242 1.6 1.5 1.4 1.3 1.2 1.2 1.1 1 0.9 1.1 1 0.9 Normal distribution 1.5 1.4 1.3 9. Financial simulation at work: some case studies Student t distribution, = 5 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 0 0.02 0.04 0.06 0.08 0.1 0.9 0 0.02 0.04 0.06 0.08 0.1 Cornish­Fisher; S = - 0.3 0.01 0.025 0.05 0.1 VaR m / N / VaR Hill t heo 0 0.02 0.04 0.06 0.08 0.1 VaR confidence level, VaR confidence level, VaR confidence level, Figure 9.4 Median of ratios VaR Hill / VaR theo for different underlying distributions (panels) and different fractions of data used, m/N (lines). 9.3. Option pricing The fair value of an option (in fact, of any asset) can be written such: fair value discount factor £ expected payoff. Let the payoff be a deterministic function of a vector Y of state variables.