## Top new questions this week:

### Explicit solution SDE

I have the following SDE: $$dY_{t}=A\left(\frac{W_{t}^{1}}{\sqrt{t}},\frac{Y_{t}}{\sqrt{t}}\right)dW_{t}^{1}+B\left(\frac{W_{t}^{1}}{\sqrt{t}},\frac{Y_{t}}{\sqrt{t}}\right)dW_{t}^{2}$$ where …

stochastic-processes stochastic-calculus sde

### Nested volatility

The introduction VIX options makes the concept of "volatility of volatility" a real life concept. The idea of "nested volatility" seems interesting, and I am wondering if there are any academic …

volatility implied-volatility vix

### How does this follow from the separating hyperplane theorem?

This is from Pliskas book in mathematical finance. I do not know what was best to write the question so I included the pages from the book. He has not written what form of the separating hyperplane …

arbitrage risk-neutral-measure no-arbitrage-theory convexity

### Modelling currency exchange rates timeseries data across re-denomation dates

I am working with data for an exotic currency, that has been re-denominated a couple of times during the twenty years of data that I have. What is the best way of 'normalising' the data, so that I …

time-series fx

### Risk Neutral Pricing Necessary Condition

Suppose that I have an option on a single stock expiring at time $T$ and I replicate the payoff of this derivative by investing in the stock market and the money market. So this condition reads X(T) …

risk-neutral-measure

### How to classify stocks by their volatility?

I would like to hear other possible ways of classifying Stocks by the Volatility of their returns. Assuming that I want to characterize each stock as Low, Medium or High Volatility Stock and assuming …

volatility equities returns

### Algorithm to detect the aggressor side of a trade

Most of the exchanges provide aggressor side property of trades (e.g. Tag=5797 AggressorSide on CME) in their raw data. But many data providers do not provide this information via their datafeed …

## Greatest hits from previous weeks:

### How do you explain the volatility smile in the Black-Scholes framework?

Does anyone have an explanation for the currently naturally forming volatility smile (and the variations) in the market?

black-scholes implied-volatility

### What's the difference between volatility and variance?

How do they differ in what they imply about an underlying's (or any variable's) movement?

volatility variance

### State Space models with Short Time Series

My problem is that I have a state space model that I estimate using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure …

time-series statistics optimization bootstrap