• The example on the second page of the attachment. What positions in the traded option and Yahoo stock can be added to the portfolio in order to make it both delta and vega neutral?
  

Delta and gamma hedging II Since a large gamma means we need to rebalance the portfolio more frequently, thus will suffer from high transaction costs, it is often preferable to form portfolios which are also gamma-neutral. Suppose you already have a portfolio P. How do you adjust the portfolio to make it delta-neutral? What about both delta and gamma neutral? One possible scheme: 1. Fix a derivative f with a non-zero gamma (e.g. a call). Choose the number of units of f to make the portfolio consisting of P and f gamma-neutral. 2. Then add the underlying stock to achieve delta-neutrality. Ruimeng Hu Stochastic Methods in Finance: Lec 20 15 / 23 Example A financial institution holds the following portfolio of over-the-counter options on Yahoo stock: Type |Delta Gamma Vega Postion Put -0.5 1.3 2 500 Call 1 0.6 1.2 -300 Call 1.2 0.8 N 200 traded 1.2 LS There is also a traded option on Yahoo stock with a delta of 1.2 gamma of 1.5 and vega of 1. What positions in the traded option and Yahoo stock can be added to the portfolio in order to make it both delta and vega neutral? Ruimeng Hu Stochastic Methods in Finance: Lec 20 16 / 23