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Please help- Option pricing

Api V.

Api V.

Joined
3/20/12
Messages
6
Points
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Im studying on derivative securities, and here is the question from lastyear final exam. im not sure what the answers are? but just want to prepare for the final examination. can anyone give me the answer and explain.

Questions
Let C(K) denote a European vanilla Call option with strike price . Assume that all options are identical except for strike price, and strike prices satisfy K1< K2<K3and 2K2 = K1+K3.

Question 1
What are the no-arbitrage lower bound, and the no-arbitrage upper bound, of the vertical spread
C(K1) −C(K2)?

Question 2

Derive the functional relationship between the no-arbitrage values of the two vertical spreads,

C(K1) - C(K2) and C(K2) - C(K3).
 
can anyone answer those 2 questions. it doesnt matter if ur answers are wrong but just want to know what you think and how you approach those questions.
 
you might want to start with looking up slope and convexity restrictions. this is a trivial question and that's probably why no one wants to spend time answering it
 
The call price is convex in strike price, so the option in the middle cannot have a price greater than the average of the other two options.

The call price also decreases with increasing strike, so c(K2) < c(K1).
 
Answer to question 1:
0 ~ K2-K1
K2-K1 is the maximum loss at the maturity after shorting the C(K1) and longing the C(K2), which gains C(K1)-C(K2) to set up spontaneously. If C(K1)-C(K2)>K2-K1, setting up the portfolio will give you 0 chance of loss and some chance of winning.

Could you complete the 0 part please?
The second question is harder and you can think of it first.
 
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