Question

4. We have we have the following information for a call and a put option on XVZ stock. Exercise price: $100 Call option price: $7 Put option price: $5 Risk-free rate: 8% Current market price of XYZ: $99 Time to maturity: 0.5 years Calculate the mispricing and show the arbitrage process if price of stock goes up to $120

Answer 1

Arbitrage using put call parity
C-P=S-PV(X)
Value of call option- value of put option= CMP of underlying - PV of strike price
PV(X)=	=100/(1+8%)^0.5
	96.225
LHS=	C-P
	=7-5
	2
RHS	S-PV(X)
	=99-96.225
	2.775
LHS & RHS are not equal. Hence, there is a possibility of arbitrage profit
Mispricing= 2.775-2= 0.775
If share price =	120
RHS	S-PV(X)
	=120-96.225
	23.775

Arbitrage trades-
Assuming no changes in the prices of call and put options
Buy a call option and sell a put option
Cash flows= 7-5=$2 outflow
At expiry-
Call option profit= 120-100= 20 inflow
Put option= Worthless

PV of cashflow at expiry
=20/(1+8%)^0.5
19.25

Net profit= 19.25-2
=17.25