# Tagged Questions

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### What is the distribution of Brownian Bridge over a given time interval?

I know from Karatzas & Shreve (1991) that a Brownian Bridge $B(t)$ from $a$ to $b$ on time interval $[0,T]$ satisfies: $$B(t)=a(1-t/T) + b*t/T + [W(t) - W(T)*t/T]$$ where $W(t)$ is a standard ...
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### Brexit implied probability

It is possible to bet on the Brexit e.g. on this page: https://sports.ladbrokes.com/en-gb/betting/politics/british/eu-referendum/uk-european-referendum/220800266/ The quotes are 8/15 for remain, and ...
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### Distribution of hitting time of the integrated CIR process

If an increasing process $X_t$ has a known Laplace transform $\mathbb{E} e^{-s X_t} = m_t(s)$, define its hitting time $\tau$ to some level $B$ to be $$\tau = \inf\{ u > 0 : X_u \geq B \}.$$ Can ...
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### How to estimate real-world probabilities

In the world of finance, Risk-neutral pricing allow us to estimate the fair value of derivatives using the risk free rate as the expected return of the underlyings. However, the behavior of ...
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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 ...
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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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### Exercise probabilities in Black Scholes [duplicate]

In the Black Scholes Formula, why are the probability of an Asset or Nothing Call and Cash or Nothing Call being exercised different. The probabilities are N(d1) and N(d2) respectively.
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### 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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### Analytical Bond Price under Rendlemen-Bartter?

Assuming the short rate $r_t$ follows the risk-neutral (so $W_t$ is a $Q$-Brownian motion) process $$dr_t = ar_t dt + \sigma r_t dW_t,$$ does anyone know of an analytical bond price formula? We ...
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### Selling two uncorrelated OTM options lowers the over all probability of profit?

I am trying to simulate shorting two uncorrelated put options, I wrote a python program and used monte carlo method to simulate the PnL on expiration: gist It seems the probability of profit is ...
I am trying to find the empirical copula linking two random variables $X$ and $Y$. I have some data available but it's limited with respect to the variable $Y$ and I am not convinced it's enough data ...