This research examines if there exists an appealing distribution for jump amplitude in the sense that with this distribution, the stochastic volatility double jump-diffusions (SVJJ) model would potentially have a superior option market fit while keeping a sound balance between reality and...

In this paper we consider several time-varying volatility and/or heavy-tailed models to explain the dynamics of return time series and to fit the volatility smile for exchange-traded options where the underlying is the main ‘Borsa Italiana' stock index. Given observed prices for the time...

Probability density function (pdf) for (weighted) sum of n correlated lognormal variables is deducted. The method uses joint pdf of multivariate correlated lognormal variables and an extended method of convolution. The formula contains (n-1)-fold integral, which can be evaluated by numerical...

Chen and Shen (2003) argue that it is possible to improve the Least Squares Monte Carlo Method (LSMC) of Longstaff and Schwartz (2001) to value American options by removing the least squares regression module. This would make not only faster but also more accurate. We demonstrate, using a large...

We present in a Monte Carlo simulation framework a novel approach for the evaluation of hybrid local volatility (Dupire 1994, Derman and Kani 1998) models. In particular, we consider the stochastic local volatility model - see e.g. Lipton et al. (2014), Piterbarg (2007), Tataru and Fisher...

Monte Carlo simulation or probability simulation is a technique used to understand the impact of risk and uncertainty in financial and other forecasting models. It is very useful when complex financial instruments need to be priced. Exotic options are listed on the JSE on its Can-Do platform....

In this paper we develop efficient Monte Carlo methods for estimating American option sensitivities. The problem can be re-formulated as how to perform sensitivity analysis for a stochastic optimization problem when it has model uncertainty. We introduce a generalized infinitesimal perturbation...

Building on previous work of Kolm and Ritter (2019) and Cao et al. (2019), this paper explores the novel application of Deep Reinforcement Learning for Delta Hedging of options in an utility based framework where an agent is faced with a trade-off between hedging error and transaction costs...

We present a numerically efficient approach for machine-learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be used to implement a stochastic implied volatility...