Abstract:
This thesis investigates the derivatives for portfolio optimization. Risk measures such as Mean Variance (MV), Value-at-Risk (VaR), and Conditional Value-at-Risk (CVaR) are minimized. However, we focus primarily on CVaR because it is a coherent and convex risk measure. We adopt the method of Rockafellar and Uryasev (Journal of Risk 2, 3 (2000)), which minimizes CVaR for shares and convert this method to use with options written on the S&P500 Mini Index. The distribution is known and the index values are simulated by using the VG distribution, over CVaR constraints. In particular, the approach can be used for minimizing the CVaR values under expected returns, and the conditions of the quotes come with the bid and ask prices as well as the sizes. We study the changes in optimized portfolios, subject to various modeling parameters. The values of CVaR depend on the standard deviation, the variance rate, the required return and the confidence level. Moreover, we compute the indifference prices to obtain the selling and accounting values and the hedging strategy. As a result, for all sigma values, the selling prices are greater than the buying prices, and when the expected return equals 1,400%, the indifference prices are between the hedging prices.
