Question

S&P 500 Index is at 2780. A European June 21, 2020 SPX call option struck at 2500 is trading at $316.94. An identical put is trading at $55.15. A T-bill with 200 days to maturity is quoted at a yield of 2.46. Which of the following positions would be included in the arbitrage strategy?

		Write the put
		Write the call
		Borrow at the risk-free rate
		Buy the stock

Answer 1

Write the put

Base for the solution

As per  call put parity

C + PV of X = P + S

Where C= Call price = 316.94.

PV of X = 2500/1.0246 = 2440,

P = Put price = 55.15

S = spot = 2780

By substituting the values in equation we get

$2,756.94 = $2,835.18

from the above ,we can conclude that arbitration is possible since parity not exits.

Possible arbitration would be

Buy a call, Invest PV of X, Sell Put and Short sell the share at spot

as a result of that the outflow would be ,call premium = $316.94 + PV of X $2440

and the inflow would be, Put premium = $55.15 + SPOT = 2780 and the net result would be inflow of  $78.21.