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Mark Joshi, Quant Interview Question problem 2.34; replicating a digital option on a 4-step symmetric binomial tree

Question: Team $A$ and team $B$, in a series of $7$ games, whoever wins $4$ games first wins. You want to bet $100$ that your team wins the series, in which case you receive $200$, or $0$ if they ...
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votes
1answer
2k views

Bloomberg terminal swap zero curve calculation

I would like to ask about swap zero curve calculation algorithm by Bloomberg terminal. This is a plain vanilla CZK interest rate swap, fixing the Prague IBOR. My task is to calculate zero rates from ...
-1
votes
1answer
152 views

Use random-shift Halton sequence to obtain 40 independent estimates for the price of a European call

Background Information: Random-shift Halton sequence: Consider the first six Halton vectors in dimension $2$, using base $2$ and $3$: $$\begin{bmatrix} 1/2\\ 1/3 \end{bmatrix}, \begin{bmatrix} 1/4\\ ...
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votes
2answers
353 views

Close form solution for Geometric Brownian Motion

I have a very fundamental problem, please help me out. I am little confused with the derivation for the close form solution for the Geometric Brownian Motion, from the very fundamental stock model: $$\...
-1
votes
1answer
270 views

Accuracy for GARCH models

How does one calculate the accuracy of forecasts given by GARCH models considering GARCH is run on returns. Assuming GARCH is a derivative of a regression based prediction model, would regular ...
-1
votes
1answer
384 views

If I am very fast (less than 10 microseconds latency) what would be the first strategy to execute? [closed]

Let's assume I found the holy grail of low-latency trading (which I didn't). For educational purposes, what would be the first strategy I would direct my trading code?
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votes
1answer
1k views

Calculating arbitrage- S&P 500 stocks vs S&P 500 Index future?

How exactly would I go about investigating whether the S&P 500 stocks were currently over-valued compared with the price of the S&P 500 Index futures contract? Is it just a case of taking each ...
-1
votes
1answer
127 views

What is the connection between the federal funds rate and US government bonds

If the Federal Funds Rate changes, does that affect bond prices? How? Also, is there any connection between the Federal Funds Rate and the coupon payment on US bonds?(for those that have a coupon ...
-1
votes
1answer
333 views

Momentum strategy cumulation of K-monthly returns over multiple months [duplicate]

In a momentum strategy, every month you form a portfolio of winners. Each of these portfolio you hold for K months. So after K months you sell the 1st portfolio, after K+1 months you sell the next and ...
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votes
1answer
103 views

Separate market and limit orders from market depth/tick data

From the website https://www.algoseek.com/equities/, we can get a sample of the full depth market/tick data. From the paper https://arxiv.org/pdf/1710.03870.pdf page 8, I would like to extract the ...
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votes
1answer
2k views

Given $S$ is a Geometric Brownian Motion, how to show that $S^n$ is also a Geometric Brownian Motion?

Suppose that a stock price $S$ follows Geometric Brownian Motion with expected return $\mu$ and volatility $\sigma:$ $$dS = \mu S dt +\sigma S dz$$ How to find out the process followed by variable $...
-2
votes
1answer
410 views

How would you price an option with payout ln(St) where St is the stock price at time t

I know it has to be done through martingales, but I am not fully sure how to do this BSM pricing.

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