3

I'd highly recommend the http://www.quantopian.com platform and the correspoding forum there, e.g. the trading strategies thread. You could pick a topic and also use a concrete example in job interview.


3

Jumps are an attempt to solve a math mistake in Modern Portfolio Theory. In the 19502-70s, economists were working on solving the variance-mean tradeoff. Furthermore, they needed to do so with punchcard computing. That radically restricted the set of computable, potential solutions. Both the normal distribution and the log-normal distribution are ...


2

I think the variance of the instantaneous shifts in the spread is meant: $V \left[ dX \right]=V \left[ dS_1-dS_2 \right]$ And the individual variances (in the conditional and local sense) are: $V \left[ dS_1 \right]= \sigma_1^2 S_1^2dt$ $V \left[ dS_2 \right]= \sigma_2^2 S_2^2dt$ And the covariance term is, assuming the two Brownians are correlated:...


1

The first step is to include jumps in the stock price. Then, you can easily add jumps into the variance process. If you only consider seldom, large jumps, you may want to use a jump-diffusion like the models from Merton (1976) and Kou (2002). The former uses a log-normal distribution for the jump size whilst Kou employs a double exponential distribution. A ...


1

Below is the link to curated topics related to programming in quant finance. https://github.com/wilsonfreitas/awesome-quant (this contains all programming languages(python, R, C++ etc) and there resources in quant finance). Apart from quantopian.com as mentioned above you can try quantiacs(https://www.quantiacs.com/) (which is actually a quant finance-algo ...


1

Jumps do not imply fat tails. See the simulation in R. Note that the excess kurtosis of [normal variable + jump] is negative. > set.seed(1) > Normal_Variable <- rnorm(1e8) > kurtosis(Normal_Variable) [1] -0.000628316 > Jump <- 2 * ((runif(1e8) < 0.5) * 2 - 1) > kurtosis(Normal_Variable + Jump) [1] -1.280009


1

The model is interesting, but rarely used in practice. One main reason is the choice of the range $\sigma_{min}, \sigma_{max}$. As Martini and Jacquier explain in their article The uncertain volatility model, the price corresponds to the worst-case scenario where the Gamma changes signs exactly when the volatility switches regimes. This will hardly ...


Only top voted, non community-wiki answers of a minimum length are eligible