

FlashChat  Actuarial Discussion  Preliminary Exams  CAS/SOA Exams  Cyberchat  Around the World  Suggestions 

Thread Tools  Display Modes 
#1




Comparing Options Time to Expiry question
I have a question on ASM 10th edition Chapter 7 P.93 Example 7C.
For a nondivedend paying stock with price 21: (i) The continuously compounded riskfree raye is 4%. (ii) A European 3month put option on the stock with strike price 20 costs 1.00. (iii) A European 6month put option on the stock with strike price 20.30 costs 0.90. You take advantage of arbitrage. Assume that you sell one 3month put option and follow the optimal strategy, and that the stock price is 19 after 3 months and 21 after 6 months. Determine your net profit after 6 months. I cannot understand the answer on the manual, can anyone help? Let's fight for 2018 Mar MFE exam!! Gook Luck All! Last edited by Peter T.W. Chen; 11022017 at 02:35 AM.. 
#2




What is given as the answer?

#4




You sold a put with strike 20. It is exercised at time 3 months. Assume you borrow the money to cover.

#5




Time 0:
3 month put with strike 20 is sold 6 month put with strike 20.3 is bought Net cash flow time 0 = +0.1 Time 3/12: Borrower exercises put Net cash flow: 20 Time 6/12: Bought put option expires worthless. We sell stock that was "put" back on us at time 3/12Time 0: 3 month put with strike 20 is sold 6 month put with strike 20.3 is bought Net cash flow time 0 = +0.1 Net cash flow: +21 AV of all cash flows: 0.1*exp(0.04*0.5)  20*exp(0.04*0.25) + 21 = 0.9010 From a logical point of view I find this easy to follow. However, I would have naturally done: Time 0: 3 month put with strike 20 is sold 6 month put with strike 20.3 is bought Net cash flow time 0 = +0.1 Time 3/12: Borrower exercises put Net cash flow: 1 Time 6/12: Bought put option expires worthless. Net cash flow: 0 AV of all cash flows: 0.1*exp(0.04*0.5)  1*exp(0.04*0.25) = .8879 I don't feel like I've discovered any other problems where the put is valued in the manor this solution does... 
Tags 
comparing option, mfe, time to expiry 
Thread Tools  
Display Modes  

