The Lifted Heston Stochastic Volatility Model

Can we capture the explosive nature of volatility skew observed in the market, without resorting to non-Markovian models? We show that, in terms of skew, the Heston model cannot match the market at both long and short maturities simultaneously. We introduce Abi Jaber (2019)'s Lifted Heston model and explain how to price options with it using both the cosine method and standard Monte-Carlo techniques. This allows us to back out implied volatilities and compute skew for both models, confirming that the Lifted Heston nests the standard Heston model. We then produce and analyze the skew for Lifted Heston models with a varying number N of mean reverting terms, and give an empirical study into the time complexity of increasing N. We observe a weak increase in convergence speed in the cosine method for increased N, and comment on the number of factors to implement for practical use.

Grantor

African Institute of Financial Markets and Risk Management

Year dc:date.issued

2020

Author dc:creator

• Broodryk, Ryan

Advisors dc:contributor.advisor

• Backwell, Alex
• Soane, Andrew

• Stochastic volatility
• Implied volatility
• Volatility Skew
• Monte-Carlo
• Cosine method
• Riccati equations
• Complexity analysis

Handle dc:identifier.uri

http://hdl.handle.net/11427/32614

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/32614