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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Calculation of $\ln\left( \frac{S_{1}(t)}{S_{2}(t)}\right)$ where $S$ are stocks

Assume we have a probability space $(\Omega,\mathcal{F},\mathbb{P})$ where $\mathcal{F} =(\mathcal{F}_t)_{0 \leq t \leq \tau}$ is a Filtration of an incomplete finance market with stocks $S_j(t)$ for $...
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Generalized First Price Auction or Generalized Second Price?

Sorry if I ask the same question again but in the other post I'm not able to edit my question because I wasn't using an account. By the way, the question: I'm running some tests to decide which type ...
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19 views

First Price Auction or Generalized Second Price

I'm running some tests to decide which type of auction is better. My settings are set randomly, I mean that budgets are random, advs' value are random .... My goal is to maximize the revenue. Which ...
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0answers
9 views

Calculate the yield curve spread to forward rates [closed]

First, using the table below I found the yield cure spread to spot curve is 0.88% using the following formula: $$100 = \frac{CF_1}{(1+\text{Spot}_1+SPD)^n} +\cdots+ \frac{CF_n}{(1+\text{Spot}_n+SPD)^...
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4answers
145 views

Compound interest: why does everyone get it wrong?

The compound interest formula is: $$A_t=A_0(1+r)^t$$ There is a simple derivation for this which works by starting with $A_1$ and then considering $A_2$ and then extrapolating. The above formula can ...
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0answers
10 views

Is there a way to view stochastic discount factors in a Lp space?

If there is, is it possible to think of T(m) = E[mx] as a bounded linear functional over Lp? Note: x here is the payoff random variable and m is the stochastic discount factors random variable. And T(...
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2answers
59 views

Definition of self-financing strategy

Consider a portfolio of two assets with prices $S_t$, $B_t$ and holdings $\Delta_t$ and $E_t$ respectively. So the portfolio value is $$ \Pi_t = \Delta_t S_t + E_t B_t$$ The portfolio is defined to ...
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2answers
47 views

Probability of N unrelated events, each with different probabilities, what is the chance X number of outcomes occur

Given the probability of N unrelated events, each with different probabilities, what is the chance X number of outcomes occur? Said specifically there are 8 unrelated contracts, what is the chance a ...
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1answer
24 views

The future and present value of an annuity of $100 payable at the start of each quarter for 15 yrs if the rate is 12% compounded quarterly is?

What are the future and present value of an annuity of $100 payable at the beginning of each quarter for 15 years if the interest rate is 12% compounded quarterly?
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31 views

Calculation probability of dynamic process model of capacity

I found this place really helpfull and now I got my first own question I cant solve. I want to unterstand the calculation of an Article im reading. Therefore we define a capacity process $C$ in a ...
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2answers
53 views

I have a 45% chance of losing money on my stock market trade and a 55% chance of winning.

I have an average $55\%$ chance of losing money on a given stock market trade and thus $45\%$ chance of winning. I want to know what my chances are of having $1$ through $12$ consecutive losing trades?...
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1answer
24 views

How to calculate the cost of debt

The bonds of ABD Ltd have a face value of $1000$ with one year remaining to maturity. The bonds pay coupons at the rate of $10\%$ p.a. If the current market price of the bonds is $1018.50$, what is ...
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2answers
27 views

principal calculation in compound interest [closed]

A sum of money at compound interest amounts to $\$3920$ after one year and $\$4390.4$ after two years. How do you find the principal?
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15 views

Finding the rates of investment of every variable in a multi-variable equation to get the most efficient output.

Math is said to be about teaching problem-solving skills for all problems, but a lot of problems have too many factors to reliably get a result. So how exactly do you get the answer to an equation ...
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2answers
36 views

Present values with denser discounting

With an annual interest rate of 10%, the present value of 100 dollars received one year from now is $PV = \frac{100}{1.1}=90.91$. If instead the 100 dollars is received in two installments of 50 ...
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2answers
55 views

Present value of a perpetuity with continuous stream of cash flow

The present value of a perpetuity (cash flows paid at the end of each year) is $PV = CF / r$ where $r$ is the interest rate. This formula is proved in the book that I'm studying (Principles of ...
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1answer
60 views

showing a process martingle from ito's lemma.. [closed]

**by ito formula, Ft: filtratoin $M(t) = (aB(t) - t) \exp( 2B(t) - 2t ) $ find constant a for $M(t)$ to be a martingale plz help!**
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Rounding puzzle loses a penny when dealing with money values

Say, you have three people and they want to buy something that costs £100. They chip in the following amounts: Person1: £60.00 Person2: £30.00 Person3: £10.00 They buy the thing, and work out that ...
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1answer
33 views

Does Change of Numeraire same as Change of Measure?

