Consider a geometric Brownian motion martingale with stochastic volatility. The logarithm of the latent volatility follows a fractional Brownian motion, with an unknown “volatility of volatility” and Hurst exponent H. (a) Write the stochastic differential equations for the system as described. (b) Assuming the model represents a stock price and given a historical price sampled every second, describe your approach for fitting the model. How would you estimate the latent volatility? Be specific. (c) The current volatility model is non-stationary. Suggest and justify an adjustment to make it stationary. What are the revised equations?
Quantitative Research Interview Questions
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Consider the following code: 1 double f ( double x ) { 2 if ( x == 0) 3 return 1.0; 4 return f (0.5 * x ) + f (0.3 * x ) ; 5 } Analyze the time and memory complexities of this function. Provide asymptotically tight bounds.
Given expected return and volatility of each asset, also given expected return of your portfolio, how to choose the weight on different assets to minimize the variance of your portfolio?
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