Dissertation writing help - Option Pricing for Discrete Hedging and Non-Gaussian Processes

Custom Dissertation Writing Service - on minimizing the portfolio risk minimizes the option price.

The Black-Scholes option pricing technique is correct under certain assumptions, among others continuous hedging and a log-normal underlying process. If any of these two assumptions is not fulfilled, a risk-less replication of an option is in general not possible. To handle this case, a pricing method was proposed by Sornette and Bouchaud.

Similar to Black-Scholes, a hedging portfolio is taken. The hedging strategy is such that the risk of the hedging portfolio is minimized. An option price is then deduced from this hedging strategy. Since a risk remains, the price adds a risk premium.

In this thesis, a new alternative method is shown, which instead of minimizing the portfolio risk minimizes the option price. This makes the option most competitive on the market. For the option writer, the ratio of return to risk is, by definition of the method, the same as for the Bouchaud-Sornette approach.

Both methods were compared with each other. For typical options, differences of up to 10 % of the price were found. The risk premium as well as fat tails in the underlying process provide rise to volatility smiles for both methods. Thus, it was found that both methods are consistent with Black-Scholes pricing. The results converge towards the Black-Scholes result in the continuous time limit for a log-normal process.