A dealer sold 1000 OTC call options. The OTC option has a delta of 0.550 and gamma of 0.025. The price of the underlying stock is $100. An exchange-traded call option has the same time to expiration, a delta of 0.450 and gamma of 0.008.

a) Write down the two equations that represent the delta-hedge and gamma-hedge conditions for hedging the OTC call options sold. Let Ns and Nc represent the number of stocks and exchange-traded calls. (2 points)

b) Determine the positions (the quantity and whether it should be bought or sold) in the stock and exchange-traded call option that will be needed to hedge the delta and gamma risk of the options sold. Show your calculations for determining the positions needed to implement the delta and gamma hedge. (2 points)