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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0
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3answers
18 views

Find Rate when compound interest for successive years are given. [on hold]

A certain sum is lent a CI. The interest earned in 2 years is 272. The interest earned in 3 years is 439. Find rate of interest? Please tell me shortcut(if possible) of these type of questions for ...
-1
votes
1answer
40 views
+50

Calculating the principal

By which formula shall I calculate the amount for the following problem: Let say I want to buy a product, for which, I need to pay monthly installment of Rs500 , for 3 Months and rate of interest is ...
1
vote
0answers
13 views

Brownian Bridge Probability

Doing a project I have found in some papers that the (discretised) probability of the Brownian Bridge (which has $S(n)$ as initial value and $S(n+1)$ as final value, where S follows a Geometric ...
0
votes
0answers
46 views

expectation and variance of an implicit estimator

Suppose the following equation holds \begin{align*} p_2=\int\limits_{-\infty}^{\Phi^{-1}(p)}\int\limits_{-\infty}^{\Phi^{-1}(p)} \frac{1}{2\pi\sqrt{1-\rho^2}}\exp\bigg({-\frac{1}{2}\frac{x^2-\rho xy+...
0
votes
0answers
40 views

Expectation and Variance of an Estimator

Imagene following equation holds \begin{align*} p_2=\int\limits_{-\infty}^{\Phi^{-1}(p)}\int\limits_{-\infty}^{\Phi^{-1}(p)} \frac{1}{2\pi\sqrt{1-\rho^2}}\exp\bigg({-\frac{1}{2}\frac{x^2-\rho xy+y^2}{...
0
votes
2answers
62 views

How to solve the given problem of simple interest?

The problem statement is: What annual instalment will discharge a debt of 1092 due in 3 years at 12% simple interest? Now, what I know is Simple interest =( principal* Rate per annum*Time in ...
0
votes
0answers
10 views

How do we get parameters from distribution?

I've estimated the distributions for options prices using $F(X_n) = e^{rT}\frac{\delta C}{\delta X} + 1=e^{rT}[\frac{C_{n+1}-C_{n-1}}{X_{n+1}-X_{n-1}}]+1$ $F(X_n) = e^{rT}\frac{\delta^2 C}{\delta X^...
0
votes
0answers
13 views

How to find (GEV) distribution parameters with optimization?

I'm currently trying to replicate this study with python. http://pages.stern.nyu.edu/~sfiglews/Docs/RND_draft7.pdf The section I'm currently working on is between p.17-20 in the study. The study ...
0
votes
0answers
16 views

Formula or approach to isolate credit card debt for one purchase

I am looking for a formula or approach to isolate all interest on a credit card for one purchase, interest that would not be charged or compounded were a specific purchase never made. Consider the ...
0
votes
0answers
26 views

Black scholes model for down and out European call option using Monte Carlo

I tried to implement Matlab program computing the price of the European down and out call option using Monte Carlo and Euler discretization scheme. I have initial price S0=50, strike K=50, barrier ...
-1
votes
1answer
33 views

Determine cash price of Treasury bond

Determine the cash price of a 6% Treasury bond that matures in 14 months using the zero rates below. The Treasury bond has semiannual coupon payments. First, I calculated the coupon payments. There ...
1
vote
1answer
35 views

The hitting time $T-\tau^{l}$ has the same distribution as $\min\{\tau^{f},T\}$ regarding an Poisson Process.

Assume we have a probability space $(\Omega,\mathcal{F},\mathbb{P})$ where $\mathcal{F} =(\mathcal{F}_t)_{0 \leq t \leq T}$ is a Filtration, with $T < \infty$. On that prbability space we want to ...
0
votes
2answers
859 views

compound interest with geometric series

Were studying geometric sequences in maths and this came up as one of the questions: A mortgage is taken out for 150000 and is repaid annually with 20000 installments. Interest is charged on the ...
1
vote
2answers
43 views

Mathematic formula for increasing a number by a percentage every other time

I'm trying to create a formula where a number is increased by a certain percentage, then next calculation it is not, then the next calculation it is, then the next calculation it is not... Basically a ...
4
votes
2answers
69 views

What's the value of $5000 in 50 year if inflation is 2%?

