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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17 views

Semi Annual Deposit Compounded Quarterly

A son planned to endow 1000000 to his son on his son's 21st birtthday. How much is his semi-annual deposit in a special account that earns 5% compounded quarterly if the first deposit was made when ...
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2answers
74 views

Retirement Fund with Interest

A young woman 22 years of age has just graduated from college. She accepts a good job and desires to establish her own retirement fund. At the end of each year thereafter she plans to deposit 2000 in ...
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1answer
30 views

Interest with Inspection Fee in Promissory Note

A man borrowed from a bank a promissory note that he signed in the amount of 25000 for a period of one year. He received only the amount 21915 after the bank collected the advance interest and an ...
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1answer
27 views

Compounded Quarterly

Money borrowed today is to be paid in 6 equal payments at the end of 6 quarters. If the interest is 12% Compounded Quarterly. How much was initially borrowed if quarterly payment is $2000 Answer is ...
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1answer
231 views

Where does this characterization of an annuity immediate come from?

I'm looking through my notes, and I don't see anywhere that an annuity immediate can be defined as $a_n = \frac{1}{a(1)} + \frac{1}{a(2)} + \cdots + \frac{1}{a(n)}$. I've always seen it as $a_n = v ...
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1answer
37 views

Money doubling in value

I understand this maybe a question for http://quant.stackexchange.com/; but I believe the math is simple enough to understand. In How many months at an interest rate of 1% per month does money have ...
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0answers
14 views

Mean and variance regime-switching model

Suppose we have the following model for stock price: $$ X_{t}=X_{0}\exp\left(\int_{0}^{t}(r-\frac{1}{2}\sigma_{\epsilon(s)}^2)ds+\int_{0}^{t} \sigma_{\epsilon(s)}dW_{s}\right) $$ This follows a normal ...
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32 views

What math preparation is needed before reading the mathematical method in financial markets?

What math preparation and books are needed before reading the mathematical method in financial markets by Marc Yor if i need to study the whole book? This is one of the advanced finance book
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1answer
25 views

Understanding the solution to a basic annuity problem involving an unknown interest rate

The following is the problem and the solution: Before looking at the solution, here is how I approached the problem: Let $X$ be the amount that each child receives. (i) and (ii) imply that ...
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1answer
26 views

Question related to profit/loss.

Guys see this question: For what sum should goods worth Rs. 1150 be insured at 8% so that in case of loss the owner may recover the premium as well as the goods? I can't understand the meaning ...
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3answers
45 views

Is this equation a parabola or a hyperbola?

In a 1972 paper by Robert Merton, the following equation is derived: $$\sigma(\mu;A,B,C,D)=\sqrt{\frac{A \mu^2-2B\mu+C}{D}}$$ This is known as the Markowitz frontier in finance. When this is ...
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2answers
66 views

Simon invests $\$6000$ and it's compounded semi-annually for ten years

Simon invests $\$6000$ and it's compounded semi-annually for ten years, at $8\%$ per annum. What is the amount of the investment at maturity? I did $(6000)(1.08)^{20}$, and got a completely different ...
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1answer
30 views

Looking for a “Black-Scholes-esque” expression for $E[\max(V-K,Y)]$

In Hull (2008, p. 307), the following equation is found (Eq. 13A.2): $$E[\max(V-K,0)]=\int_{K}^{\infty} (V-K)g(V)\:dV$$ Where $g(V)$ is the PDF of $V$, $K$ is a constant, and both $V,K>0$. He ...
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1answer
11 views

Show that for martingale and predictable process, it is not possible to gain almost surely in some step

Let $X_t, t = 0, 1,\ldots, T$ be a martingale and $V_t, t = 1,2,\ldots, T$ a predictable process, I want to show that for $t = 1,2,\ldots, T$ we have $$ V_t\cdot (X_t - X_{t-1}) \ge 0 \textrm{ ...
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1answer
33 views

Currency Conversion Math

Here is my question. If I have the following exchange rates: 1 Euro = 1.13 USD 1 British Pound = 1.56 USD Is it possible to calculate the value of Euros to British Pounds given that I only have ...
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0answers
26 views

Annuity formula proof $\frac{a_{\overline{n}|}}{a_{\overline{k}|}}$

I have the actuarial exam FM in 2 days and there is one more thing that I would like to understand. I cam across a problem having to do with identities and this is the following. A perpetuity ...
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1answer
43 views

Distribution of Black Scholes call option price at time 0<t <T

Does anyone know how to find the probability law (distribution) under P* of a Black Scholes Call Option price $C_t$ for $0 < t < T $? (Under P*, $ dC_t = \frac{\partial c}{\partial s}\sigma S_t ...
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0answers
35 views

Compound Interest Calculation (Years + Months)

My question is with regards to the calculation of "Compound Interest". I have the formula below where I would get an answer to the total value of the investment over a period of "years". $A$ = ...
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0answers
19 views

How to do fixed point iteration with matrices?

