# 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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### 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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### Actuarial Science FM Question

$$a(t)=Zt^2+Bt+1$$ If \$100 at$t=0$grows to \$152 at $t=4$ and \$200 at$t=0$grows to \$240 at $t=2$, what are $Z$ and $B$? Please show work. Also, what would \$1600 invested at$t=6$grow to at$...
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### How to split the rent if two roommates live there from the beginning and a third one joins in the middle of the month?

I've been thinking over it and I can't figure it out. Consider the rent of the house is $X$. Now there are two roommates from the beginning and a third one joins in the middle of the month. Now ...
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### Is the following a martingale?

Let $X_{n}$ be a martingale with respect to a filtration $\mathbb{P}_{n}$. Define: $Y_{n}$ := $X_{n}^{3}$ Is $Y_{n}$ a martingale? Supermartingale?
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### Calculate interests

Simply wants to calculate interests of an initial amount $N$, with a monthly payback $m$, and a year interest rate of $R$ I guess the interests are not cumulated each month, but just at the end of ...
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### Effective Annual Rate Calculation: Tricky periods and payout frequencies

For calculating the Effective Annual Rate (EAR) from various stated interest rates, I'm using the formula: $$EAR= \left(1+\frac{r}{p}\right)^{pt}-1$$ where, $p$ = no. of payouts in a period, $t$ = ...
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### Baseball betting and probablity

Here is a question that came up during class discussions on Friday: Your favorite baseball team is playing against your uncle's favorite team in the World Series. At the beginning of each game, you ...
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### Simple vs compound interest rates and Taylor expansion

I am having trouble deciphering a portion from my finance text. Let $i = \text{interest rate}$, $n = \text{Some arbitrary time period}$ and $C = \text{Cash invested}$ And also $C(1+i)^n$ (...
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### Methods of solving this exam FM problem with geometric-investments.

The problem I am working on is as follows. Matthew makes a series of payments at the beginning of each year for $20$ years. The first payment is $100$. Each subsequent payment through the tenth ...
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### HJM model - Differentiation Problem

starting from the folowing SDE (HJM model): $$df(t,T)=\left(\sigma(t,T)'\int_t^T{\sigma(t,u)du}\right)dt+\sigma(t,T)'dW_t$$ And having $r(t)=f(t,t)$, I have two questions : 1) how do we obtain the ...
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### Pricing a Europen style put option

So I'm enrolled in a Mathematics for Finance course, and we received this question on the last Problem Set. I'm completely stuck on how to solve this problem. I tried applying the formula xS(t) + yA(t)...