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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44 views

Math for Future Value of Growing Annuity

Am I working this out correctly? I need to verify that my code is correct... $$1000 \cdot \left(\frac{(1 + 0.1 / 12)^{40 * 12} - (1 + 0.06 / 12)^{40 * 12}}{(0.1 / 12) - (0.06 / 12)}\right)$$ ...
1
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1answer
15 views

Interest Accumulation - Geometric Sequence

Hello I have just worked a question in which I get an answer different to the answer in my book. The question states: If a person deposits 500 at the end of each month for 20 years at an AER of ...
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0answers
12 views

Show that the risk-neutral probability of a European call option ending in money is N(d2)

Show that the risk-neutral probability of a European call option ending in money is N(d2). I was trying to using Risk-Neutral Valuation Formula, but how to show the result is N(d2)? Thanks
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0answers
19 views

How to Maximize the Probabilty of Doubling Your Money!

This is an interesting questions I have heard mentioned a few times but don't know how to solve. Consider a geometric Brownian motion with some finite time horizon $T$ and a money market account with ...
1
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1answer
34 views

Changing variables for a partial differential equation

If I have the following systems of PDE \begin{align} u_t+x^2u_{xx}-\dfrac{h_1(t)}{h_0(t)}e^{-(v-u)}-\dfrac{h_0'(t)}{h_0(t)}=0\\ v_t-\dfrac{h_0(t)}{h_1(t)}e^{-(u-v)}-\dfrac{h_1'(t)}{h_1(t)}=0, ...
-2
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15 views

side information from equations

Consider system of equations (linear or nonlinear) generated from financial or physical problems. First, the solution to the equations will give information about the problem. Besides the solution, is ...
0
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0answers
38 views

Year to go calculation [closed]

After two months of sales a company sold 190 000 dollars and the last month is 95 000 dollars. The budget for the remaining of the year is 1 260 000. Consequently the company needs to do an average of ...
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0answers
19 views

financial mathematics: n financial assets in p states of the world.

Suppose there are two dates, $0$ and $1$. Suppose the world will be in one of $p$ states at date $1$, but the true state of the world at date $1$ is unknown at date $0$. Let there be $n$ financial ...
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0answers
31 views

Second Fundamental Theorem of Asset Pricing

It seems that there is a step missing in the proof of the second Fundamental Theorem of Asset Pricing in Shreve's Stochastic Calculus for Finance II: Does anyone know how to show the following: If ...
1
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0answers
22 views

Expected value of multiplied and squared Wiener Process

May someone help me how to calculate the following thing: E0[z^2[2] Exp[-2 z[2]] ] Where z[2] is Wiener process. How to find exact expected value? I am new to this stuff, not sure how to do this. ...
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1answer
14 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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0answers
20 views

Proposition from Oksendal Stochastic Calculus

I am reading Oksendal's Malliavin Calculus with applications to Finance and there is a part that I do not understand. First we have a proposition which is fine: If $\zeta_1$,$\zeta_2$,... are ...
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0answers
17 views

Financial Mathematics - Security Market Line and CAPM

not sure if this is the correct place to be posting this but I couldn't find a relevant stack exchange site (albeit this is part of my financial mathematics university course.) I have to write a ...
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0answers
24 views

Application of Ito's formula

I recently learned about Ito's formula and integral and now i have to do the following exercise, but I actually don't really know, how to start: Apply Ito's formula to prove that $$Z_t=exp(\sigma ...
0
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0answers
34 views

Black-Scholes derivation assumption contradiction

In many books and derivations of the Black-Scholes PDE one sees that $$\Pi=V-\Delta F \Rightarrow d\Pi=dV-\Delta dF$$ which implicitly assumes that $d\Delta=0$. Somewhere down the road one then ...
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0answers
18 views

Calculate breakeven point for business

I have a question with which I am somewhat stuck. Specifically I need to calculate the break-even figure for the following scenario. Peter is a business consultant. As well as providing ...
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0answers
12 views

Parameter estimation using characteristic function

Is it possible to do parameter fitting using log-returns data & the characteristic function(CF) in Matlab? I have been trying it on the Variance Gamma Scaled Self-Decompasable (VGSSD) model CF for ...
0
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1answer
51 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 ...
0
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0answers
33 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
28 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 ...
0
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0answers
5 views

Tangency portfolio in multiple periods model (Finance)

This might be a bit specific, but i'm stuck at this "little" problem. I've got a little problem now that i'm writing my BA thesis in dynamic asset allocation. It might be a very specific question, but ...
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1answer
60 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 ...
2
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1answer
35 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 ...
1
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0answers
22 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
27 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 ...
2
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1answer
28 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
42 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
9 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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0answers
10 views

dividend payout ratio??

Laurel company expects $3.81 earnings per share, has a 30% retention rate which is constant. It's equity cost of capital is 9%, which is also its expected return on new investment. Its earning are ...
0
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0answers
13 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
27 views

Corporate Finance Problem

A recent college graduate has taken a new job at Work LLC and since the company does not offer a traditional pension plan, she plans to take advantage of a tax-free investment account backed by a ...
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0answers
73 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
32 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
29 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
29 views

Annual Interest Rate

Your credit card has a balance of $6100 and an annual interest rate of 1%. You decide to pay off the balance over two years. if there are no further purchases charged to the card, a. how much must ...
0
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1answer
27 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 ...
0
votes
2answers
26 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 ...
2
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2answers
72 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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0answers
8 views

How to solve for maturity and interest when only given future borrowing & annual debt service

Consider this example: Debt Issued in 2015: 250,000 Projected Annual Debt Service due to Future Borrowings: 16,441 Debt Issued in 2016: 270,000 Projected Annual Debt Service due to Future ...
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1answer
27 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
79 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 ...
0
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1answer
17 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 ...
0
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1answer
21 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 $3n$ ...
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0answers
20 views

What is the present value of the annuity?

The effective annual interest rate is 3%. A perpetuity pays $3000 at the end of the first year and the payments are increasing 5% each year for the first 10 years. From then on, the payments remain ...
1
vote
1answer
52 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 ...
1
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1answer
30 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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0answers
29 views

Stop-Loss reinsurance, Determine the premium?

I have a question regarding the stop-loss reinsurance and the detail of this question is given as follow,
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1answer
38 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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0answers
47 views

Is $8^{W(t)}$ a martingale?

I have a standard Wiener process: $W(t)$ I need to determine if the following is a Martingale: $8^{W(t)}$ I know the two conditions for a Martingale; that the expected value of the absolute value ...
1
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1answer
35 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 ...