I am trying to follow solution to solve $$\min[\mathbf{z},\mathbf{q+Mz}]=0$$ by fixed point iteration. If $\mathbf{M=C+B}$ then a recursive algorithm with $k$ showing the iteration can be written as ...
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1answer
25 views

Maximizing the Sharpe ratio by finding the optimal weights

In calculating the Sharpe Ratio: $S = (\frac{\bar r_p - r_f}{\sigma_p})$ Where: $\bar r_p$ = Portfolio return (See below) $r_f$ = Risk free rate = 0.03 (for simplicity) $\sigma_p$ = Portfolio ...
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0answers
62 views

Why hold $Stock=(1−Delta_{put})$

You would like to be holding a protective put position on the stock of XYZ Co. to lock in a guaranteed minimum value of USD 80 at year-end. XYZ currently sells for USD 80. Over the next year, the ...
2
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1answer
28 views

how to derive the stochastic differential equation of this process

How can I derive the SDE for the vasicek model : $$r_t = 0.1 + 0.1 e^{-t} + e^{-t}\int_0 ^t e^s dB_s$$ From observation, the SDE vasicek's model is such that: $$dr_t = b(a-r_t)dt + \sigma dB_t$$ ...
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120 views

What is the name of this symbol ( ┐) and what does it mean

Sorry bout the dumb question, it's just that I'm taking a mathematical finances class and the teacher started using this symbol today but I've never seem it before, was trying to google it but don't ...
2
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1answer
109 views

Stochastic calculus book recommendation

I'm a quantitative researcher at a financial company. I have a PhD in math, but I'm an algebraist, so I only took the two required analysis courses in grad school (measure theory for the first, and I ...
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1answer
101 views

Calculus in Economics

A company is planning to manufacture and market a new headphone set. After conducting extensive market surveys, the research department provides the following estimates: Marginal costs function: ...
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0answers
12 views

Sample variance matlab geometric brownion motion

I have a question about the geometric Brownian motion. I want to sample many paths and then showing that the sample variance equals the exact variance: $$\mathrm{Var}\left[S(t)\right]=S_{0}^2 e^{2 \mu ...
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3answers
48 views

Financial Mathematics, Simple interest question. Help.

Laurie deposits $\$60,000$ in a bank at $5\%$ interest per annum. Andrew deposits $\$40,000$ in bank at $8\%$ per annum. How long wil it take, by simple interest, for Andrew to have more money ...
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1answer
14 views

Improper integral confusing step

The following passage is in my textbook: $$A(S) = \int_0^{\infty} f(E) \max(S-E,0)dE$$ This simplifies to $$A(S) = \int_0^{S} f(E)(S-E) dE$$ Now this is from a finance textbook so it might ...
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1answer
66 views

Lemme itô and Martingale [closed]

I want to to find values of $a$, $b$ such that the process: $$e^{W_{t}^2+at+b\int_\limits{0}^{t}W_{s}^2\,ds}$$ be a martingale Could you please help me do that Thank you
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0answers
24 views

Estimating compound growth

I have a compound interest function with the following parameters: Value at time 0 = 13.8 Interest rate = 0.05 time interval = 10 I need to check quickly, (without a calculator, only pen and paper) ...
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3answers
77 views

I'm trying to reverse engineer a formula to find answers without trial and error.

As an example, I need to pay €100 to this business, and there are 2 separate fees I need to also pay, the fee for the payment processor and the VAT (Value Added Tax). I know that the fee for the ...
1
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1answer
53 views

What is the difference between simple interest and simple discounting?

