We are given a one-step binomial model with B(0) = 10, B(1) = 11, S(0) = 100 and S(1) = 120
with probability p = 0.5 and S(1) = 80 with probability (1 −p) = 0.5.
(a) Is the market (B, S) (consisting of a bond and a stock) arbitrage-free?
(b) Assuming no-arbitrage exists in the extended market (B, S, P ), find the price P (0) of a put option with strike price K, maturity date T = 1.
(c) Show that there exists a unique q ∈(0, 1) such that P (0) = (B(0)/B(1))(q(K −Su)+ + (1 −q)(K −Sd)+ ). How does q depend on K? Is q = p?
(d) Let q ∈(0, 1) be as in part (c). What can you say about B(0)/B(1)(qSu + (1 −q)Sd )?
(e) Suppose that the put option from parts (b) and (c) is in fact traded at time 0 for ̃P < P (0), where P (0) is as in part (c). Find an arbitrage opportunity by trading in the market (B, S, P ). qSu + (1 −q)Sd ?

Answer rating: 100% (QA)

a Yes the market is arbit rage free This is because the price of the st... View the full answer