Question

The current price of a non-dividend paying stock is $2600. The volatility of the stock is 20% per annum: σ[R] = 20%. The annually compounded risk-free interest rate is r = 2%. For this question, assume that European options on the stock exist and you will be considering the European options with a maturity T of one year and a strike price X = $2650.

(b) Suppose that the market prices for the call and the put options in (a) are: C = 210, and P = 203. Assume there are no transaction costs. Using the put-call parity, show that arbitrage profits exist under these conditions and explain how you would exploit the opportunity to earn such a risk-free profit.

Answer 1

To determine if arbitrage profits exist, we use the put-call parity equation and compare market prices of call and put options. If the equation does not hold true, there is an opportunity for arbitrage profits.

Step-by-step explanation:

To determine if arbitrage profits exist under the given conditions, we need to use the put-call parity equation: C - P = S - X / (1+r)^T

C is the market price of the call option, P is the market price of the put option, S is the current stock price, X is the strike price, r is the risk-free interest rate, and T is the time to maturity.

Plugging in the given values: C - P = 210 - 203 = 7

S - X = 2600 - 2650 = -50

Simplifying the equation: 7 = -50 / (1+0.02)^1

7 = -50 / 1.02

7 = -49.02

Since the equation does not hold true, the market prices of the call and put options violate the put-call parity and create an opportunity for arbitrage profits.