| CHAPTER 8 |

Delta Neutral Positions and Dynamic Hedging

1.  The process of delta hedging an option position to remain delta neutral is an important part of using a theoretical pricing model. In a delta neutral position all the deltas add up to approximately zero, or at least as close to zero as is practically possible.

a.   You buy 25 July 80 calls. From the table of delta values above, what do you need to do (buy? sell? how many?) to hedge your position as close to delta neutral as possible using each of the following contracts?

b.   You sell 50 July 70 puts. What do you need to do (buy? sell? how many?) to hedge your position as close to delta neutral as possible using each of the following contracts:

c.   You sell 15 underlying contracts. You would like to hedge half your delta position using July 80 puts and the other half using July 90 calls. As close as possible, how many of each contract do you need to buy or to sell?

2.  In each of the option positions below, how many underlying contracts do you need to buy or sell in order to create an initial delta neutral position? Then, as the delta changes, how many underlying contracts do you need to buy or sell in order to maintain a delta neutral position, or a position that is as close to delta neutral as possible? Delta values are given in the whole number format.

a.   long 10 calls

b.   short 30 calls

c.   long 62 puts

d.   short 44 puts

3.  In theory an option’s value should be equal to the present value of its intrinsic value at expiration, plus the present value of all the cash flows resulting from the delta neutral dynamic hedging process.

In the two scenarios below, assume that the option is hedged at each given underlying price and delta. If interest rates are zero (no present valuing is necessary), what are the values of each option?

a.   55 call

b.   70 put