3 research outputs found
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A realized volatility approach to option pricing with continuous and jump variance components
Stochastic and time-varying volatility models typically fail to correctly price out-of-the-money put options at short maturity. We extend realized volatility option pricing models by adding a jump component which provides a rapidly moving volatility factor and improves on the fitting properties under the physical measure. The change of measure is performed by means of an exponentially affine pricing kernel which depends on an equity and two variance risk premia, associated with the continuous and jump components of realized volatility. Our choice preserves analytical tractability and offers a new way of estimating variance risk premia by combining high-frequency returns and option data in a multicomponent pricing model
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A Jump and Smile Ride: Jump and Variance Risk Premia in Option Pricing
We introduce a discrete-time model for log-return dynamics with observable volatility and jumps. Our proposal extends the class of realized volatility heterogeneous auto-regressive gamma (HARG) processes adding a jump component with time-varying intensity. The model is able to reproduce the temporary increase in the probability of occurrence of a jump immediately after an abrupt large movement of the asset price. Belonging to the class of exponentially affine models, the moment generating function under the physical measure is available in closed form. Thanks to a flexible specification of the pricing kernel compensating for equity, volatility, and jump risks, the generating function under the risk-neutral measure inherits analytical tractability too. An application of the leveraged HARG model with dynamic jump intensity to the pricing of a large sample of S&P500 Index options assesses its superior performances with respect to state-of-the-art benchmark models