# Tagged Questions

The tag has no usage guidance.

4answers
2k views

### 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 ...
1answer
2k views

### Baye's rule for conditional expectations (Proof review)

The Baye's rule for conditional expectations states $$E^Q[X|\mathcal{F}]E^P[f|\mathcal{F}]=E^P[Xf|\mathcal{F}]$$ With $f=dQ/dP$ - thus being the Radon-Nikodyn derivative and $X$ being ...
5answers
3k views

### Random matrix theory (RMT) in finance

The new kid on the block in finance seems to be random matrix theory. Although RMT as a theory is not so new (about 50 years) and was first used in quantum mechanics it being used in finance is a ...
8answers
7k views

### Probability of touching

For a vanilla option, I know that the probability of the option expiring in the money is simply the delta of the option... but how would I calculate the probability, without doing monte carlo, of the ...
2answers
655 views

### on “recovering probability distributions from option prices” - how to subtract influence of stochastic volatility?

This is based on a 1995 paper by Rubinstein/Jackwerth by the above title where the authors produces a distribution of stock prices inferred from option prices. But their approach only produces a joint ...
9answers
3k views

### Lévy alpha-stable distribution and modelling of stock prices.

Since Mandelbrot, Fama and others have performed seminal work on the topic, it has been suspected that stock price fluctuations can be more appropriately modeled using Lévy alpha-stable distrbutions ...
5answers
2k views

### How to estimate the probability of drawdown / ruin?

A fairly naive approach to estimate the probability of drawdown / ruin is to calculate the probabilities of all the permutations of your sample returns, keeping track of those that hit your drawdown / ...
2answers
750 views

### How do you distinguish “significant” moves from noise?

How do you distinguish between losses that are within the normal range for day-to-day shifts and situations with a real potential for loss? The specific application I have in mind is pattern ...
6answers
15k views

### How to calculate stock move probability based on option implied volatility and time to expiration? (Monte Carlo simulation)

I am looking for one line formula ideally in Excel to calculate stock move probability based on option implied volatility and time to expiration? I have already found a few complex samples which took ...
1answer
484 views

### Arbitragefree Pricing: Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if and only if there exists an equivalent martingale measure Q, under which the discounted asset price ...
2answers
449 views

### Distribution of Geometric Brownian Motion

Please let me know where I have been mistaken! Let the SDE satisfied by the GBM $S(t)$ be $$\frac{dS(t)}{S(t)} = \mu dt + \sigma dW(t).$$ Then, the underlying BM $X(t)$ will satisfy  dX(t) = \...
1answer
345 views

### Quantum Mechanics and Economics… What

I was reading this paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2002698&download=yes The author has the model presented here: http://modelingcommons.org/browse/one_model/3443#...
1answer
399 views

### What distribution should I apply to estimate the likelihood of extreme returns?

Say I have a limited sample, a month of daily returns, and I want to estimate the 99.5th percentile of the distribution of absolute daily returns. Because the estimate will require extrapolation, I ...
2answers
862 views

### Heuristics for calculating theoretical probabilities of being ITM at time T for listed options

I'm looking for a heuristic way to calculate the probabilities of being in the money at expiry for non-defined risk options combinations (listed options). I use delta as a proxy for this probability ...
2answers
394 views

### Confidence Intervals of Stock Following a Geometric Brownian Motion

In preparation for my Options, Future's and Risk Management examination next week, I have been presented with a series of questions and their answers. Unfortunately, my lecturer, one of the less ...
1answer
172 views

### Effects of random-generator-choice on derivative's price

There is a plethora of pseudo-random-generators out there. Some of them are definetly better and some of them severily underperform. My standard tool is Mersenne Twister - when I need to generate ...
1answer
1k views

### what is the best way to calculate the probability of an equity option ending in the money?

Given historical implied volatility and all other know variables (stock price, option strike price, option expiration date, dividend rate, interest rate) what is the best way to calculate the ...
2answers
61 views

1answer
69 views

### Prove $E_{\mathbb Q}[X_t | \mathscr F_u] = X_u$ given $Y_t$ is a martingale

We are given a filtered probability space $(\Omega, \mathscr{F}, \{\mathscr{F}_t\}_{t \in [0,T]}, \mathbb{P})$, where $\{\mathscr{F}_t\}_{t \in [0,T]}$ is the filtration generated by standard \$\mathbb ...