Global ETD Search
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Showing 1 to 13 of 13 for “"local volatility"”.
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Gaussian Process Regression for a Single Underlying Autocallable Security
… its traditional pricing under the Stochastic Local Volatility (SLV) model. An autocallable is a structured product which allows for early redemption when the underlying meets certain barrier conditions. Due to its path dependency, autocallables are typically priced using Monte Carlo simula- …
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Implied volatility: general properties and asymptotics
This thesis investigates implied volatility in general classes of stock price models. To begin with, we take a very general view. We find that implied volatility is always, everywhere, and for every expiry well-defined only if the stock price is a non-negative martingale. We also derive sufficient …
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Pricing stochastic volatility models using random grids
… under the Heston model as well as the stochastic local volatility model. Consistent results are obtained for a call option under the various pricing methods using similar parameters as those used in the random grids paper. More specifically, when using a Heston model, consistent prices are …
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2-Factor Models in Credit and Energy Markets
… credit crisis. In Part B a 2 – factor model with local volatility for oil market is developed. For the first part three structural form models; Merton’s (1974), Leland – Toft (1996) and Longstaff – Schwartz (1995); were implemented using different assumptions for volatility and debt maturity (i) …
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Forward and inverse American option pricing via a complementarity approach
… the pricing of American options under a local volatility model and two jump diffusion models: Kou's jump diffusion model and the Dupire system. In Chapter 2, we establish partial differential complementarity systems for pricing American options under the aforementioned three models. We …
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Estimating Long Term Equity Implied Volatility
… case, practitioners have to estimate the implied volatility surface across a range of expiries and moneyness levels. A detailed evaluation is performed for different estimation techniques to assess the strengths and weaknesses of each of the models. The estimation techniques considered include …
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Path-dependent volatility: an application to the South African market
… have thus far focussed on three classes of volatility models, namely, constant volatility, local volatility and stochastic volatility. Pathdependent volatility models are a lesser known class of models which possess the key characteristic of completeness together with the ability to generate …
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Derivative pricing with options.
… if we restrict ourselves to diffusions, then the local volatility surface can be determined by a simple equation which involves differentiating the option prices with respect to their maturity and strike price. We considerably extend this result of Dupire. First, we show that if we generalise the …
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Calibration of Option Pricing in Reproducing Kernel Hilbert Space
A parameter used in the Black-Scholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in the valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem …
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Hedging volatility: different perspectives compared
… set by the Heston (1993) model in a stochastic volatility environment. The Black-Scholes portfolio was implemented using a fixed volatility and by implying volatility from the market. Additionally, a portfolio based on the Dupire (1994) local volatility model was also compared. It was found that …
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Option pricing with physics-informed neutral networks (PINNS)
… The problem is also extended by incorporating a local volatility model. Here, we derive the PDE of a vanilla European option under the constant elasticity of variance (CEV) model. We then construct and train a PINN to solve the PDE and compare it to the true analytical solution of a special case …
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Local Stochastic Volatility—The Hyp-Hyp Model
Volatility modelling is used predominantly in order to explain the volatility smile observed in the market. Stochastic volatility models are mainly used to capture the curvature of a volatility smile while local volatility models generally model the skew. Jackel and Kahl ¨ (2008) present a …
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Analytical Solutions of the SABR Stochastic Volatility Model
… to the practice of option trading, in which the volatility parameter of the Black-Scholes-Merton's model has become the market "language'' of quoting option prices. Despite its tremendous success, the Black-Scholes-Merton model has exhibited a few well-known deficiencies, the most important of …