Consider a stock paying continuous dividends of 1%. Assume r = 0.06, = 0.32 and
ID: 2729826 • Letter: C
Question
Consider a stock paying continuous dividends of 1%. Assume r = 0.06, = 0.32 and today’s stock price of S0 = 33. You sell 100 Calls with strike K = 35 and expiration in 68 days (assume 365 days in a year). You also construct a delta-hedge to manage your risk.
• If tomorrow (1 day later) stock price rises to $34.50, find your net profit/loss from your hedged portfolio. Hint: don’t forget about dividends!
• Repeat this problem for the case of selling 100 Puts with strike K = 35 and all other parameters staying the same.
Explanation / Answer
Answer: RunningBSCall (0,68/365,33,35,0.06,0.01,0.32,0)
we nd C0= 1.1415 and 0= 0.3854. So the initial Delta-hedge is to
After 1-day we haveS1/365= 34.50, and the Call premium rises toC1/365= 1.7984. Sothe net changes are
Net portfolio change is-65.69 + 57.85-0.19 =-$8.04 loss.b) RunningBSCall(0,68/365,33,35,0.06,0.01,0.32,1)We ndP0= 2.8138 and0=-0.6128. So the initial Delta-hedge is to
So the net changes are: