Q4) A financial institution has the portfolio of OTC options on the ASX SPI 200 index. The delta of the portfolio is 500 and the gamma of the portfolio is -5000. An exchange traded index option has a delta of 1.5 and a gamma of 0.6. (a) What positions in the above exchange traded option and the spot index would make the portfolio both delta neutral and gamma neutral? (b) What positions in the above exchange traded option and six- month index futures would make the portfolio both delta neutral and gamma neutral? Assume that the risk-free rate is 4.5% per annum with continuous compounding and the dividend yield on the index is 1.1% per annum with continuous compounding Gamma neutrality:p + wor, + w,fs-0 Delta neutrality: Ap Woo WsAs 0 8