questions on options

Hi ,
I have a few questions regarding options. Could you help me out with those please? Thank you so much in advance.
1) the price for a call option ,XYZ ,that will expire in June 2012 is worth $40 today. Will the price for XYZ still be $40 in March 2012 since the time to maturity decreases?
2) Questions on put-call parity.
Portfolio A: One European call Option+ a zero-coupon bond that pays K at T
Portfolio C: One European Put option + one share
The call and put options have the same strike price and time to maturity, so put-call parity comes into play.
Say C is overpriced. Then the strategy of an arbitrage is-buy the callshort the put+ short the stockinvest in risk free interest rate
I wonder
a) is the “risk free interest rate” equal to “zero coupon bond that pays K at T?”
b)when the stock price is more than the strike price, the call is exercised, and the “net profit” will be risk free interest rate value-strike price. Why do we ignore the transaction of put then? If we short the put, don’t we pay the price for put and then buy the put back? How does the borrowing and buying back costs of put option work?

3) the following 2 questions are from the textbook “fundamentals of futures and options markets” 7th edition by John Hull.
Question 10.11-a four month European call option on a dividend-paying stock is currently selling for $5. The stock price is $64, the strike price is $60, and a dividend of $0.80 is expected in one month. The risk free interest rate is 12% per annum for all maturities. What opportunities are there for an arbitrageur?
The solution is:
Minimum price for a call option-64-60e^(-0.12x4/12)-0.8e^(-0.12x4/12)=$5.58, but now it is sold for $5, so there is an arbitrage opportunity.
Short stock, buy call-64-5=$59, invest $0.79 from $59 for 0.80 dividends later.
Question 10.14-the price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. The term structure is flat, with all risk-free interest rates being 10%. Explain the arbitrage opportunities if the European put price is $3.
Put call parity— 2+30e^(-0.1X6/12)+0.5e^(-0.1x2/12)+0.5e^(-0.1x5/12)=p+29
SoPrice of put should be $2.51
But now it is offered at 3. So should buy call, short put and stock, and invest in risk free rate.
-2+3+29=$30
$30e^(0.1x6/12)
I wonder why in question 10.11, the arbitrageur would invest for dividends (as in he invests 0.79 from the $59 for 0.80dividens later), but not in question 10.14 (as in he invests all 30 in risk free rate)?

 
Best Response

[quote=cyl90089] 1) the price for a call option ,XYZ ,that will expire in June 2012 is worth $40 today. Will the price for XYZ still be $40 in March 2012 since the time to maturity decreases?

There is a probability that it could be, as call options have more pricing factors than just maturity.

2) Questions on put-call parity. Portfolio A: One European call Option+ a zero-coupon bond that pays K at Time What is the Call option on the bond?

Portfolio C: One European Put option + one share

Lol, put options are generally for for 100 shares.

The call and put options have the same strike price and time to maturity, so put-call parity comes into play. Say C is overpriced. Then the strategy of an arbitrage is-buy the callshort the put+ short the stockinvest in risk free interest rate

Ok!

I wonder a) is the “risk free interest rate” equal to “zero coupon bond that pays K at T?”

What... the risk free interest rate is the 3 month treasury.... currently .02

b)when the stock price is more than the strike price, the call is exercised, and the “net profit” will be risk free interest rate value-strike price.

Should be minus transaction costs and taxes.

Why do we ignore the transaction of put then?

English, please.

If we short the put, don’t we pay the price for put and then buy the put back? How does the borrowing and buying back costs of put option work?

If you are shorting the put you are paying interest to the borrower. You buy the put back at a lower price and give it to the owner and say TYVM.

3) the following 2 questions are from the textbook “fundamentals of futures and options markets” 7th edition by John Hull. Question 10.11-a four month European call option on a dividend-paying stock is currently selling for $5. The stock price is $64, the strike price is $60, and a dividend of $0.80 is expected in one month. The risk free interest rate is 12% per annum for all maturities. What opportunities are there for an arbitrageur? The solution is:

Minimum price for a call option-64-60e^(-0.12x4/12)-0.8e^(-0.12x4/12)=$5.58, but now it is sold for $5, so there is an arbitrage opportunity.

Short stock, buy call-64-5=$59, invest $0.79 from $59 for 0.80 dividends later.

Question 10.14-the price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. The term structure is flat, with all risk-free interest rates being 10%. Explain the arbitrage opportunities if the European put price is $3. Put call parity— 2+30e^(-0.1X6/12)+0.5e^(-0.1x2/12)+0.5e^(-0.1x5/12)=p+29

I hope you don't use this old arcane pricing model in real life.

SoPrice of put should be $2.51 But now it is offered at 3. So should buy call, short put and stock, and invest in risk free rate. -2+3+29=$30
$30e^(0.1x6/12) I wonder why in question 10.11, the arbitrageur would invest for dividends (as in he invests 0.79 from the $59 for 0.80dividens later), but not in question 10.14 (as in he invests all 30 in risk free rate)

Recheck your maths.

 

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