Monte Carlo option pricing with asymmetric realized volatility dynamics

The impact of COVID-19 on commodity options market: Evidence from China

“…While, many other researchers focus on taking the method of comparing a fixed number of different frequencies (tick-by-tick, 5-min, 15-min and 30-min) to find the most accurate volatility based on S&P500 or some individual stocks. (see Bandi et al (2008) , Allen et al (2011) Jou et al (2013) , Christoffersen et al (2014) , C¸ elik and Ergin (2014) , Liu et al (2015) and Naimoli et al (2022) , C¸ elik and Ergin (2014) and Liu et al (2015) ).…”

Simulation hedge investment portfolios through options portfolio

“…According to the modeling, the compensation that the option would have is determined, this compensation is taken to present value using the risk-free rate as the discount rate. Geometrical Brownian motion with Monte Carlo simulation is applied with 50,000 iterations and average compensation at present value is the value of the premium financial option [18,19]. As shown in (4) shows Geometric Brownian Motion for option premium valuation.…”

Further properties of random orthogonal matrix simulation

“…from the class of multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models, which capture the volatility and correlation clustering which is usually present in financial risk factor returns, but nevertheless requires time-consuming simulations for forecasting -see [37], [10], [38] and many others. Even in problems where only the terminal distribution is modeled (as it is when pricing European options, for example) simulation is still required under non-affine continuous-time models: see [33] for advanced simulation methods and see [4] and [21] for the evaluation of various non-affine models.…”

“…4 In our n-dimensional ROM simulations (4) we will apply A c c e p t e d M a n u s c r i p t orthogonal matrices R n which are products of n − 1 upper Hessenberg matrices. In general these have no zero elements, since the product of k upper Hessenberg matrices only has zeros below the k-th sub-diagonal.…”