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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97 views

Expected value of multiplied and squared Wiener Process

Can someone help me how to calculate the following: $E0[z^2[2] \mathrm{Exp}[-2 z[2]] ]$ Where $z[2]$ is Wiener process. How to find exact expected value? I am new to this stuff and not sure how to ...
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1answer
101 views

Where to find Geman 1995's proof on Changes of Numaraire?

Geman, H., El Karoui, N., Rochet, J.C. (1995) published paper "Changes of Numeraire, Changes of Probability Measures and Pricing of Options", on "Journal of Applied Probability " vol 32, pg 443-458. ...
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1answer
352 views

Gremlins are investing in stock

Gremlin Industries will pay a dividend of \$1.80 per share this year. It is expected that this dividend will grow by 4% each year in the future. The current price of gremlins stock is \$22.40 per ...
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1answer
63 views

Girsanov's theorem and simulation of bond prices

Assume that we want to calculate the time $t=0$ price of a bond: $B(0,T) = E_P[\exp(-\int_0^T r_s ds)]$, where $r$ is the interest rate following the SDE $dr_t=k(\theta-r_t)dt+\sigma ...
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0answers
54 views

Why does the price term in Vega disappear for a European call option?

In my course, I have been asked to prove a number of statements about "the Greeks" from the Black-Scholes model for pricing a European call option with no dividends and a strike price of $K$. One of ...
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1answer
231 views

Option Pricing, A Practitioners Guide, Martingale's, Drift Change and Radon-Nikodym

Im slightly confused about this section of the booklet regarding option prices byIain J. Clark. 1) Regarding the part of obtaining a martingale property we require that the last exponential term ...
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1answer
95 views

Why is that a risk averse consumer buys the optimum insurance when there is actuarially fair insurance?

I've asked the same question at the Quantitative Finance StackExchange. Consider the following example: "As a risk-averse consumer, you would want to choose a value of x so as to maximize expected ...
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0answers
42 views

On finance problem: saving money

First of all, sorry for my pour English. Consider the situation: I'd like to save an amount $P$ of money every month for $240$ months consecutively ($m_1,\ldots,m_{240}$). The gain with money is ...
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0answers
200 views

Put-Call-Parity of Asian Options

I could need some help with deriving the put-call-parity for asian options. Let $S_t$ be the price of the underlying asset at time $t$ and set $Y_t = \int_0^t S_t dt$. Then the payoff of an asian ...
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1answer
40 views

Arbitrage opportunity for call price set on avarage

I have the following problem. Let C(K) be the market price of a Option Call with respect to the strike K. Let $C(100) = \frac{C(110)+C(90)}{2}$, then show that there exists an arbitrage opportunity. ...
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1answer
72 views

Finding the mortgage interest rate

Given the principal and term payment and number of terms, how can I calculate the interest rate of this mortgage? Been searching the internet for formulas, but to no avail. What is being calculated ...
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0answers
39 views

Partial differential of sharpe ratio of a portfolio with n ( =4 )equities with respect to the allocation for each equity.

Sharpe ratio is the mean of the daily returns from the portfolio divided (minus a constant )by the standard deviation of the return from the portfolio. Daily return of the portfolio is calculated by ...
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1answer
46 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 + ...
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0answers
310 views

What do two number on top of each other in square brackets mean?

Im currently going through "Universal Portfolios with Side Information" by Cover and Ordentlich [96]. Near the end of the paper, they provide a formula for calculating weights of a Universal Portfolio ...
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1answer
39 views

What is present value of the carbon expense for five years?

