Questions tagged [probability]
A probability expresses quantitatively how likely an event is to occur. We often encounter probabilities as conditional probabilities which express how likely an event is to occur in light of certain (given) information.
398 questions
1 vote
1 answer
162 views
Use Options Vertical Spreads to Find Probability of Distribution
I saw this interesting argument that you can use the value of a put spread to find the approximate market implied probability of underlying finishing below the mid point of the two strikes, assuming ...
- 43
1 vote
1 answer
177 views
Why is the forward measure needed for options on futures when the risk-neutral measure suffices?
I have been running around in circles with this attempting to make sense of this. Universal pricing theorem Given a numéraire asset $(N(t))_{t \geq 0}$ such that for all tradeable assets $(S(t))_{t \...
- 481
1 vote
0 answers
106 views
Information-theoretic upper bound on portfolio log-growth
I recently formulated and successfully solved a simple model portfolio optimization problem. I'm not a mathematician, but the result seems to have close ties to information theory. I've tried ...
- 11
2 votes
0 answers
149 views
Optimal Strategy in Sequential Gladiator Duels with Probabilistic Outcomes, Colosseum Fight II
I did find this problem on https://www.quantguide.io/questions/colosseum-fight-ii which is as follows: Alice and Bob are in ancient Roman times, each commanding a team of 4 gladiators. Alice’s ...
- 21
1 vote
0 answers
38 views
Mechanism design for information priority
Assuming that there are 3 situation of a game: win, lose, and draw (no one wins). You can bet X on any situation, you'll get 2X if you win and 0 otherwise. Originally, you know nothing about the ...
- 11
2 votes
1 answer
122 views
Questions on calibrating risk-neutral/risk-adjusted densities to match realized densities
In Market Timing with Option-Implied Distributions: A Forward-Looking Approach by Kostakis et al. (2011), the authors imply a risk-neutral density (from a cross section of option prices) $\rightarrow$ ...
- 2,886
0 votes
0 answers
140 views
Expected value is the normalized odds?
So I was given a problem with around 10 sportsbooks with different moneylines, and I needed to find which team to bet on and which sportsbook. I know the sportsbook that is correct has one team at <...
- 101
0 votes
0 answers
67 views
How to Calculate Probability and Expected Return for Staggered Stop-Loss Levels Based on ATR
In my backtesting, my win rate varies depending on the stop-loss size, which is based on the 14-period ATR (ATR14). A stop loss of 1 unit is set as 1 × ATR14, resulting in a 70% win rate. A stop loss ...
0 votes
0 answers
47 views
I am looking for an options profit/loss calculator allowing two underlyings at the same time
Etrade's tradelab would be perfect except it only allows one underlying at a time. I need two at the same time. Thanks. Clive
- 1
2 votes
0 answers
195 views
Tail Probability Expectation Formula
On page one of the following paper: The Probability Conflation: A Reply by Nassim Nicholas Taleb et al., the following calculation is made: Begin Quoted Passage $K \in R^+$ is a threshold f(.) density ...
- 901
2 votes
0 answers
333 views
Game Theory Brainteaser
Seeking help / thought process guidance on the following interview problem, which seems centred on game theory Setup: there’s a number X which we can measure once with error following N(0, 1). We can ...
- 21
2 votes
1 answer
200 views
Continuous-time two-state Markov process
$\lambda_t$ is binary with $\lambda_H$ and $\lambda_L$, with instantaneous transition probailities of $\mu_H$ and $\mu_L$. What is $\mathbb{E}_t[\lambda_T]$, assuming $\lambda_t=\lambda_H$ or $\...
- 53
1 vote
2 answers
764 views
Flip a coin $5$ times in a row. If you get $5$ Heads, you get $\$28$. How much would you pay to play?
In preparation for quant interview season, I tried out interview questions and came across the following one: Flip a coin $5$ times in a row. If you get $5$ Heads, you get $28$ dollars. How much ...
- 330
0 votes
1 answer
152 views
Relationship between Beta distribution and its inverse
I am attempting to transform a real world density into risk-neutral density via calibration through the beta distribution. Calibration in this context is transforming the rw density into the rn ...
- 31
1 vote
2 answers
121 views
How to count number of sets in a sigma-algebra?
Here is an example for the construction of a probability space in Shreve's stochastic calculus, page 4, what is the meaning for $2^{(2^0)}$? it seems like a method to calculate number of subsets, but ...
- 13