I have been given the following statements: "Simple interest: $C$ now $\equiv (1+in)C$ in $n$ years; $C$ in $n$ years $\equiv \frac{C}{1+in}$ now. Simple discounting: $C$ in $n$ years $\equiv ...
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0answers
34 views

why hull white model has normal distribution?

consider hull white model $dr(t)=[\theta(t)-\alpha(t)r(t)]dt+\sigma(t)dW(t)$ when we solve the SDE above we have $r(t)=e^{-\alpha t}r(0)+\frac{\theta}{\alpha}(1-e^{-\alpha t})+\sigma e^{-\alpha ...
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0answers
29 views

Risk-neutral (i.e. martingale) measure if density is given for a single random variable (i.e. asset)

Let $(\Omega,\mathcal F, P)$ be a probability space. And let $S : \Omega \to \mathbb R$ be a random variable, called an asset, also we are given $\pi > 0$ called a price and some $r \ge 0$ called ...
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1answer
29 views

Maximum value for a dependent variable in a marginal effect model

I am unsure as to whether my calculations are correct. Currently, the model given is: The first question was to derive an equation for the marginal effects of EDU on In(Wage). I obtained the ...
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1answer
26 views

Ratio vs Difference in terms of growth

Suppose we have the following data: start date end date quantity 01/05/2014 07/05/2015 5 07/06/2015 02/06/2016 8 What ...
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0answers
27 views

Automatic differentiation for finance

we're estimating sensitivities with automatic differentiation. What we have read about it the adjoint (reverse) should perform more efficiently than the forward mode when there are more input ...
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1answer
22 views

How would I solve for a rate that compounds m times per annum?

Please excuse me, this is my first time using the site and I have absolutely no idea what I'm doing with the notation. Anyways, I am attempting to prove that: $$R_m = ...
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0answers
52 views

Optimal Insurance Coverage - risk neutral and risk loving consumers

I'm struggling with understanding a problem in finance: We have 2 states: $S_1$: bad state $Y-K = 2000$; probability $\pi$ = 10% $S_2$: normal state $Y = 5000$; probability $1-\pi$ = 90 ...
2
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0answers
32 views

Term Structure and short rates

If I have a term structure/yield curve given by: $$f(t, T) = f(0, T) + σ^2t(T − \frac{t}{2}) + σB_t $$ and want to find the short/spot rate $r_t$, is this simply: $$f(t,t) = f(0,t) + ...
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1answer
37 views

No arbitrage iff there EMM $P^*$ theorem [closed]

The definition of an arbitrage I was given: "An arbitrage strategy is an admissible strategy with zero initial value and positive probability of a positive final value." I think that an initial ...
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0answers
34 views

Interpretation of the Snell Envelope wrt European and American options.

In lectures we were taught that the Snell envelope U of a process Z, passes from European to American option prices. I thought that price processes are supposed to be martingales, but the Snell ...
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1answer
69 views

Promissory note example Financial Math

Brenda owes Cathy $\$8500$ and has signed a promissory note to repay the debt in 15 months from the signing date. The note was signed on December 6, 2009, and the maturity value of the note is ...
3
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1answer
73 views

Ornstein–Uhlenbeck SDE.

I am trying to understand the solution to the following exercise, however it is kind of poorly written. Can someone please explain it to me? For $V = (V_t)$ the solution to the Ornstein-Uhlenbeck SDE ...
2
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2answers
48 views

Brownian motion and covariance

Show that for $B = (B_t)$ Brownian motion, its covariance is $cov(B_s, B_t) = min(s, t)$. The solution I was given was: For $s ≤ t$, $B_t = B_s + (B_t − B_s)$, $B_sB_t = B_s^2 + Bs(Bt − Bs)$ ...
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0answers
30 views

Common term for “present value” and “future value”

In the past, I have always used the term "present value" for the value of a payment made at some point in time $t$ from the perspective of some other valuation point in time $T$. I did not distinguish ...
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1answer
45 views

Martingale Properties

Here is a proof of a property of a martingale $X$ relative to the filtration $(F_{n})$: $n\gt m,\\$ $\\ \\ E[X_n|F_m]=E[E[X_n|F_{n-1}]|F_m]=E[X_{n-1}|F_m]=...=E[X_m|F_m]=X_m$ In the definition of a ...
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1answer
133 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 ...
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1answer
15 views

Ito's formula for this stochastic differential - please explain this step?

Referring to those two lines, can someone please explain how those results were obtained? My understanding is, the following formula is being referenced: $$dV_t = dV(S_t,t) = \frac{\partial ...
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0answers
46 views

Is this a self-financing portfolio?

I have $S_t = 10 + B_t$, $\beta_t = 1$, $a_t = 2B_t$, $b_t = -t - B_t^2 - 20B_t$ Then the value, $V = a_t S_t + b_t \beta_t$ Is this a self financing portfolio? Note, $B_t$ is brownian motion I am ...