Does Change of Numeraire same as Change of Measure? It is a bit confusing since both looks same. Do they have same meaning, or just mathematically alike.
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0answers
11 views

Why is a risk neutral measure unique in a discrete time market with continuous states?

Why is the radon nikodym derivative unique in a discrete time market with continuous states? By radon nikodym derivative, I meant the derivative with respective to the risk neutral measure and the ...
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0answers
35 views

Formula for continuous interest with compounding principal

I'm trying to figure out a formula for compounding interest along with a compounding principal that is added to every month and paid in full (please bear with me as my terminology may be incorrect). I'...
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1answer
55 views

Credits - cost of borrowing

Can you help me with this exercise ? Totally don't know how to solve it. Im good in math but not in financial issues. I would be grateful for any help :) Enterprise ABC has contracted a credit for ...
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1answer
63 views

Why is the Black-Scholes PDE called degenerate

I am working in Mathematical Finance and know that the Black-Scholes PDE is degenerate at $x=0$ (I assumed that this was because at 0 the convection and diffusion terms vanish and one is left $V_{t} = ...
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2answers
50 views

Compound interest: how to use the textbook formula?

To derive a general compound interest formula we can say: $$A_1=A_0 + rA_0=A_0(1 + r)$$ $$A_2=A_0 + rA_0 + r(A_0 + rA_0)=A_0 + 2rA_0 + r^2A_0=A_0(1 + r)^2$$ and so on. In general: $$A_t=A_0(1 + r)^t$$ ...
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1answer
38 views

Loss probability and VaR

I would like to estimate Value-at-Risk analytically and through delta-gamma aproximation. I don't know if my idea is ok, but i would like to build a portfolio of European option. Suppose that in this ...
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1answer
37 views

Value price of Bond

Hi, can you help me with this exercise ? I'm good in maths but don't understand these financial problems. I would be grateful for any help One morning, Mr. Kowalski purchased a two-year bond with the ...
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0answers
33 views

How to calculate optimal monthly withdrawals from an investment with compound interest [migrated]

I have 1.25M dollars. I want to put it in an investment with 60% annual return paid monthly and re-invest the interest to achieve compound interest. After 15 years, my principal would have grown to ...
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2answers
70 views

Interpretation of correlation (coefficient)

In an discussion we were confronted with a very special opinion about correlation in respect of financial assets. The widely used correlation coefficient is used here to give an idea about how ...
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0answers
32 views

Mortgage amortization schedule issue

I wrote a program that does a mortgage schedule. When comparing it with other online sites that are doing the same calculations I seem to be off $0.01 on every payment except the first. Here is an ...
2
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3answers
30 views

How to model a checking account with continuous-time compounding?

"Say you have a bank account in which your invested money yields 3% every year, continuously compounded. Also, you have estimated that you spend $1000 every month to pay your bills, that are withdrawn ...
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2answers
22 views

Replication a options portfolio

I'm not too sure I'm going about answering this question correctly. I have used the following to derive my answer. I see that the portfolio above is a combination of a short-call(strike price 20) ...
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1answer
30 views

What is the difference between these two formulas that price a stock? [closed]

What is the difference between these two formulas? They are both related to the price of a stock in the black-scholes model. The fact that the second one uses $t$ as a subscript which means it's not a ...
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0answers
23 views

Conditional expectation and set times random variable??

