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Predicting food prices in Kenya using machine learning: a hybrid model approach with XGBoost and gradient boosting. [PDF]
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ASYMPTOTICS OF IMPLIED VOLATILITY IN LOCAL VOLATILITY MODELS
Mathematical Finance, 2010Using an expansion of the transition density function of a one‐dimensional time inhomogeneous diffusion, we obtain the first‐ and second‐order terms in the short time asymptotics of European call option prices. The method described can be generalized to any order.
J. Gatheral +4 more
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2020
In this chapter, we start first by presenting some typical properties of the local volatility surface, namely: the At-The-Money volatility, skew and curvature. We then move on to the implied volatility dynamics embedded in the local volatility model.
Othmane Kettani, Adil Reghai
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In this chapter, we start first by presenting some typical properties of the local volatility surface, namely: the At-The-Money volatility, skew and curvature. We then move on to the implied volatility dynamics embedded in the local volatility model.
Othmane Kettani, Adil Reghai
openaire +1 more source
2016
We present here the main characteristics of local volatility models in which the volatility of the risky assets is a function of time and of the spot value of the underlying. It is a standard in the industry. They are flexible enough to fit the vanilla option prices of all maturities, while preserving the completeness of the market.
Bruno Bouchard +1 more
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We present here the main characteristics of local volatility models in which the volatility of the risky assets is a function of time and of the spot value of the underlying. It is a standard in the industry. They are flexible enough to fit the vanilla option prices of all maturities, while preserving the completeness of the market.
Bruno Bouchard +1 more
openaire +1 more source
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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Collocating Local Volatility: A Competitive Alternative to Stochastic Local Volatility Models
SSRN Electronic Journal, 2018We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) model, introduced in Grzelak (2016). The CV model consists of two elements, a 'kernel process' that can be efficiently evaluated and a local volatility function. The latter, based on stochastic collocation – e.g. Babuska et al.
Anthonie van der Stoep +2 more
openaire +1 more source
2014
So far, we have looked at two modelling approaches to explain the implied volatility smile: local volatility and stochastic volatility. If we choose a stochastic volatility approach, we have seen that there are many possible models, each having the ability to generate a smile. This is rather unsatisfactory since it leaves us wondering which approach or
openaire +2 more sources
So far, we have looked at two modelling approaches to explain the implied volatility smile: local volatility and stochastic volatility. If we choose a stochastic volatility approach, we have seen that there are many possible models, each having the ability to generate a smile. This is rather unsatisfactory since it leaves us wondering which approach or
openaire +2 more sources