Exam 16: Beyond Black-Scholes

The Black-Scholes model is time-inconsistent in the way it is applied in practice. This is because the model assumes that volatility is constant, even though the trader changes it every day to obtain a new price. Using this definition of time-inconsistency, which of the following statements is valid?

The Merton (1976) model

The asymmetric GARCH model was developed to mimic the following feature of other models that is not captured in the standard GARCH formulation:

GARCH models

Local volatility models

A Wall Street trading firm is using a jump-diffusion model to price their index options. They determine that the arrival rate of jumps in the market is 4 times a year, and that the jumps have a mean size of $- 2 \%$ and standard deviation of 10%. If the implied volatility of the stock index is 40%, what is the diffusion parameter ( $\sigma$ ) that they should use in their model?

Stochastic volatility models commonly assume