CHAPTER 18Simulating Asset Prices

In this chapter, we provide a framework to simulate multivariate stochastic volatility process with jumps. We build the framework step by step, and wherever we need to introduce some new functions, we build them on the fly. This chapter is motivated by Novotny and Urga (2017). The paper provides a test for co-jumps in asset prices. One section of the paper is a simulation exercise to assess the size and power of the tests. In order to do that, we need to simulate a realistic price generating process. The choice was made for a stochastic volatility process with price jumps in both the price and volatility. This chapter illustrates that q can be naturally used for academic research as well.

18.1 STOCHASTIC VOLATILITY PROCESS WITH PRICE JUMPS

We start with a simulation of the Stochastic Volatility Model with an intraday volatility pattern and price jumps both in the volatility process and the price process, as proposed by Andersen et al. (2012). The price generating process is defined by the following equations:

(18.1)