Suppose I have computed the cost of carbon per mile for my car at 0.009 per mile. Assume that the interest rate is 5% and that I drive the car 20,000 miles per year. What is present value of the ...
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2answers
117 views

Loan repayment calculations when interest compounding frequency does not match repayment frquency

Is there a formula for calculating loan repayments where interest is compounded daily, but repayments are made only monthly, for instance? I would like to be able to calculate the repayment amount ...
0
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1answer
144 views

Calculating Upside Potential

I have a story problem in my finance class. I can't figure out how to determine if my math is correct or not. The problem is: You purchase stock for 0.015 (one and a half cent) per share. You ...
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2answers
57 views

perpetuity valuation

A perpetuity paying 1 every 6 months has present value of 20. A perpetuity paying X every 2 years has the same present value. Assuming equal effective annual rates, what is X? I know X is 3.71 from ...
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2answers
115 views

Understanding basic stochastic differential equations

This is from a physics course in economics, the literature provides a bare minimum of mathematical explanations. I am trying to understand how to work with stochastic differential equations given in ...
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1answer
88 views

How can I calculate in Excel the price of something with inflation

I live in Argentina, and we have 30% anual rate of inflation. I am paying a car also, in a plan of 84 payments. Each payment has a 27.7% of "Administrative Costs". For example, for a ...
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3answers
243 views

Paying Debt Off in a year

I want to know how to calculate minimum fixed monthly payment needed in order to pay off a credit card balance within 12 months. I just want to understand the concept, and how to work around this ...
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1answer
23 views

Compounding interest + continuing eposit

If i deposit $3,000$ dollars every year for $10$ years, with an annual compound of $10 \%$ return, what is the formula that I would use to figure this out? I can't wrap my head around this. I have ...
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1answer
45 views

Accumulated value of annuity

An annuity pays 1 for the first n years, 2 for the second n years and 3 for the third n years with the effective annual interest rate $i$. Find the accumulated value of this annuity at time $3n$ ...
1
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1answer
87 views

mortage with monthly payment - mathematical modeling

$Question:$ Suppose that $x_n$ is the amount owed on a mortgage after n years, $\$m$ is the monthly repayment and $r$ is the annual percentage interest rate charged on the amount of the mortgage ...
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1answer
207 views

nominal rates and effective rates

I would like some help understanding some basic concepts about converting nominal rates into effective rates, and vice-versa. Some of the terms are a little confusing to me. Some examples I would ...
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1answer
50 views

Writing $A(t)=1+S_1S_2^{-1}$ as an Ito diffusion process.

Let $W$ be a Wiener process/Brownian motian and let $$ \begin{align} \mathrm{d}S_1 &= 2S_1(t)dt +3S_1(t) dW\\ \mathrm{d}S_2 &= 4S_2(t)dt +5S_2(t) dW \end{align} $$ Now I'd like to write ...
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1answer
61 views

What is the minimum Premium to be asked for a risk X?

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? I got some hint for this, but I could not understand ...
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0answers
66 views

Need help with partial derivatives

So here's the question: The monthly payment $P$ on a mortgage loan of $A$ dollars at an APR of $r$ (as a decimal) for $t$ years is given by this formula. $$P(A,r,t)$= ...
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1answer
38 views

Calculating duration and interest Rate for an investment

I'm trying to build a calculator to determine different Factors for specific Investments. I have a Formula to calculate the Grand Total, but I can't see any way to get either the Duration or the ...
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1answer
87 views

Question about the risk analysis.

In the above one can see the detail of this question, I am beginner in this kind of mathematics. I will be very greatful if any one can help me to solve them.
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2answers
207 views

find the amount of loan, principal and the interest.

A borrower is repaying a loan at 5% effective with payments at the end of each year for 12 years, such that the payment at the end of the first year is 220, at the end of the second year is 210 and so ...
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1answer
40 views

What is my interest rate?

