# Questions tagged [probability]

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### What is the connection between the risk neutral implied density and the real world density?

I understand that we can use option prices to imply volatilities and ultimately to imply a risk neutral density. I also understand that this implied density is not the same as the "real world density"....
35 views

### Classical Ruin Theory - Lundberg Model

In classical risk/ ruin theory, I see this formula crop up in my notes but my lecturer didn't explain to me why/ when it's employed: $M_X(r) = \int_{-\infty}^{\infty} e^{rx} f(x) dx$ I understand ...
2k 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 ...
59 views

### Two commodities which are normal distributed and perfectly correlated

The daily price change in commodity 1 is distributed $N(0,0.15^2)$ and the daily price change in commodity 2 is distributed $N(0,0.3^2)$. The two commodities are 100% correlated. 1) Does the relative ...
96 views

### Two Probability Questions from Quantitative Finance Interview Book

I posted the two questions in math stack exchange one month ago but cannot get an answer, so I post it here and appreciate your advice:) I'm reading an interview book called A Practical Guide to ...
91 views

### What's the expected value of a repeated game with 50% chance to win 0.5 and 50% to lose 0.5?

Assume we start with 1. In the first bet the expected value of remained balance is 1.5 * 0.5 + 0.5 * 0.5 = 1 For N times, is it still 1 according to E(XYZ)=E(X)E(Y)E(Z)? But 1.5^50 * 0.5^50 is not 1. ...
529 views

### credit risk - marginal default probability

I have been working on an assignment trying to calculate marginal/conditional probability of default. Using a logistic regression framework, I was able to compute the 12-month unconditional PD for ...
58 views

### GBM probability of hitting non constant barrier

I know there is a formula for probability of hitting a constant barrier for GBM/BM (See page 651 in Martinagle Methods in Financial Modelling). Is there a formula for non-constant barrier? The ...