We consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have an arbitrage ? Reminder: anarbitrage is an opportunity to obtain a positive profit without risk.(c) If you were the investor, which strategy would you adopt and why ? (This is anopen question without a right or wrong answer. Feel free to elaborate.)
We consider the one-period model studied in class as an example. Namely, we assume
that the current stock price is S0 = 10. At time T, the stock has either moved up to
St = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).
We consider a call option on this stock with maturity T and strike price K = 10. The
interest rate on the money market is zero.
As in class, we assume that you, as a customer, are willing to buy the call option on
100 shares of stock for $120. The investor, who sold you the option, can adopt one of the
following strategies:
Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380.
Strategy 2: Buy 55 shares of stock and borrow $430.
Strategy 3: Buy 60 shares of stock and borrow $480.
Strategy 4: Buy 40 shares of stock and borrow $280.
(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,
and at time T for each possible movement of the stock.
(b) For each of strategies 2-4, does the investor have an arbitrage ? Reminder: an
arbitrage is an opportunity to obtain a positive profit without risk.
(c) If you were the investor, which strategy would you adopt and why ? (This is an
open question without a right or wrong answer. Feel free to elaborate.)
Step by step
Solved in 2 steps
