A Petit Trio on Option Pricing
Henry Horng-Shing Lu
|關鍵字:||隨機波動率模型;GARCH模型;損失函數;stochastic volatility model;GARCH model;loss function|
Option pricing may be one of the most important and fascinating topics in modern finance. Complex models and algorithms can be applied here so that researchers and practitioners may bring their quantitative skills into full play. In practice, pricing is also the core of different types of arbitrage strategies. For more precise pricing, structural models are generally necessary where continuous time stochastic volatility model can be one of the candidates. However, volatility, the most important state variable, is in fact unobservable and the likelihood cannot be available in close form for the stochastic volatility models. The sets of articles explore related statistical issues about option pricing with stochastic volatility models. Especially, the unobservability of volatilities is taken into considerations. By the fact that a GARCH model would converge weakly to the corresponding stochastic volatility model, statistical inference including estimation and pricing can be made based on a specially designed partially observed GARCH model whose likelihood will be obtained through MCMC methods. In this context, some drawbacks from the current practices can be improved. Finally, an investigation on the loss functions for option pricing is also made. Although the pricing theory does not restrict to any specific loss functions, the statistics that correspond to the information contents, for example implied volatilities, should be used as a basis for the construction of loss functions. Furthermore, due to the fact that pricing is generally based on some equilibrium conditions, the model implied statistics would just play as the target of mean reversion of the real price implied process, instead of an absolute reference of prices.
|Appears in Collections:||Thesis|
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