A carregar...
Publicação
The rBergomi rough volatility model
| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 1.03 MB | Adobe PDF |
Autores
Orientador(es)
Resumo(s)
Simulation schemes to estimate volatility from high frequency data lead some authors
to start studying local volatility models, where the local volatility of the stock varies with
the stock price and the stock price is itself stochastic. Hence, in local volatility models,
volatility is stochastic, but only because it is a function of the stochastic stock price. This
typically produces a skew in implied volatility (known as volatility smile), which can also
be obtained by using stochastic volatility models (like, for example, the Heston stochastic
volatility model), where the constant volatility of the Black-Scholes model is replaced by
a stochastic process driven by a random factor correlated with the random factor that
drives the price of the underlying asset.
Recently, Bayer et al. in [1] have gone a step further from local and stochastic
volatility modelling, proposing rough fractional stochastic volatility (RFSV) models
stating that log-volatility behaves as a fractional Brownian motion with Hurst exponent
H less than 0.5, which is essentially a non-Markovian process with stationary but not
independent increments. As a particular case for the RFSV model, these authors proposed
the so-called rough Bergomi (rBergomi) model. In this dissertation, the rBergomi model
is implemented by using the hybrid scheme proposed by Bennedsen et al. in [3], and the
implied volatility smiles over the SPX options are estimated for different maturities.
Finally, as the model depends only on three parameters: H, η (related to increments of
log-volatility) and ρ (correlation factor), these were calibrated to market data.
Descrição
Mestrado Bolonha em Mathematical Finance
Palavras-chave
rough Bergomi model fractional Brownian motion option pricing volatility smile
Contexto Educativo
Citação
Resco San José, Iñigo (2022). “The rBergomi rough volatility model”. Dissertação de Mestrado. Universidade de Lisboa. Instituto Superior de Economia e Gestão
Editora
Instituto Superior de Economia e Gestão