Abstract
In the presence of jumps, the financial market is no longer complete, and option payoffs cannot be replicated by a portfolio of primitive assets. The state price density and the pricing kernel are not unique. In order to price options in an incomplete market, either a candidate pricing kernel is used for the risk-neutral evaluation approach, or a general pricing framework built on the equilibrium exchange economy of Lucas (Econometrica, 46:1429–1445, 1978) is required.
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Notes
- 1.
With S&P 500 index options, Santa-Clara and Yan (2010) come to a similar conclusion that the risk premium is a function of both the stochastic volatility and the jump intensity.
- 2.
There is a difference in that the jump risk priced in Merton’s model is not priced because it is assumed to be diversifiable. Here it is not priced because the representative agent is risk-neutral given the restrictions on utility function.
- 3.
The continuous diffusion volatility is unchanged when moving from the risk-neutral measure to the physical measure. See for example Liu et al. (2007). For simplicity, the stochastic volatility is replaced by a constant volatility.
- 4.
The impact of fanning \(\varphi \) shown here is opposite to the conclusion of Ma and Vetzal (1997) because we assume a negative jump while they assume a positive jump.
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© 2018 Xiamen University Press and Springer Nature Singapore Pte Ltd.
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Chen, J. (2018). Simulation Comparison. In: General Equilibrium Option Pricing Method: Theoretical and Empirical Study. Springer, Singapore. https://doi.org/10.1007/978-981-10-7428-8_3
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DOI: https://doi.org/10.1007/978-981-10-7428-8_3
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