Question

13. Suppose that the current price of an asset is $31. The asset is expected to pay a dividend of S3 in one month. The asset also has an upfront carrying cost associated to it of $1. The risk-free rate is 5%. The price of a 3-month European call on this asset with strike $30 is $4. The price of a 3-month European put with strike $30 is $3.25. Construct a risk-free profit involving one call and one put.

no hand writing please

Answer 1

Let portfolio A be the call $ ke^- rt m cash Let portfolio B be the put and one shore of stock These must be worth the same so will check to see if put call parity holds c + k.e^- rt = 3 + 30 .e^- 0.1 times 3/12 = 32.26 P + S_0 = 2.25 + 31 = 33.25 Portfolio B is over priced compared to portfolio A so buy portfolio A & sell portfolio B At time 0, our cash is 33.25 - 32.26 = $ 0.96 M 3 months , no matter what happens, our cash flow is max (s_t . k) - max (s_t, k) = 0