News for hackers. Stuff that matters.

A comment on Option Pricing with Fourier Transform and Exponential Lévy Models [pdf].

Re:Option Pricing with Fourier Transform and Exponential Lév... by cosmic_ape on Saturday October 27, 2018 @03:46AM (#18314762)
>> The answer is that these three models are special cases of more general exponential Lévy models. Options cannot be priced with general exponential Lévy models using the traditional approach of the use of the risk-neutral density of the terminal stock price because it is not available.

Does this mean there is no hedging strategy in these general exponential models? My understanding is the Black-Scholes gives the price, such that if the price was different, there would be an arbitrage strategy (under some assumptions on the variance). And this arbitrage strategy is used for hedging.

[ Parent | on HN ]
Re:Option Pricing with Fourier Transform and Exponential Lév... by conistonwater on Saturday October 27, 2018 @05:04AM (#18314948)
That's right, in the Black Scholes model for any option you can construct essentially a portfolio of money market+stock that replicates the option. So if you sell the option and buy and track the replicating portfolio, there is no hedging error. But you can't hedge perfectly when there are jumps, there is no replicating portfolio, only ways to minimize the hedging error.
[ Parent | on HN ]