Question

A European call option and put option on a stock both have a strike price of $25 and an expiration date in four months. Both sell for $4. The risk-free interest rate is 6% per annum, the current stock price is $23, and a $1 dividend is expected in one month. Identify the arbitrage opportunity open to a trader.

Answer 1

Here,

X= 25 T -t = 4 month = 1/3 C = P = 4 r = 6% = 0.06 St = 23 D1 = 1 t1 - t = 1 month= 1/12

The call price is $4 ,

using put call formula for above information

= C + Xe-r(T- t) + D1e- r(t1-t)

4+ 25e -0.1 1/3 + 1e 0.1 -1/12 = P + 23

it above 4 so, the put is undervalued relative to call.

here arbitrage opportunity is buy the stock. ( buy the put and short the call)

The cost is 23 and the stock price in four month greater than 25.

Put call formula are given below ;-