Tagged Questions

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0answers
14 views

Replicating portfolio under the Black-Scholes model

I have a two-asset Black-Scholes model: $dB_t = B_t r dt$ $dS_t = S_t (\mu dt + \sigma dW_t)$ I introduce a European claim $\xi = \max(K,S_T)$ with maturity $T$, for some fixed $K$. I have ...
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0answers
79 views

pricing of heat rate-linked derivative [migrated]

It's a simplified model. Suppose $U_t$ is a random variables subject to Lognormal($x_1$, $z_1^2$)distribution. $V_t$ is a random variables subject to Lognormal($x_2$, $z_2^2$)distribution. Suppose ...
2
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2answers
56 views

Probability related finance question: Need a more formal solution

You are offered a contract on a piece of land which is worth $1,000,000$ USD $70\%$ of the time, $500,000$ USD $20\%$ percent of the time, and $150,000$ USD $10\%$ of the time. We're trying to max ...
0
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0answers
45 views

A few finance probability and logic questions. Help? I did some work, but I'm stuck on a few. [closed]

I'm currently trying to study for some probability questions for a job interview that I have a couple weeks and I was wondering if you could help me refresh... to be honest this is kind of fun. It's ...
0
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1answer
54 views

Random Stock Stop-Loss/Stop

Assuming a Stock's price changes in a random manner. If you buy this Stock, you are required to set a stop-return and stop-loss price. I am looking for the equation that shows the probability for ...
0
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3answers
48 views

A fund of $30,000 is used to award scholarships…If i=0.09, find the number of scholarships which can be awarded

A fund of $30,000 is used to award scholarships of amount 3000, one per year, at the end of each year for as long as possible. If i=0.09, find the number of scholarships which can be awarded and the ...
1
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2answers
55 views

at a nominal rate of interest of 8% converted semiannually…Find the initial amount of the loan.

A loan is to be repaid with level instalments payable at the end of each half-year for $3$ and $\frac{1}{2}$ years, at a nominal rate of interest of 8% converted semiannually. After the $4^{\rm th}$ ...
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0answers
55 views

TVaR proof of formula question

I'm trying to prove that $TVaR_p(X) = \frac{\int_{\pi_p}^{\infty} x*f(x)dx}{1- F(\pi_p)}$ is equal to $\frac{\int^1_p VaR_u(X)du}{1-p}$ ? I obviously see that the denominators are the same since ...
2
votes
1answer
207 views

How to get Annualized volatility from monthly return?

Suppose the average monthly return is $\mu$, the monthly standard deviation is $\sigma$ and denote the autocorrelation of monthly returns by $corr(r_i,r_{i+h}) = \rho(h)$ Prove that, when $\sigma$ ...
0
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1answer
563 views

Need a Master's Thesis Topic - Want it to be Applicable to Finance [closed]

So I'm a senior undergraduate but I'm also getting a Master's and consequently need to write a Master's Thesis, but I'm having trouble coming up with a topic. I'm working in finance last year and ...
4
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1answer
160 views

Maximizing gambling performance over the long run

Background. We can play a game in which we can put one dollar and get out $X$ dollars, where $X$ is 2 dollars with probability $p>1/2$, or zero dollars with probability $1-p$. We also assume that ...
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2answers
144 views

Resolving a paradox concerning an expected value

We have a coin that has a probability $p>1/2$ of coming up heads (and probability $1-p$ of coming up tails). We now play the following game: We start with a fortune of one dollar. We toss the ...
3
votes
2answers
289 views

Maximizing a function containing an integral

Problem. Let $\rho\colon[-1,\infty)\to\mathbb{R}$ be a function such that $$\int_{-1}^\infty\rho(x)\,dx=1.$$ Let $G\colon[0,1]\to\mathbb{R}$ be a function that is defined with $$G(f) := ...
2
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2answers
301 views

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 ...
3
votes
1answer
241 views

Applications of Compound Poisson Processes

I'm reading the book Non-Life Insurance Mathematics, an introduction with Stochastic Processes by Thomas Mikosch and I'm interested in applications of the Cramer-Lundberg Process to concrete examples ...
1
vote
1answer
146 views

Binomial model of stock price

I've got a homework question which I think I have solved but am not certain if the answers are correct. The question goes like this: Consider a stock which has a 50% chance of increasing by 80% by the ...
2
votes
2answers
308 views

Using Black-Scholes Equation to “buy” stocks

From what I understand, Black-Scholes equation in finance is used to price options which are a contract between a potential buyer and a seller. Can I use this mathematical framework to "buy" a stock? ...
0
votes
1answer
340 views

proof that value at risk VaR is monotonic

I want to show that if $X$ and $Y$ are the two loss variables such that $X\leq Y$, then $\text{VaR}_\delta(X)\leq\text{VaR}_\delta(Y)$.
4
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5answers
3k views

Understanding Black-Scholes

Assume I have only basic math knowledge, what specific areas of math would I need to learn in order to understand the following webpage: Black-Scholes Many thanks.