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On a Heath-Jarrow-Morton approach for stock options. (English) Zbl 1390.91302
Summary: This paper aims at transferring the philosophy behind Heath-Jarrow-Morton to the modelling of call options with all strikes and maturities. Contrary to the approach by R. Carmona and S. Nadtochiy [ibid. 13, No. 1, 1–48 (2009; Zbl 1199.91202)] and related to their recent contribution [ibid. 16, No. 1, 63–104 (2012; Zbl 1259.91047)], the key parameterisation of our approach involves time-inhomogeneous Lévy processes instead of local volatility models. We provide necessary and sufficient conditions for absence of arbitrage. Moreover, we discuss the construction of arbitrage-free models. Specifically, we prove their existence and uniqueness given basic building blocks.

##### MSC:
 91G20 Derivative securities (option pricing, hedging, etc.) 60G51 Processes with independent increments; Lévy processes 91G30 Interest rates, asset pricing, etc. (stochastic models)
##### Keywords:
Heath-Jarrow-Morton; option price surfaces; Lévy processes
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##### References:
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