On page 62, what in the world is the meaning of equation (5.2)? $\mathcal{F}_t$ is a $\sigma$-algebra, so $Z_t \in \mathcal{F}_t$ is a set. $X_u$ is a random variable, so what is $Z_t X_u$?
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28 views

Linear functional and Riesz' Rep theorem

On page 59 in these Finance notes, a positive linear functional is defined, and then Riesz' representation theorem is used (the scalar product is defined on bottom part of page 56). I don't ...
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2answers
65 views

help for an integral

I need help calculating this integral: $$\int_0^x \frac{2(e^{\gamma u}-1)}{(\gamma+\kappa)(e^{\gamma u}-1)+2\gamma} du$$ I tried with the integration by parts but the situation seems to get ...
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0answers
31 views

implied volatility

I have a question about calculating the implied vol. Assuming the implied vol that a option will expire in 1 day is $\sigma_1$, and the implied vol that the option will expire in 2 days is $\sigma_2$. ...
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1answer
20 views

Transpose Present Value of an Ordinary Annuity Formula for Interest Rate

I'm having trouble transposing the formula for Present Value of an Ordinary Annuity in order to find the interest rate. The formula is: Where P=Present Value of an Ordinary Annuity PMT=Payment ...
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2answers
29 views

Why does $\operatorname{var}\sum_{i=1}^n w_ir_i=w^\top\Sigma w$ hold?

Let $r_1,\ldots, r_n$ be real-valued random variables, $\Sigma$ be the covariance matrix, $\mu_i=E(r_i)$, and let $w=(w_1,\ldots,w_n)^\top$ be an arbitrary vector in $\Bbb{R}^n$. Why does $$\mathrm{...
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1answer
32 views

Question on share valuation involving rate of return and dividend

BLC industries is expected to pay a dividend of $1.50$ and the dividend is expected to grow at a constant rate of $7$%. This stock is $15$% less risky than the market as a whole. The risk-free rate ...
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1answer
38 views

How to find the standard deviation from the given information and what is $B(0)$ equal to?

Assume that the risk free rate is $0$ and that the stock price is given by the equation $S(t)=6e^{2t+2B(t)}$ where $B(t)$ is the standard Brownian motion. Determine the price at time $0$ of the ...
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1answer
34 views

Nominal rate of interest for interest reinvested.

Sally lends $10000$ to Tim. Tim agrees to pay back the loan over $5$ years with monthly payments at the end of each month. Sally can reinvest the the monthly payments from Tim in a savings account ...
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1answer
13 views

Interest re-invested given Force of interest

Jason deposits $3960$ into a bank account at $t=0$. The bank credits interest at the end of each year at a force of interest $\delta_t=\frac{1}{8+t}$ Interest can be reinvested at an annual ...
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1answer
39 views

Re-investment of interest

Thomas invests X into Fund $1$ at the beginning of each year for $10$ years. Fund $1$ pays interest annually into Fund $2$. Fund $1$ earns $7$% annually while Fund $2$ earns $6$% annually. After $10$ ...
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1answer
12 views

Net present value given cash flows for 2 different projects

Project P requires an investment of $4000$ at time $0$. The investment pays $2000$ at time $1$ and $4000$ at time $2$. Project Q requires an investment of X at time 2. The investment pays $2000$ at ...
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3answers
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question on force of interest with investment at 2 different times

You invested $500$ on Jan $1$ $2012$. To save for this amount, you invest $x$ on Jan $1$ $2008$ and $2x$ on July $1$ $2008$. The force of interest is $\delta_t=0.02t$ where $t$ is $0$ on Jan $1$ $...
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1answer
33 views

Buyer's price in terms of risk-neutral measures

Let us consider a finite arbitrage-free market model $(B,S)$, where $B$ is a bank account and $S$ is a share. Let $X$ be a claim. We define a buyer's price of $X$ as follows:$$\Pi^b_0(X)=\sup \lbrace ...
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0answers
13 views

Help optimizing payments on 3 loans - planning to use AMPL program but I have math problems first.

So the basis is that I have 3 loans with different interest rates and different principal amounts as well as different minimum monthly payments and different amortization (is that the right word? Time ...
3
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2answers
78 views

If A can either increase by 100% or decrease by 50% with equal probability, what will be the arithmetic mean return over n periods?

This is more of a finance related question but deals with some discrete probability and or combinations. The question goes like this. If you buy stock A, and it has a 50% chance of going up 100% in ...
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0answers
27 views

subaddivity of VaR

It is known that the VaR (Value at risk) doesn't fulfill subadditivity, i.e. $VaR(X)+VaR(Y) \le VaR(X+Y)$. But for elliptical distributions subadditivity is true. Questions: (1) Which ...
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1answer
49 views

Differentiating an Option Payoff

Okay this is probably going to be an extremely easy/straightforward question but I thought I should post it here just to double check. Suppose I have a payoff $\Phi = (S_{T}-K)^{+}$. Now let's say I ...