretation

Using Mathematica I took the Discrete Fourier Transform (DFT) of a vector whose entries are volumes of a particular stock. The power spectrum is plotted below: There are two questions that I have ...
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2answers
24 views

Deriving Geometric Brownian Motion's solution?

The Black Scholes model assumes the following underlying dynamics, known as Geometric Brownian Motion: $$dS_t=S_t(\mu dt+\sigma dW_t)$$ Then the solution is given: ...
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28 views

Finding inflation rate

This is my maths problem: A car cost $19,335 in 1989, and it is worth $40,000 in today's money, adjusting for inflation. How much is the inflation rate? What ...
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2answers
94 views

Partial Differential equations and applications- Reference request

I will be taking up a PDEs course next semester and would like to find some good references. The topics covered in the syllabus is given below. Partial differential equations: Conservation laws, ...
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1answer
54 views

What is the Most Efficient Way to Calculate the Internal Rate of Return?

I have built a program that prices financial assets and it does this in part by calculating the IRR. The problem is that it does not run as quickly as I would like it to. I currently use the ...
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25 views

Betfair Odds Percentage Movements & Hedging

I want to determine if the odds on Betfair have decreased by a certain percentage and then calculate the hedged profit when hedging on that percentage, but it's made tricky by the fact that decimal ...
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2answers
40 views

Bond valuation question

Trying to solve the following question, but I am a bit stuck. The 2IFM1 Corporation has two different bonds currently outstanding. Bond M has a face value of $\$20,000$ and matures in $20$ years. ...
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1answer
34 views

Actuarial Science - Amortization

Kevin takes out a $10$-year loan of $L$, which he pays by the amortization method at an annual effective interest rate of $i$. Kevin makes payments of $1000$ at the end of each year. The total amount ...
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1answer
35 views

Math Finance: Arbitragefree Pricing Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if there exists a riskneutral equivalent martingale measure Q~P, under which the discounted asset price ...
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2answers
42 views

Solving $a_1x_1 + \cdots +a_nx_n = b$

I'm glad to ask my first question on the maths site! So here we go. I'm trying to set up prices right now and here is my problem : I know that my customer has a certain amount of money available. ...
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23 views

Matlab Optimization problem with Matrices

I'm trying to solve an optimization problem in Matlab. The equations you will find below. Problem is it is all Matrices, and I have no idea which solver to use for that. w is of size (n x 1) mu_BL (1 ...
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41 views

Solutions to exercises in Nelson's “An Introduction to Copulas”

I am paving my way through Nelson's "An Introduction to Copulas". The book has exercises (quite good actually), but no solutions. Does anybody have a solution manual for (some of those) exercises? ...
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2answers
32 views

Homework question compound interest

If $ \$ 6000$ are invested at 7% compounded continuously, what amount after 2 years? I know how to set it up but at one point I get lost $$A=Pe^rt$$ $$A=6000^{0.07}(2)$$ Somebody please help.
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1answer
104 views

Calculating FV and Payments for an inflation indexed savings (graduated annuity)

I have searched high and low but I can't seem to find the right calculation to work out exactly what I need. What I need is an equation. To work out the FV of an inflation indexed savings plan. The ...
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1answer
28 views

Is there any way to find compound interest easily?

What will be the compound interest on a sum of Rs. $25,000$ after $12$ years at the rate of $12%$ per annum?
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1answer
50 views

Questions about the field Business Mathematics

What interests should one have to decide to pursue a master's degree in Business Mathematics? Which subjects are related with this field? What career opportunities are there having this master's ...
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51 views

Finding criteria for a household financial budget falsification

I’m working on a financial problem about budget of households. Households in a state fill a form about their net budget in every year and our insurance company investigate their financial status and ...
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13 views

Finding the continuity of the mapping of a solution to a PDE to its partial derivative

Here is a modified version of the Black-Scholes PDE: $\frac{\partial \phi(t,S,i)}{\partial t}$ + $r_iS\frac{\partial \phi(t,S,i)}{\partial S}$ + $\frac{1}{2} \sigma^2_i S^2 \frac{\partial^2 ...
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0answers
36 views

Calculating VaR, CVaR

I am supposed to calculate the value at risk and expected shortfall of an asset with revenue given by a density function: $f(x)=0.5\exp{(-|x-0.05|)}$. My workings: If I understand it correctly, than ...
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1answer
50 views

How to find the expectation value?

Suppose that an insurer has an exponential utility function $u(x)=−2e^{-2x}$. What is the minimum premium $P^{-}$ to be asked for a risk X? After solving this we reached the following, So,only ...
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1answer
68 views

Fair Value Of a Call Option

I am dealing with the following question/information (which may not be complete): The price of the underlying asset is $100$. European call option with exercise price $150$ in a year. The price of ...
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1answer
23 views

the relationship between fractional difference and ACF of a time sequence

When reading the GARCH modeling part of book Analysis of Financial Time Series, I read the following statement. In specific, I do not understand how does the author ...
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2answers
63 views

Figuring out a growing monthly payment based on constraints

I'm working on a problem where I need to calculate the monthly payments for a loan given a few constraints. These payments grow at a constant rate every 2 years (24 months) and pay off the entire loan ...
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1answer
55 views

Derive the Black– Scholes formula for the European call option.

Consider the standard Black–Scholes model. Derive the Black– Scholes formula for the European call option. thanks for help.
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1answer
31 views

Including future value into calculation of interest rate

There is a discussion on this page regarding the back-calculation of the interest rate, given the other parameters of a typical finance calculation (present value, repayments and term length). Three ...
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2answers
63 views

How to rearrange this equation to solve for 'r' in closed form?

I'm taking a finance course, and I can't afford the financial calculator which can be used to solve this, so I would like to know how to solve this algebraically by hand (I don't care if it uses ...
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68 views

I want the solution of Bjork Arbitrage Theory in Continuous Time

I am working on Financial Mathematics and also work on Bjork Arbitrage Theory in Continuous Time sometimes I have problem in the Exercises. Does any body know about solution of this book ?