Question

A one-month European call option on a non-dividend-paying stock is currently selling for $2.50. The stock price is $55, the strike price is $50, and the risk-free interest rate is 6% per year. What opportunities are there for an entrepreneur?

Answer 1

Current stock price (S0) = $55

Strike price (K) = $50

Call Price (C) = $2.50

Maturity in years = 1/12 = 0.0833

risk free rate = 6%

Intrinsic value of Call option(V0):

So, Intrinsic value of Call option is more than its market price which means Call option is under-priced in the market.

An entrepreneur can earn risk free profit from this opportunity with following strategy:

• Sell stock at current price i.e $55
• Buy Call option at $2.50
• lend remaining amount i.e $52.5 at risk free rate.

On expiration date:

• Collect lent money with interest i.e 52.5*(1+0.06)^0.0833 = $52.76
• Exercise the call option and buy the stock at strike price i.e $50

Risk free Profit = 52.76-50 = $2.76