# 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.

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### Estimating Recovery Rates

What are some methods for estimating recovery rates for an entity? For example, say I am trying to find the recovery rate that would be used to price a single name CDS on JPMorgan. The true ...
1k views

### Modeling Call Price w.r.t. Strike w Models that Capture Vol Smile

I am trying to model $C(K)$, the price of the call $C$ as a function of strike $K$. Because this is tied to Prob ITM - and in fact the probability density function of that particular expiration (https:...
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### Implied Probability Density with Puts

The second derivative of the call price at K gives the probability of that strike (implied probability density). In practice, what adjustments or acknowledgements (if any) need to be made to produce ...
547 views

### How to estimate the probability of a scenario in general

For my finance lecture we are currently on the topic of operation risk. Scenarios play a vital role in the estimation of low frequency (or probability), high impact (or severity) events. How could ...
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### $P(S_T > S_u \mid S_v = s_*)$

Let $u < v < T$ and assume $S_t$ follows a lognormal $((\mu - \sigma^2/2)t, \sigma^2 t)$ process. I'm interested in computing the conditional probability $$P(S_T > S_u \mid S_v = s_*)$$ ...
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### A priori selection of acceptable backtesting errors (type I and II)

Is it possible to a priori select an acceptable values of type I and II errors in backtesting (f.e. in case of the unconditional coverage test)? Type I error is directly connected to the significance ...
195 views

### How do I find this Expectation?

I have an expectation given as: $\mathbb{E}\left(S_{T}\mathbb{1}_{S_{T}\geq K} \right)$ where $K$ is just an arbitrary number (i.e. the strike price, but that's unimportant) and $S$ can be modelled ...
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### interview question : replication strategy of a betting game

Here is a question I found in a book I am not able to finish. Your help will be much appreciated! I also included where I have been so far. Q: Team A plays team B in a series of 7 games, whoever wins ...
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### Probability Distribution that fits my parameters?

I'm trying to create a PDF that has the max values at its tails, and a P(x) of 0 at its mean. Essentially it would be something like two normal distributions lined up side to side. Is there any ...
542 views

### How to calculate Empirical Cumulative Probability in R

I have a dataset of S&P500 returns. How can I calculate the value of $F(X ⩽ x)$. My code is as below: ...
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### Box-Muller Method Proof

Here we want to show that the Box-Muller method generates a pair of independent standard Gaussian random variables. But I don't understand why we use the determinant? For me when you have two ...
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### How much to invest to reach a target?

Your current wealth is $W$. Each day you can invest some of it; there's a probability $p$ that you will win as much as you invested, $1-p$ that you will lose it. You want to reach a target wealth $W_T$...
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### Girsanov theorem and default rates in bond credit rating

Default rates are kind of probabilities, right? Is it possible to use the Girsanov theorem in that context? For example if we have a table of real world probabilities, could we use the Girsanov ...
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### What are the answers to these questions on card deck and option pricing?

here are 3 questions I have some trouble dealing with. Your help will be greatly appreciated! 1 - We have a deck card: 26 red, 26 black. we play a game: you draw a card from the deck without putting ...
191 views

### BSM Model - Actual probability

Actual probability of exercise of put option under BSM model is: PD = N(-d2(u)) (using expected return of stock, u) Risk-neutral equivalent is ...
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### Scaling of probability mass function

Given a histogram and the probability mass function values for each observation, when plotting the histogram and the curve (this is bell curve since the data is assumed to be normal) on the same ...
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### Creating the histogram for the distribution of the portfolio returns

Given log returns for some stocks $A$ and $B$, which are the constituents of our hypothetical portfolio in equal weights, how does one actually come up with a distribution of the log returns of the ...
404 views

### Large deviations theory and extreme value theory

I'll enter into details of both, sooner or later, but for the moment I'm concerned about the differences (and relationships, if any) between these two theories. Can someone give me a brief, but still ...
131 views

### Calculating probability of Yuan's slump from options market

http://www.bloomberg.com/news/articles/2016-01-06/if-options-traders-are-right-the-yuan-s-slump-is-far-from-over Contract prices indicate a 79 percent probability that the currency will weaken ...
156 views

### How much would one pay for the max of two stocks?

I'm trying to figure out if stochastic calculus is the right approach for this problem... but I only vaguely understand it and I am trying to gauge if I need to spend the time learning measure theory ...
152 views

### Compute stock price probability distribution from option data (IB method & negative probabilities issue)

I'm using a procedure as described in the interactive brokers article here (https://www.interactivebrokers.com/en/index.php?f=5910&ns=T) to compute a probability distribution from option (call) ...
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### Pricing when arbitrage is possible through Negative Probabilities or something else

Assume that we have a general one-period market model consisting of $d+1$ assets and $N$ states. Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option, with ...
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### Radon-Nikodym: Changing Distribution vs Changing Random Variable

Let $X \sim \mathcal{N}(\mu,\sigma^2)$ under the probability measure $P$ on the measurable space $(\Omega, \mathcal{F})$. We may define a Radon-Nikodym derivative $Z$, also defined on \$(\Omega, \...