5.27 get_basket_volatility

Function File: [basket_vola, basket_dict ] = get_basket_volatility (valuation_date, value_type, option, instrument_struct, index_struct, curve_struct, riskfactor_struct, matrix_struct, surface_struct)

Return diversified volatility for synthetic basket instruments. The diversified volatility is dependent on the option maturity and strike, so the volatility has to be calculated for each basket option valuation. The following two methods are implemented:

• Levy 1992: Levy uses a log-normal density as a first-order approximation to the true density. This holds for small maturities or volatilities only, since a weighted sum of log-normal distribution is not a log-normal distribution by itself.
• VCV approach: Assuming a normal distribution of underlying, the basket volatility is calculated by sigma = sqrt(w’*C*w) with Covariance Matrix C and the linear-combinations vector w.
• Beisser: Calculate lower limit of option prices by adjusting input volatilities and strikes. Also returns modified strike basket_dict.