# Tagged Questions

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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### 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 ...
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### What is the difference among three kinds of continuous income stream?

In the chapter of our book , we discuss "Tolal value of continuous income stream:$\int_a^bR(t)dt$" "Future value of continuous income stream:$\int_a^bR(t)e^{r(b-t)}dt$" "Present value of continuous ...
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### Replicant portfolio with commissions (Jarrow rudd)

I have created a Jarrow Rudd three for a call option that I know how to replicate with a portfolio. A replicating portfolio of a option works this way: At time 0 we form a replicating portfolio ...
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### SDE Solution: Hull-White extension of Vasicek model

I am trying to figure out the particular ansatz (if that's all there is) for the solution to the SDE: $dr_t = [v_t - ar_t]dt + \sigma dW_t,$ where $a$ is constant and $v,t$ are, potentially, time-...
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### Deciding whether a maximum asset price process is a markov process

I understand how Mn has been drawn. For the second computing part, after computing, I have no idea how to decide if Mn is a markov process I don't understand the solution at all, don't know what the ...
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### Finance Algeabra: Converting a Discount Polynomial Function to an Interest Rate Polynomial Function

I have a finance problem that is 99% mathematical. In finance, the price of a bond could be modelled as the discounted value of its future cash flows, so something like: ...
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### Solve for the interest rate while we are not told if it is simple or compound.

You are offered to have a discount of \$20 if you pay cash now for \$1500 due in 120 days. If you pay cash now, at what rate may you consider your money to be earning interest for the next 120 days? ...
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### Financial Mathematics--Finding Compounding Period given Annual and Effective Interest Rates

I'm trying to find a compounding period C when given an annual interest rate r and effective annual yield i. I'm working with the following equation: $i=(1+r/C)^C-1$ I'm having trouble re-writing ...
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### Loan to be repaid with the interest of the last payment given

A $60$-month loan is too be repaid with level payments of $1000$ at the end of each month. The interest in the last payment is $7.44$. Calculate the total interest paid over the life of the loan. Let ...
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### continuous local martingale brownian motion

$B$ is a one-dimensional Brownian motion and $X_t$ is defined as$\\$ $X_t:=f_{1-t}(B_t)$, $0\le t<1$ and $0$, $1\le t<\infty$ where $f_s(x)=\frac{1}{\sqrt{2\pi s}}e^{-\frac{x^2}{2s}}$. I have to ...
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### Integral Representation of Brownian Motion [duplicate]

B is a Brownian motion with values in $\mathbb{R}$. I have to find a process $(F_t)_{t\in[0,T]}$ such that $X=E[X]+\int_0^T F_s dB_s$, for $X=B_T$, $X=\int_0^T B_tdt$, $X=B^2_T$, $X=B^3_T$ and find a ...
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### Repayment of a loan with non level annual payments

A loan of $10,000$ is being repaid with 20 non-level annual payments. The interest rate on the loan is an annual effective rate of$6$% . The loan was originated 4 years ago. Payments of $500$ at the ...
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### Asymptotic distribution of zero-drift Geometric Brownian Motion as $t \to \infty$

If we fix the drift at $\mu = 0$, then my geometric brownian motion will have stationary mean, but it seems that the variance will grow without bound. What does the limiting distribution look like for ...