Put intrisict value = Max(0,X-S0) = Max(0,104.67-108.83) = 0
Time value = option price - intrinsic value = 8,18 - 0 = 8,18
There are 2 European put options with identical time to expiration. One has exercise
price of 150 and a premium of 3. Another one has exercise price of 155 and a premium
of 8. If the market is efficient, are the 2 puts price appropriate?
a.Yes, the 2 puts are fairly priced. there is no arbitrage opportunity.
b.No, the 2 puts are not fairly priced. there is an arbitrage opportunity.
At expiration:
● If the stock price is above 155, both puts expire worthless, and we keep the $5 profit
risk-free.
● If the stock price is below 150, the intrinsic value of the spread is:
(155−S)−(150−S)=5(155 - S) - (150 - S) = 5(155−S)−(150−S)=5
Since we received 5 upfront, our total profit is $0, meaning no loss.
For American call with underlying asset is stock: when the stock pays dividends, early-exercise
should be conducted before ex-dividend date.
For American put, when the stock pays dividends. the likelihood of early-exercise decreases .
Intrinsic value = Max(0,106,78-110,36) = 0
Time value = option value - IV = 8,23
When comparing 2 call options, the call with lower exercise price often has higher price. The
American options often have higher price comparing to European ones.
IV = Max (0, 98 - 110) =0
Lower bound = 𝑀𝑀𝑀[0, 𝑀(1 + 𝑀)−𝑀 − 𝑀0 + ∑𝑀
𝑀𝑀 (1 + 𝑀)−𝑀 ] =
𝑀=1
= 134.08(1+7%)^(-1) - 119.09 + 4.5(1+7%)^(-3/12) = 2,79
C = 𝑀 + 𝑀0 − 𝑀(1 + 𝑀)−𝑀 = 9.8 + 123,1 − 118,2(1 + 8%)−7/12 = 19,89