Since my bank is not proud enough to display their interest rate on their home page anymore I am struggling to figure this out. I have an escrow account that looked like 639.14 960.77 1282.4 ...
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1answer
28 views

Find $R$ in $ B = \sum_{i=1}^{60}P_i\left(1+R\right)^{60-i} $ given $B$ and $P_1, P_2, …, P_{60}$

I don't have much training in financial math and was unsure of where to start tackling the following... Given a series of payments $P_1, P_2, ..., P_{60}$ which are increasing sporadically from one ...
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1answer
51 views

How to calculate two asset portfolio (problem finding the Population correlation coefficient)

I have two assets: A has an expected value of $12$ % and a standard deviation of $8$%. B has an expected value of $15$ % and a standard deviation of $12$ %. Suppose that we invest $75$ % in A and ...
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1answer
35 views

Find APR with loan balance

Here is the problem: L: original loan amount B: current balance after P periods P: number of periods that have been paid A: period payment **you do not know the number of periods remaining, so ...
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1answer
39 views

Short and long positions of call options

I am on part c), and I want to know: Since I am the seller of this call option, I sold it for 0.44, and the option is worth 1 dollar at expiration. Assuming the buyer wants to make profit he will ...
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1answer
36 views

Forward contracts

How do I do this one? I'm assuming it's not as simple as "the initial value is just $50 since thats what the stock sells at"
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1answer
21 views

Difference Between Generalized and Alternative Compounded Interest Equations

I am currently studying a chapter called "An Economic Interpretation of e" in my Economics class and we are finding amounts of compounded interest. I am not actually looking for help on the problems ...
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0answers
163 views

Engineering Economics Cash Flow Diagram

I have the following question and solution below. What I don't understand is why is the 100,000 seen as savings/revenue when clearly it is coming out of pocket? Additionally, the monthly loan payment ...
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1answer
37 views

Simple Interest troubling with new formula

I have learn in my school day Simple Interest can be calculated by $PNR/100,$ where $P$ is principle amount, $N$ is number of years and $R$ is rate of interest. For example, if I take$ P = 100, N = ...
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1answer
133 views

Interest Rate Tree in Matlab

I would like to calibrate a interest rate tree using the optimization tool in matlab. Need some guidance on doing it. The interest rate tree looks like this: How it works: 3.73% = 2.5%*exp(2*0.2) ...
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2answers
1k views

What's the math formula that is used to calculate the monthly payment in this mortgage calculator?

What's the math formula that is used to calculate the monthly payment in this mortgage calculator? I would like to know this math formula so that I can plug in the following values ...
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2answers
66 views

Find percentage increase per period to match a different percentage over the same period

Bob has an account with £1000 that pays 3.5% interest that is fixed for 5 years and he cannot withdraw that money over the 5 years Sue has an account with £1000 that pays 2.25% for one year, and is ...
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1answer
57 views

Bonds and zero rates

I don't get how to do this one, is a bond similar to compounding interest?
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1answer
82 views

Asset Depreciation - Logarithms

How many years would it take for the value of a car purchased at 30 000 to fall to 15 000 if it depreciates by 15% in the first year and 12% every year after that? This is not actually graded ...
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1answer
198 views

Formula for compound interest with N withdrawals

I have a calculator that allows users to see how much they need to save per period (month, year, etc) when putting money into a savings account. There are N withdrawals made in the end, with N ranging ...
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1answer
29 views

Financials Maths- Credited Interest

You invest £1,000 in an account for 5 years at 9% pa nominal. How much will you get at the end of the 5 years if the interest is is credited: a) annually; b) 6 monthly; c) 3 monthly; ...
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1answer
72 views

Math / Accounting problem

I have been stuck for over an hour with the following problem. In my textbook the following is written: "Suppose, for example, that Polany Manufacturing Company enters into a long-term lease July 1 ...
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1answer
38 views

finding the optimal decision value for two dependent random events.

I have been struggling with this problem regarding options (bermuda) for some time now. You can exercise this option on two seperate occasions namely at $T_1$ or $T_2$ with a strike price $E$. The ...
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1answer
25 views

Find sweet spot between 'Effect' and 'Resource Consumption'

This question is rather of economical nature. Let's say we have a function $f(x)$ that describes the result of some action depending on the amount of resource used $x$, for example: ...