My boss asked a simple question today but I couldn't find the right answer. He asked: If I had \$5,000 today in cash, the inflation is 2% year-over-year, then then what's its buying power (value) ...
1
vote
1answer
36 views

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 ...
0
votes
1answer
40 views

Interest rate, probability of tuition

A new government introduces tuition of 10.000 Euro/year, increasing yearly with the inflation rate of 2%. At the same time, a prospective 'perpetual student' enrolls at the university. She expects ...
0
votes
1answer
31 views

Bivariate lognormal distributions properties - Option pricing [closed]

I'm wondering if there is an easy way to compute the following expectation : $E[X(T)max(S(T)-K,0)]$ if $X(T)$ and $S(T)$ are two lognormals with parameters ($\mu_1,\sigma_1)$ and ($\mu_2,\sigma_2) $...
0
votes
1answer
846 views

Redington vs full immunization?

I understand that the present values and duration of liabilities and assets are required to be equal to each other under both cases, and furthermore for Redington immunization the convexity must also ...
1
vote
1answer
48 views

Probability of an Ornstein-Uhlenbeck process

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, with $\tau < \infty$. The following definition is ...
3
votes
1answer
1k views

Easy proof of Black-Scholes option pricing formula

I use this Book to read the option pricing in Black-Scholes model in pages 93-99, The proof of the formula given by $$c(s,t)= N(d_1(s,t)- Ke^{-rT}N(d_2(s,t)))$$ where $$d_{1,2}=\frac{\ln(s/K)+(r\pm \...
0
votes
0answers
24 views

Solving for the growth rate in a growing annuity formula

Firstly, If there is a better forum for this question, please help direct me. I looked in the quantitative finance forum, but someone already asked this and the question was closed because "its too ...
1
vote
1answer
39 views

Relationship between averages of $x^tx$ and $xx^t$ for column vector $x$

If we have data set $x$ as $m$ of $n \times 1$ vectors, and we know the average over index $m$ of $xx^t$ is $<xx^t> = C$, where $C$ is $ n \times n$ matrix. What is the average of scalar $ x^...
1
vote
1answer
1k views

Comparing annualised volatility from monthly and annual data

I fear there is a very simple answer to this question and its killing me that I can't see it. I am interested in calculating historical volatility: I have monthly index values starting in Jan 2005 ...
2
votes
1answer
122 views

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 $...
3
votes
4answers
155 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 ...
1
vote
2answers
68 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 ...
0
votes
0answers
11 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(...
1
vote
2answers
51 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 ...
1
vote
1answer
27 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?
0
votes
0answers
42 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 ...
0
votes
2answers
59 views

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

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?...
0
votes
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 ...
1
vote
1answer
811 views

Formula for APR with Odd Days

I need to programmatically calculate APR based on the following inputs: Principal Amount Number of payments (for example, 3 months loan is 3 if paying monthly, or 6 bi-weekly payments) Payment each ...
0
votes
2answers
37 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 ...
-2
votes
2answers
29 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?
0
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0answers
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 ...
-2
votes
1answer
61 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!**
-1
votes
2answers
61 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 ...
0
votes
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 ...
3
votes
1answer
38 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.
0
votes
1answer
107 views

Value of an Asian option with squared integral

Is it possible to find a closed form solution of the value of an asian option paying $(\int_0^T S_u du)^2 $ at maturity? I know there is no closed form solution if the payoff is of the type $(\int_0^T ...
1
vote
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 ...
0
votes
0answers
37 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'...
1
vote
1answer
68 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} = ...
2
votes
2answers
52 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: $$A_t=A_0(1 + r)^t$$ ...
0
votes
1answer
39 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 ...
0
votes
1answer
40 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 ...
0
votes
2answers
78 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 ...
0
votes
0answers
35 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 ...