Option Valuation with Conditional Heteroskedastic Hidden Truncation Models

While asymmetric mixture models improve option pricing over generic pricing models, mispricing remains due to their inability to capture the effect of economic factors on price levels. This paper uses the hidden truncation normal $$\mathcal {(HTN)}$$ ( HTN ) distribution introduced by Arnold et al. (1993) and the NGARCH model of Engle and Ng (J Finance, 48:1749–1778, 1993) to price options. Compared to the Black–Scholes model, the $$\mathcal {HTN}$$ HTN -NGARCH option pricing model has extra parameters linked to economic dynamics and with economic interpretations. The model integrates some stylized facts underlying option prices such as a time-varying price of risk, non-normal innovations, asymmetry, and kurtosis. The model can be estimated by maximum likelihood. With an application to market data, we show that the $$\mathcal {HTN}$$ HTN -NGARCH model accurately prices index options and captures adequately the smirk of implied volatility.