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Stochastic Local Volatility [PDF]
SSRN Electronic Journal, 2008 There are two unique volatility surfaces associated with any arbitrage-free set of standard European option prices, the implied volatility surface and the local volatility surface. Several papers have discussed the stochastic differential equations for implied volatilities that are consistent with these option prices but the static and dynamic no ...
Carol Alexander, Leonardo Nogueira
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2008
Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic time-varying volatility and codependence found in financial markets. Such dependence has been known for a long time; early commentators include Mandelbrot (1963) and Officer (1973). It was also clear to the founding
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Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic time-varying volatility and codependence found in financial markets. Such dependence has been known for a long time; early commentators include Mandelbrot (1963) and Officer (1973). It was also clear to the founding
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Structural Stochastic Volatility
SSRN Electronic Journal, 2020We use a local (in time) expansion of the characteristic function of the equity process in continuous time to derive short-maturity option prices. The prices, along with data on short-maturity options, are employed to jointly identify equity characteristics (spot volatility, spot leverage and spot volatility of volatility) which have been the focus of ...
Federico M. Bandi +2 more
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2005
Abstract Neil Shephard has brought together a set of classic and central papers that have contributed to our understanding of financial volatility. They cover stocks, bonds and currencies and range from 1973 up to 2001. Shephard, a leading researcher in the field, provides a substantial introduction in which he discusses all major ...
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Abstract Neil Shephard has brought together a set of classic and central papers that have contributed to our understanding of financial volatility. They cover stocks, bonds and currencies and range from 1973 up to 2001. Shephard, a leading researcher in the field, provides a substantial introduction in which he discusses all major ...
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IMPLIED AND LOCAL VOLATILITIES UNDER STOCHASTIC VOLATILITY
International Journal of Theoretical and Applied Finance, 2001For asset prices that follow stochastic-volatility diffusions, we use asymptotic methods to investigate the behavior of the local volatilities and Black–Scholes volatilities implied by option prices, and to relate this behavior to the parameters of the stochastic volatility process.
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2016
Stochastic volatility models are used when the option price is very sensitive to volatility (smile) moves, and when they cannot be explained by the evolution of the underlying asset itself, see e.g. [34]. This is typically the case for exotic options.
Bruno Bouchard +1 more
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Stochastic volatility models are used when the option price is very sensitive to volatility (smile) moves, and when they cannot be explained by the evolution of the underlying asset itself, see e.g. [34]. This is typically the case for exotic options.
Bruno Bouchard +1 more
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Stochastic Volatility and Realized Stochastic Volatility Models
2023Makoto Takahashi +2 more
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Stochastic Volatility Processes
2013In a stochastic volatility process, the positivity and mean reversion of the volatility should be enforced. The mean reversion can be achieved by the drift, equivalent to an Ornstein–Uhlenbeck process. The positivity can be enforced either by an exponential or by taming down the stochastic term by the volatility as done in the Heston process.
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2011
A natural generalization of the Black–Scholes model is to allow the volatility to be stochastic. This is motivated by the fact that a historical analysis shows that the volatility indeed behaves as if it was stochastic. In this chapter we consider various techniques for solving stochastic volatility models.
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A natural generalization of the Black–Scholes model is to allow the volatility to be stochastic. This is motivated by the fact that a historical analysis shows that the volatility indeed behaves as if it was stochastic. In this chapter we consider various techniques for solving stochastic volatility models.
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