TOPIC: The pricing of stock and currency derivatives: BlackScholes

Given Sect.3.6 is Gamma Hedging

2. Consider delta and gamma hedging a short call option, using the under- lying and a put with the same strike and maturity as the call. Calculate the position in the underlying and the put that you should take, using the analysis in Sect. 3.6. Will you ever need to adjust this hedge? Related your result to put-call parity. 3 Black-Scholes GAMMA HEDGING 6 Gamma Hedging Delta hedging is perfect if we can continuously rebalance the hedging portfolio . in reality, this is very costly (trading costs) the problem is r# 0, so it is only possible to rebalance portfolio discretely > To improve the discrete delta hedge, we can use a delta/gamma hedging strategy this has to use another option (a liquid one) let s' and r' be the delta and gamma of this option 3 Black-Scholes GAMMA HEDGING using a shares of stock and b shares of option to hedge the underlying option > delta neutral -8+a+b8' = 0 > gamma neutral -r+br'=0 solving a and b yields the delta/gamma neutral strategy > vega neutral? 2. Consider delta and gamma hedging a short call option, using the under- lying and a put with the same strike and maturity as the call. Calculate the position in the underlying and the put that you should take, using the analysis in Sect. 3.6. Will you ever need to adjust this hedge? Related your result to put-call parity. 3 Black-Scholes GAMMA HEDGING 6 Gamma Hedging Delta hedging is perfect if we can continuously rebalance the hedging portfolio . in reality, this is very costly (trading costs) the problem is r# 0, so it is only possible to rebalance portfolio discretely > To improve the discrete delta hedge, we can use a delta/gamma hedging strategy this has to use another option (a liquid one) let s' and r' be the delta and gamma of this option 3 Black-Scholes GAMMA HEDGING using a shares of stock and b shares of option to hedge the underlying option > delta neutral -8+a+b8' = 0 > gamma neutral -r+br'=0 solving a and b yields the delta/gamma neutral strategy > vega neutral